(1288378 . 3662084403)       
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Vector| *4))
   (|ofCategory| *4 (|Join| (|Ring|) (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Vector| (|Fraction| (|Integer|))))
   (|isDomain| *1 (|IntegerLinearDependence| *4))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Vector| *4))
   (|ofCategory| *4 (|Join| (|Ring|) (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Vector| (|Integer|)))
   (|isDomain| *1 (|IntegerLinearDependence| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *4))
       (|ofCategory| *4
                     (|Join| (|Ring|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|IntegerLinearDependence| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *5 (|Join| (|ConvertibleTo| *2) (|CommutativeRing|)))
       (|isDomain| *2 (|Pattern| *4))
       (|isDomain| *1 (|ComplexPattern| *4 *5 *3))
       (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *3 (|ComplexCategory| *5))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *1 (|FramedAlgebra| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2 (|Vector| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|FunctionSpace| *3))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|GeneralPolynomialSet| *3 *4 *5 *6))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|InputForm|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ConvertibleTo| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *1 (|ConvertibleFrom| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *1 (|MonogenicAlgebra| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Polynomial| *3)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))))
 ((*1 *1 *2)
  (OR
   (AND #1=(|isDomain| *2 (|Polynomial| (|Integer|)))
        #2=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
        (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))
             (|ofCategory| *3 (|Algebra| (|Integer|)))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #3=((|ofCategory| *3 (|Ring|))
              (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
              (|ofCategory| *5 (|OrderedSet|))))
   (AND #1# #2#
        (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #3#)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|))))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8)))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *4 *5 *6 *7 *8))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8)))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *8 (|SquareFreeRegularTriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|String|))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *4 *5 *6 *7 *8))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *1 *2 *3 *2)
  (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|TexFormat|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|TexFormat|))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *5)))
   (|ofCategory| *4
                 (|Join| (|OrderedRing|) (|EuclideanDomain|)
                         (|CharacteristicZero|) (|RealConstant|)))
   (|ofType| *5 (|List| (|Symbol|)))
   (|isDomain| *2
    (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6)))
   (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
   (|ofType| *6 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *4))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|Polynomial| (|RealClosure| (|Fraction| *4))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6)))
   (|ofCategory| *4
                 (|Join| (|OrderedRing|) (|EuclideanDomain|)
                         (|CharacteristicZero|) (|RealConstant|)))
   (|ofType| *6 (|List| (|Symbol|)))
   (|isDomain| *2 (|Polynomial| (|RealClosure| (|Fraction| *4))))
   (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
   (|ofType| *5 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2
        (|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| *4))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|SquareFreeRegularTriangularSet| *4
                                      (|IndexedExponents|
                                       (|OrderedVariableList| *6))
                                      (|OrderedVariableList| *6)
                                      (|NewSparseMultivariatePolynomial| *4
                                                                         (|OrderedVariableList|
                                                                          *6))))
   (|ofCategory| *4
                 (|Join| (|OrderedRing|) (|EuclideanDomain|)
                         (|CharacteristicZero|) (|RealConstant|)))
   (|ofType| *6 (|List| (|Symbol|)))
   (|isDomain| *2
    (|List| (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *6))))
   (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
   (|ofType| *5 (|List| (|Symbol|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|IntegerFactorizationPackage| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *6 *4 *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7)))
       (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *7))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Factored| *1))
       (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|PolynomialSquareFree| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
       (|isDomain| *2
        (|Factored| (|SparseUnivariatePolynomial| (|Fraction| *7))))
       (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| *7)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Factored| *1))
       (|ofCategory| *1 (|UniqueFactorizationDomain|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|UnivariatePolynomialSquareFree| *4 *3))
       (|ofCategory| *3
                     (|Join| (|UnivariatePolynomialCategory| *4)
                             (|IntegralDomain|)
                             (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)))))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|RegularChain| *4 *5))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|ofType| *5 (|List| (|Symbol|)))
       (|isDomain| *2
        (|List|
         (|SquareFreeRegularTriangularSet| *4
                                           (|IndexedExponents|
                                            (|OrderedVariableList| *6))
                                           (|OrderedVariableList| *6)
                                           (|NewSparseMultivariatePolynomial|
                                            *4 (|OrderedVariableList| *6)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *6 (|List| (|Symbol|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|RegularChain| *4 *5))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|ofType| *5 (|List| (|Symbol|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *6 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|)))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|List| (|Polynomial| (|Integer|))))
       (|isDomain| *4 (|List| (|Symbol|)))
       (|isDomain| *2 (|List| (|List| (|Float|))))
       (|isDomain| *1 (|RealSolvePackage|)) (|isDomain| *5 (|Float|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|RegularChain| *4 *5))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|ofType| *5 (|List| (|Symbol|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *6 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4 *4 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *4)))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|RegularChain| *4 *5))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|ofType| *5 (|List| (|Symbol|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4))
                   (|:| |coordinates| (|List| (|Polynomial| *4))))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *6 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4 *4 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5))
                   (|:| |coordinates| (|List| (|Polynomial| *5))))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5))
                   (|:| |coordinates| (|List| (|Polynomial| *5))))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5))
                   (|:| |coordinates| (|List| (|Polynomial| *5))))))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|OrderedRing|) (|EuclideanDomain|)
                         (|CharacteristicZero|) (|RealConstant|)))
   (|isDomain| *2
    (|List|
     (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4))
               (|:| |coordinates| (|List| (|Polynomial| *4))))))
   (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
   (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofType| *5 (|List| (|Symbol|)))
   (|ofType| *6 (|List| (|Symbol|)))))) 
(((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|RegularChain| *5 *6)))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5))) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|RegularChain| *5 *6)))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7))
       (|ofType| *6 (|List| (|Symbol|))) (|ofType| *7 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofCategory| *4
                     (|Join| (|OrderedRing|) (|EuclideanDomain|)
                             (|CharacteristicZero|) (|RealConstant|)))
       (|isDomain| *2 (|List| (|RegularChain| *4 *5)))
       (|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6))
       (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|List| (|Symbol|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| #1=(|Stream| *4) #1#))
       (|isDomain| *2 (|Stream| *4))
       (|isDomain| *1 (|ParadoxicalCombinatorsForStreams| *4))
       (|ofCategory| *4 (|Type|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| #2=(|List| (|Stream| *5)) #2#))
       (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| (|Stream| *5)))
       (|isDomain| *1 (|ParadoxicalCombinatorsForStreams| *5))
       (|ofCategory| *5 (|Type|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|YoungDiagram|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Partition|)) (|isDomain| *1 (|YoungDiagram|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *6 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Expression| *6)))
       (|isDomain| *1 (|DegreeReductionPackage| *5 *6))
       (|isDomain| *3 (|Expression| *6)) (|ofCategory| *5 (|Ring|))))
 ((*1 *2 *1)
  (AND (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|IntegrationResult| *5))
       (|ofCategory| *5
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *4)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|List| *5))
       (|isDomain| *1 (|IntegrationResultToFunction| *4 *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|IntegrationResult| (|Fraction| (|Polynomial| *4))))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|List| (|Expression| *4)))
       (|isDomain| *1 (|IntegrationResultRFToFunction| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SegmentExpansionCategory| *3 *2))
       (|ofCategory| *3 (|OrderedRing|))
       (|ofCategory| *2 (|StreamAggregate| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|SegmentExpansionCategory| *4 *2))
       (|ofCategory| *4 (|OrderedRing|))
       (|ofCategory| *2 (|StreamAggregate| *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|XDistributedPolynomial| (|Symbol|) *3))
       (|isDomain| *1 (|XPolynomial| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4))
       (|isDomain| *1 (|XRecursivePolynomial| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|XDistributedPolynomial| (|Symbol|) *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|XPolynomial| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|XRecursivePolynomial| *3 *4))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|List| (|Record| (|:| |k| (|Symbol|)) (|:| |c| (|XPolynomial| *3)))))
   (|isDomain| *1 (|XPolynomial| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|List| (|Record| (|:| |k| *3) (|:| |c| (|XRecursivePolynomial| *3 *4)))))
   (|isDomain| *1 (|XRecursivePolynomial| *3 *4))
   (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|AbelianMonoid|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|AbelianSemiGroup|))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|Color|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|Color|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|)))
       (|isDomain| *1 (|DenavitHartenbergMatrix| *3))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|SemiGroup|))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|SemiGroup|))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *3)
  (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *2 (|CancellationAbelianMonoid|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|FreeGroup| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *1 (|FreeGroup| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|FreeModule1| *3 *2)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2 *3)
  (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|FreeMonoidCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|FreeMonoidCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *6
                     (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))
       (|ofType| *7
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *6))
                   (|Record| (|:| |index| *5) (|:| |exponent| *6))))
       (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *2))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2
                     (|PolynomialCategory| *4 *6 (|OrderedVariableList| *3)))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|GradedModule| *2 *3))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|GradedModule| *2 *3))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *2 (|Field|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *3))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|InputForm|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|InnerTaylorSeries| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|LeftLinearSet| *2)) (|ofCategory| *2 (|SemiGroup|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *7 *6)) (|isDomain| *4 (|Mapping| *6 *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Mapping| *7 *5))
       (|isDomain| *1 (|MappingPackage3| *5 *6 *7))))
 ((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *2 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|FiniteLinearAggregate| *3))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))))
 ((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *2 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|Monad|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Vector| *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *3 *4))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RightLinearSet| *2))
       (|ofCategory| *2 (|SemiGroup|))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SemiGroup|)))
 ((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *2 *5))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2 (|DirectProductCategory| *3 *4))
       (|ofCategory| *5 (|DirectProductCategory| *3 *4))))
 ((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *2))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *5 (|DirectProductCategory| *3 *4))
       (|ofCategory| *2 (|DirectProductCategory| *3 *4))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *2))
       (|ofCategory| *2 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Point| (|DoubleFloat|)))
       (|isDomain| *3 (|DoubleFloat|)) (|isDomain| *1 (|TubePlotTools|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *2 (|Monoid|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *2 (|Monoid|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|VectorCategory| *3))
       (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|AbelianGroup|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *2))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|OrderedMonoid|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|OrderedAbelianMonoid|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|AntiSymm| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofType| *3 (|List| (|Symbol|)))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|DeRhamComplex| *2 *3))
       (|ofCategory| *2 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *3 (|List| (|Symbol|)))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *1)
  (AND (|ofType| *2 (|List| (|Symbol|))) (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *5
                     (|DirectProductCategory| (|#| *2) (|NonNegativeInteger|)))
       (|ofType| *6
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *4) (|:| |exponent| *5))
                   (|Record| (|:| |index| *4) (|:| |exponent| *5))))
       (|isDomain| *1 (|GeneralModulePolynomial| *2 *3 *4 *5 *6 *7))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *7
                     (|PolynomialCategory| *3 *5 (|OrderedVariableList| *2)))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3))
       (|ofCategory| *2 (|BasicType|)) (|ofCategory| *3 (|OrderedType|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|LaurentPolynomial| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|MonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|Monoid|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|OrderedMonoid|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|DomainTemplate|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Partition|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|XPolynomialRing| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedMonoid|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|XPolynomialsCat| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|OrderedFreeMonoid| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|OrderedMonoid|))
       (|isDomain| *1 (|XPolynomialRing| *3 *2)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|OrderedFreeMonoid| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|OrderedMonoid|))
       (|isDomain| *1 (|XPolynomialRing| *3 *2)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|XRecursivePolynomial| *4 *2))
       (|ofCategory| *1 (|FreeLieAlgebra| *4 *2))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *2))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|OrderedFreeMonoid| *4))
       (|ofCategory| *1 (|XFreeAlgebra| *4 *2))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|XPolynomialRing| *2 *3))
       (|ofCategory| *3 (|OrderedMonoid|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ElaboratedExpression|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|XPolynomialRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedMonoid|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *5)) (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *2 (|Mapping| *5 *4))
       (|isDomain| *1 (|MappingPackage2| *4 *5))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|PatternMatchAssertions|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|FunctionSpaceAssertions| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *2))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|XPolynomialRing| *2 *3))
       (|ofCategory| *3 (|OrderedMonoid|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|XPolynomialRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedMonoid|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|OrderedMonoid|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DoubleFloat|))))
 ((*1 *1 *1 *1)
  (OR
   (AND #1=(|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Field|))
        . #2=((|ofCategory| *2 (|Type|))))
   (AND #1# (|ofCategory| *2 (|Group|)) . #2#)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|Field|)))
 ((*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Float|))))
 ((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|Group|)))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *3))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|InputForm|)))
 ((*1 *1 *2 *3)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *1 (|LocalAlgebra| *2 *4 *3))
       (|ofCategory| *2 (|Algebra| *4))
       (|ofCategory| *3 (|SubsetCategory| (|Monoid|) *4))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *1 (|LocalAlgebra| *3 *4 *2))
       (|ofCategory| *3 (|Algebra| *4))
       (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|LieAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *2 *3)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *1 (|Localize| *2 *4 *3)) (|ofCategory| *2 (|Module| *4))
       (|ofCategory| *3 (|SubsetCategory| (|Monoid|) *4))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *1 (|Localize| *3 *4 *2)) (|ofCategory| *3 (|Module| *4))
       (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Field|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *1)
  (|partial| AND (|isDomain| *1 (|OrdinaryWeightedPolynomials| *2 *3 *4 *5))
   (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Ring|))
   (|ofType| *3 (|List| (|Symbol|)))
   (|ofType| *4 (|List| (|NonNegativeInteger|)))
   (|ofType| *5 (|NonNegativeInteger|))))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *2)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *2 *5 *6))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *5 (|DirectProductCategory| *4 *2))
       (|ofCategory| *6 (|DirectProductCategory| *3 *2))
       (|ofCategory| *2 (|Field|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|VectorSpace| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *1 *1)
  (|partial| AND (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Ring|))
   (|ofCategory| *3 (|OrderedSet|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofType| *6 (|List| *3))
   (|isDomain| *1 (|WeightedPolynomials| *2 *3 *4 *5 *6 *7 *8))
   (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3))
   (|ofType| *7 (|List| (|NonNegativeInteger|)))
   (|ofType| *8 (|NonNegativeInteger|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|XPolynomialRing| *2 *3)) (|ofCategory| *2 (|Field|))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedMonoid|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *2)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|OrderedAbelianMonoid|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DeRhamComplex| *3 *4))
       (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *3))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ExtAlgBasis|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *8))
       (|isDomain| *4 (|List| *6)) (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|Ring|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|FactoringUtilities| *5 *6 *7 *8))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|NonNegativeInteger|))))
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  (AND (|ofCategory| *1 (|GradedModule| *3 *2))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *2 (|AbelianMonoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|LaurentPolynomial| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *6))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *2 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *2 (|OrderedAbelianMonoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|XPolynomialsCat| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|FreeLieAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|XPolynomialsCat| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|))
       (|ofType| *6 (|Vector| (|Matrix| *3)))
       (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6))
       (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Any|)) (|isDomain| *1 (|AnyFunctions1| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| (|Matrix| *4)))
       (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|Vector| (|Matrix| (|Fraction| (|Polynomial| *4)))))
       (|isDomain| *1 (|CoerceVectorMatrixPackage| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SegmentBinding| (|Expression| *4)))
       (|ofCategory| *4
                     (|Join| (|OrderedSet|) (|IntegralDomain|)
                             (|ConvertibleTo| (|Float|))))
       (|isDomain| *2 (|SegmentBinding| (|Float|)))
       (|isDomain| *1 (|DrawNumericHack| *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|ExtAlgBasis|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *4 *5 *6))
       (|ofCategory| *4
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *3)))
       (|ofType| *5 (|Symbol|)) (|ofType| *6 *4)
       (|ofCategory| *3
                     (|Join| (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|GcdDomain|)))
       (|isDomain| *1 (|ExponentialExpansion| *3 *4 *5 *6))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4))
       (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2))
       (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4))
       (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3))
       (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *1 *2)
  (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Fraction| *3))))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Polynomial| (|Fraction| *3)))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| *3)) (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|FourierComponent| *4))
       (|ofCategory| *4 (|Join| (|OrderedSet|) (|AbelianGroup|)))
       (|isDomain| *1 (|FourierSeries| *3 *4))
       (|ofCategory| *3
                     (|Join| (|CommutativeRing|)
                             (|Algebra| (|Fraction| (|Integer|)))))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|FourierSeries| *2 *3))
       (|ofCategory| *2
                     (|Join| (|CommutativeRing|)
                             (|Algebra| (|Fraction| (|Integer|)))))
       (|ofCategory| *3 (|Join| (|OrderedSet|) (|AbelianGroup|)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FortranScalarType|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|FortranScalarType|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|FortranScalarType|)) (|isDomain| *1 (|FortranType|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| (|Fraction| (|Polynomial| *3))))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofType| *6 (|Vector| (|Matrix| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *1 (|GraphImage|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)
       (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|ImportAst|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|JoinAst|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *1 (|AssociatedJordanAlgebra| *3 *2))
       (|ofCategory| *2 (|NonAssociativeAlgebra| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|CoercibleTo| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *1 (|CoercibleFrom| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2))
       (|ofCategory| *2 (|NonAssociativeAlgebra| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|MappingAst|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *3)) (|isDomain| *1 (|MappingPackage1| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *4 *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *2 (|FiniteLinearAggregate| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|MathMLFormat|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Record| (|:| |coef| *3) (|:| |monom| *4))))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|))
       (|isDomain| *1 (|MonoidRing| *3 *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|NonAssociativeRing|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|None|)) (|isDomain| *1 (|NoneFunctions1| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OrdSetInts|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| (|AlgebraicNumber|)))
       (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|PolynomialAN2Expression|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|AlgebraicNumber|))))
       (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|PolynomialAN2Expression|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Permutation| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Permutation| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Factored| *3)))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|PartialFraction| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Pi|)) (|isDomain| *2 (|Expression| *4))
       (|isDomain| *1 (|PiCoercions| *4))
       (|ofCategory| *4 (|IntegralDomain|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ResolveLatticeCompletion| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Exit|)) (|isDomain| *1 (|ResolveLatticeCompletion| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6))
       (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5))
       (|ofType| *6 (|List| *2))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|RationalFunction| *3))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *2))
       (|ofCategory| *2 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|))
       (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *2 *4))
       (|ofCategory| *4 (|PolynomialCategory| *3 (|IndexedExponents| *2) *2))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Character|)) (|ofCategory| *1 (|StringAggregate|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Stream| *3))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|SparseUnivariateLaurentSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|SparseUnivariateTaylorSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)
       (|isDomain| *1 (|SparseUnivariateTaylorSeries| *3 *4 *5))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|TexFormat|)) (|isDomain| *1 (|TexFormat1| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Polynomial| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|TaylorSeries| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TaylorSeries| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|UnivariateLaurentSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Segment| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|UniversalSegment| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)
       (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|GraphImage|))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|ViewportPackage|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|LiePolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *1 (|XPBWPolynomial| *3 *4))))) 
(((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4))
   (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))
   (|isDomain| *1 (|LiePolynomial| *3 *4))))
 ((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|LiePolynomial| *3 *4))
   (|isDomain| *1 (|XPBWPolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|))
   (|ofCategory| *4 (|CommutativeRing|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *2 (|FunctionSpace| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|SegmentBinding| *2))
       (|ofCategory| *2 (|FunctionSpace| *4))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|SegmentBinding| *1))
       (|ofCategory| *1 (|CombinatorialOpsCategory|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|CombinatorialOpsCategory|))
       (|isDomain| *2 (|Symbol|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|GradedAlgebra| *2 *3))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|))))
 ((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|XPBWPolynomial| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|AntiSymm| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|LiePolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4
                     (|Join| (|CommutativeRing|)
                             (|Module| (|Fraction| (|Integer|)))))
       (|isDomain| *1 (|LieExponentials| *3 *4 *5))
       (|ofType| *5 (|PositiveInteger|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|)))))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|XExponentialPackage| *4 *5 *2))
       (|ofCategory| *2 (|XPolynomialsCat| *5 *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|XPBWPolynomial| *3 *4))
       (|ofCategory| *4 (|Module| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|)))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Factored| *4)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| *4))))
       (|isDomain| *1 (|FactoredFunctions| *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|LiePolynomial| *3 *4))
       (|isDomain| *1 (|LieExponentials| *3 *4 *5))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4
                     (|Join| (|CommutativeRing|)
                             (|Module| (|Fraction| (|Integer|)))))
       (|ofType| *5 (|PositiveInteger|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|)))))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|XExponentialPackage| *4 *5 *2))
       (|ofCategory| *2 (|XPolynomialsCat| *5 *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|XPBWPolynomial| *3 *4))
       (|ofCategory| *4 (|Module| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |k| (|OrderedFreeMonoid| *3)) (|:| |c| *4)))))) 
(((*1 *2 *2 *1)
  (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4))
       (|ofCategory| *1 (|FreeLieAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|FreeMonoidCategory| *2))
   (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (|partial| AND (|isDomain| *1 (|OrderedFreeMonoid| *2))
   (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|OrderedFreeMonoid| *3))
       (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *2 *1)
  (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4))
       (|ofCategory| *1 (|FreeLieAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|FreeMonoidCategory| *2))
   (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (|partial| AND (|isDomain| *1 (|OrderedFreeMonoid| *2))
   (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|OrderedFreeMonoid| *3))
       (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *2 *3)
  (AND (|ofCategory| *1 (|FreeModuleCat| *3 *2)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|Stream| *3))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|OrderedFreeMonoid| *4))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *1 (|XFreeAlgebra| *4 *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|LaurentPolynomial| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|MonoidRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|LieExponentials| *2 *3 *4))
       (|ofCategory| *2 (|OrderedSet|))
       (|ofCategory| *3
                     (|Join| (|CommutativeRing|)
                             (|Module| (|Fraction| (|Integer|)))))
       (|ofType| *4 (|PositiveInteger|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|OrderedFreeMonoid| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *3 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|List| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|FreeMagma| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|LieExponentials| *3 *4 *5))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4
                     (|Join| (|CommutativeRing|)
                             (|Module| (|Fraction| (|Integer|)))))
       (|ofType| *5 (|PositiveInteger|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|LyndonWord| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|OrderedFreeMonoid| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|XFreeAlgebra| *3 *4))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|List| *3))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *6))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4))
       (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|Field|))
       (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|)))
       (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4))
       (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|)))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4))
       (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofCategory| *4 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|NormRetractPackage| *3 *4 *5 *2 *6))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
       (|ofType| *6 (|PositiveInteger|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|))
       (|ofCategory| *3 (|Finite|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|ExtensionField| *2)) (|ofCategory| *2 (|Field|))
       (|ofCategory| *2 (|Finite|))))) 
(((*1 *2 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|)))))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|XExponentialPackage| *4 *5 *2))
       (|ofCategory| *2 (|XPolynomialsCat| *5 *4))))) 
(((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|List| *6))
   (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|WuWenTsunTriangularSet| *3 *4 *5 *6))))
 ((*1 *1 *2 *3 *4)
  (|partial| AND (|isDomain| *2 (|List| *8))
   (|isDomain| *3 (|Mapping| (|Boolean|) *8 *8))
   (|isDomain| *4 (|Mapping| *8 *8 *8))
   (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
   (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|OrderedSet|))
   (|isDomain| *1 (|WuWenTsunTriangularSet| *5 *6 *7 *8))))) 
(((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|List| *6))
   (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|WuWenTsunTriangularSet| *3 *4 *5 *6))))
 ((*1 *1 *2 *3 *4)
  (|partial| AND (|isDomain| *2 (|List| *8))
   (|isDomain| *3 (|Mapping| (|Boolean|) *8 *8))
   (|isDomain| *4 (|Mapping| *8 *8 *8))
   (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
   (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|OrderedSet|))
   (|isDomain| *1 (|WuWenTsunTriangularSet| *5 *6 *7 *8))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *2 (|List| (|WuWenTsunTriangularSet| *4 *5 *6 *7)))
       (|isDomain| *1 (|WuWenTsunTriangularSet| *4 *5 *6 *7))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|List| *9))
       (|isDomain| *4 (|Mapping| (|Boolean|) *9 *9))
       (|isDomain| *5 (|Mapping| *9 *9 *9))
       (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8))
       (|ofCategory| *6 (|IntegralDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|isDomain| *2 (|List| (|WuWenTsunTriangularSet| *6 *7 *8 *9)))
       (|isDomain| *1 (|WuWenTsunTriangularSet| *6 *7 *8 *9))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|OrdinaryWeightedPolynomials| *4 *5 *6 *7))
       (|ofCategory| *4 (|Ring|)) (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|List| *3)) (|ofType| *7 *3)))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofType| *8 (|List| *5))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|WeightedPolynomials| *4 *5 *6 *7 *8 *9 *10))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
       (|ofType| *9 (|List| *3)) (|ofType| *10 *3)))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IfAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingNode| *3 *2))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|WhileAst|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|WhereAst|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|WhereAst|))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *3
                 (|Join| (|EuclideanDomain|)
                         (CATEGORY |domain|
                          (SIGNATURE |squareFree| ((|Factored| $) $)))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|isDomain| *2
    (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3)
              (|:| |basisInv| (|Matrix| *3))))
   (|isDomain| *1 (|FunctionFieldIntegralBasis| *3 *4 *5))
   (|ofCategory| *5 (|FramedAlgebra| *3 *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2
        (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3)
                  (|:| |basisInv| (|Matrix| *3))))
       (|isDomain| *1 (|NumberFieldIntegralBasis| *4 *5))
       (|ofCategory| *5 (|FramedAlgebra| *3 *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2
        (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3)
                  (|:| |basisInv| (|Matrix| *3))))
       (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *4 *3 *5 *6))
       (|ofCategory| *6 (|MonogenicAlgebra| *3 *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2
        (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3)
                  (|:| |basisInv| (|Matrix| *3))))
       (|isDomain| *1 (|WildFunctionFieldIntegralBasis| *4 *3 *5 *6))
       (|ofCategory| *6 (|FramedAlgebra| *3 *5))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))))
 ((*1 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|EuclideanDomain|)
                         (CATEGORY |domain|
                          (SIGNATURE |squareFree| ((|Factored| $) $)))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|isDomain| *2
    (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3)
              (|:| |basisInv| (|Matrix| *3))))
   (|isDomain| *1 (|FunctionFieldIntegralBasis| *3 *4 *5))
   (|ofCategory| *5 (|FramedAlgebra| *3 *4))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))
       (|isDomain| *2
        (|Record| (|:| |basis| (|Matrix| (|Integer|)))
                  (|:| |basisDen| (|Integer|))
                  (|:| |basisInv| (|Matrix| (|Integer|)))))
       (|isDomain| *1 (|NumberFieldIntegralBasis| *3 *4))
       (|ofCategory| *4 (|FramedAlgebra| (|Integer|) *3))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2
        (|Record| (|:| |basis| (|Matrix| *4)) (|:| |basisDen| *4)
                  (|:| |basisInv| (|Matrix| *4))))
       (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *3 *4 *5 *6))
       (|ofCategory| *6 (|MonogenicAlgebra| *4 *5))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2
        (|Record| (|:| |basis| (|Matrix| *4)) (|:| |basisDen| *4)
                  (|:| |basisInv| (|Matrix| *4))))
       (|isDomain| *1 (|WildFunctionFieldIntegralBasis| *3 *4 *5 *6))
       (|ofCategory| *6 (|FramedAlgebra| *4 *5))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *6 (|Field|))
       (|isDomain| *4 (|TaylorSeries| *6))
       (|isDomain| *2 (|Mapping| #1=(|Stream| *4) #1#))
       (|isDomain| *1 (|WeierstrassPreparation| *6))
       (|isDomain| *5 (|Stream| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|List| (|TaylorSeries| *5)))
       (|isDomain| *1 (|WeierstrassPreparation| *5))
       (|isDomain| *4 (|TaylorSeries| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|isDomain| *2
        (|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| *4))
                   (|Polynomial| *4)))
       (|isDomain| *1 (|WeierstrassPreparation| *4))
       (|ofCategory| *4 (|Field|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|Stream| (|Stream| (|Polynomial| *5))))
       (|isDomain| *1 (|WeierstrassPreparation| *5))
       (|isDomain| *4 (|Stream| (|Polynomial| *5)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2
        (|Mapping| (|Stream| (|Polynomial| *4)) (|Stream| (|Polynomial| *4))))
       (|isDomain| *1 (|WeierstrassPreparation| *4))
       (|ofCategory| *4 (|Field|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2
        (|Mapping| (|Stream| (|Polynomial| *4)) (|Stream| (|Polynomial| *4))))
       (|isDomain| *1 (|WeierstrassPreparation| *4))
       (|ofCategory| *4 (|Field|))))) 
(((*1 *2)
  (AND (|ofType| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Type|))
       (|isDomain| *2 (|CardinalNumber|))
       (|isDomain| *1 (|DirectProductCategory&| *3 *4 *5))
       (|ofCategory| *3 (|DirectProductCategory| *4 *5))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|CardinalNumber|))
       (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4))
       (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 *2)
       (|ofType| *4 *2) (|ofCategory| *5 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PointCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|VectorSpace| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|CardinalNumber|))))) 
(((*1 *1) (|isDomain| *1 (|Void|)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|List| (|String|)))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|List| (|String|)))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|String|)))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|ViewDefaultsPackage|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *1) (|isDomain| *1 (|ThreeDimensionalViewport|)))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *3 (|String|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *1 *1) (|isDomain| *1 (|ThreeDimensionalViewport|)))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|SubSpace| 3 *3))))
 ((*1 *1)
  (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Point| *4))
       (|ofCategory| *1 (|ThreeSpaceCategory| *4)) (|ofCategory| *4 (|Ring|))))
 ((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *4 (|Point| (|DoubleFloat|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|DrawOption|)))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|DrawOption|)))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|DrawOption|)))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|DrawOption|)))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3 *3 *4 *4)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3 *3 *4 *4)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|))
              (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|))
              (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|))
              (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))))
   (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND
   (|isDomain| *2
    (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|))
              (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|))
              (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|))
              (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))))
   (|isDomain| *3 (|List| (|DrawOption|)))
   (|isDomain| *1 (|DrawOptionFunctions0|))))
 ((*1 *2 *1 *3 *3 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *3 *3 *4 *4 *4)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Float|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *3)
  (AND
   (|isDomain| *3
    (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|))
              (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|))
              (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|))
              (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))))
   (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|))
              (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|))
              (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|))
              (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))))
   (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *3 *3 *3 *3 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Palette|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *1 *1 *2 *2)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *1 *2 *2 *2)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))
 ((*1 *2 *1 *3 *3 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *1 *2 *2 *2)
  (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)))))
 ((*1 *2 *1 *3 *4 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Float|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3 *3 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Float|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Color|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *2 *3)
  (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *2 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *2 *3)
  (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *2 *2)
  (AND (|isDomain| *2 (|String|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|String|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SubSpaceComponentProperty|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphImage|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ThreeDimensionalViewport|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Point| (|DoubleFloat|))))
       (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *1) (|isDomain| *1 (|TwoDimensionalViewport|)))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|GraphImage|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *1 *1) (|isDomain| *1 (|TwoDimensionalViewport|)))) 
(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|DoubleFloat|))
       (|isDomain| *5 (|Integer|)) (|isDomain| *6 (|Palette|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Vector|
     (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|))
               (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))
               (|:| |points| (|Integer|)) (|:| |connect| (|Integer|))
               (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|))
               (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|))
               (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))))
   (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Vector| (|Union| (|GraphImage|) "undefined")))
       (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|GraphImage|)) (|isDomain| *4 (|PositiveInteger|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|GraphImage|))
       (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| (|Float|)))
       (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|GraphImage|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|GraphImage|))))
 ((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Palette|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))
 ((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *1 *2 *2 *2)
  (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *1 *3 *4 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Float|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|String|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|GraphImage|)) (|isDomain| *4 (|PositiveInteger|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TwoDimensionalViewport|))))) 
(((*1 *2 *3 *4 *4 *5 *6)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *4 (|Palette|)) (|isDomain| *5 (|PositiveInteger|))
       (|isDomain| *6 (|List| (|DrawOption|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|ViewportPackage|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *4 (|List| (|DrawOption|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|ViewportPackage|))))) 
(((*1 *2 *3 *4 *4 *5 *6)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *4 (|Palette|)) (|isDomain| *5 (|PositiveInteger|))
       (|isDomain| *6 (|List| (|DrawOption|))) (|isDomain| *2 (|GraphImage|))
       (|isDomain| *1 (|ViewportPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *2 (|GraphImage|)) (|isDomain| *1 (|ViewportPackage|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *4 (|List| (|DrawOption|))) (|isDomain| *2 (|GraphImage|))
       (|isDomain| *1 (|ViewportPackage|))))) 
(((*1 *1 *2 *1 *1 *3)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *2 *1 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|OneDimensionalArray| *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|OneDimensionalArray| *6))
       (|isDomain| *1 (|OneDimensionalArrayFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *8 *7))
       (|isDomain| *4 (|CartesianTensor| *5 *6 *7)) (|ofType| *5 (|Integer|))
       (|ofType| *6 (|NonNegativeInteger|))
       (|ofCategory| *7 (|CommutativeRing|))
       (|ofCategory| *8 (|CommutativeRing|))
       (|isDomain| *2 (|CartesianTensor| *5 *6 *8))
       (|isDomain| *1 (|CartesianTensorFunctions2| *5 *6 *7 *8))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Complex| *5))
       (|ofCategory| *5 (|CommutativeRing|))
       (|ofCategory| *6 (|CommutativeRing|)) (|isDomain| *2 (|Complex| *6))
       (|isDomain| *1 (|ComplexFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *7 *6))
       (|isDomain| *4 (|DirectProduct| *5 *6))
       (|ofType| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *7 (|Type|)) (|isDomain| *2 (|DirectProduct| *5 *7))
       (|isDomain| *1 (|DirectProductFunctions2| *5 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Equation| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|Equation| *6))
       (|isDomain| *1 (|EquationFunctions2| *5 *6))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *1 *1)) (|isDomain| *3 (|Kernel| *1))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *2 *6)) (|isDomain| *4 (|String|))
       (|isDomain| *5 (|Kernel| *6)) (|ofCategory| *6 (|ExpressionSpace|))
       (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|ExpressionSpaceFunctions1| *6 *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *2 *5)) (|isDomain| *4 (|Kernel| *5))
       (|ofCategory| *5 (|ExpressionSpace|))
       (|ofCategory| *2 (|ExpressionSpace|))
       (|isDomain| *1 (|ExpressionSpaceFunctions2| *5 *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Expression| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|Expression| *6))
       (|isDomain| *1 (|ExpressionFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *9 *5))
       (|isDomain| *4 (|FiniteDivisor| *5 *6 *7 *8))
       (|ofCategory| *5 (|Field|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
       (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7))
       (|ofCategory| *9 (|Field|))
       (|ofCategory| *10 (|UnivariatePolynomialCategory| *9))
       (|ofCategory| *11 (|UnivariatePolynomialCategory| (|Fraction| *10)))
       (|isDomain| *2 (|FiniteDivisor| *9 *10 *11 *12))
       (|isDomain| *1 (|FiniteDivisorFunctions2| *5 *6 *7 *8 *9 *10 *11 *12))
       (|ofCategory| *12 (|FunctionFieldCategory| *9 *10 *11))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *8 *5))
       (|ofCategory| *5 (|UniqueFactorizationDomain|))
       (|ofCategory| *8 (|UniqueFactorizationDomain|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
       (|ofCategory| *9 (|UnivariatePolynomialCategory| *8))
       (|ofCategory| *2 (|FunctionFieldCategory| *8 *9 *10))
       (|isDomain| *1
        (|FunctionFieldCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2))
       (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7))
       (|ofCategory| *10 (|UnivariatePolynomialCategory| (|Fraction| *9)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|))
       (|ofCategory| *2 (|FiniteLinearAggregate| *6))
       (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *6 *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Factored| *5))
       (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *6))
       (|isDomain| *1 (|FactoredFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Fraction| *5))
       (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| *6))
       (|isDomain| *1 (|FractionFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *9 *5))
       (|isDomain| *4 (|FractionalIdeal| *5 *6 *7 *8))
       (|ofCategory| *5 (|EuclideanDomain|))
       (|ofCategory| *6 (|QuotientFieldCategory| *5))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|ofCategory| *8 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6)))
       (|ofCategory| *9 (|EuclideanDomain|))
       (|ofCategory| *10 (|QuotientFieldCategory| *9))
       (|ofCategory| *11 (|UnivariatePolynomialCategory| *10))
       (|isDomain| *2 (|FractionalIdeal| *9 *10 *11 *12))
       (|isDomain| *1 (|FractionalIdealFunctions2| *5 *6 *7 *8 *9 *10 *11 *12))
       (|ofCategory| *12
                     (|Join| (|FramedAlgebra| *10 *11)
                             (|RetractableTo| *10)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|CommutativeRing|))
       (|ofCategory| *6 (|CommutativeRing|))
       (|ofCategory| *2 (|FramedNonAssociativeAlgebra| *6))
       (|isDomain| *1 (|FramedNonAssociativeAlgebraFunctions2| *4 *5 *2 *6))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|Ring|)) (|ofCategory| *2 (|FunctionSpace| *6))
       (|isDomain| *1 (|FunctionSpaceFunctions2| *5 *4 *6 *2))
       (|ofCategory| *4 (|FunctionSpace| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *2 (|FiniteSetAggregate| *6))
       (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *6 *2))
       (|ofCategory| *4 (|FiniteSetAggregate| *5))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|Functorial| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|IntegrationResult| *5)) (|ofCategory| *5 (|Field|))
       (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|IntegrationResult| *6))
       (|isDomain| *1 (|IntegrationResultFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Mapping| *6 *5))
   (|isDomain| *4
    (|Union| (|Record| (|:| |ratpart| *5) (|:| |coeff| *5)) "failed"))
   (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Field|))
   (|isDomain| *2 (|Record| (|:| |ratpart| *6) (|:| |coeff| *6)))
   (|isDomain| *1 (|IntegrationResultFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Mapping| *2 *5))
   (|isDomain| *4 (|Union| *5 "failed")) (|ofCategory| *5 (|Field|))
   (|ofCategory| *2 (|Field|))
   (|isDomain| *1 (|IntegrationResultFunctions2| *5 *2))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Mapping| *6 *5))
   (|isDomain| *4
    (|Union|
     (|Record| (|:| |mainpart| *5)
               (|:| |limitedlogs|
                    (|List| (|Record| (|:| |coeff| *5) (|:| |logand| *5)))))
     "failed"))
   (|ofCategory| *5 (|Field|)) (|ofCategory| *6 (|Field|))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *6)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *6) (|:| |logand| *6))))))
   (|isDomain| *1 (|IntegrationResultFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|InfiniteTuple| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|InfiniteTuple| *6))
       (|isDomain| *1 (|InfiniteTupleFunctions2| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *8 *6 *7))
       (|isDomain| *4 (|InfiniteTuple| *6))
       (|isDomain| *5 (|InfiniteTuple| *7)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|))
       (|isDomain| *2 (|InfiniteTuple| *8))
       (|isDomain| *1 (|InfiniteTupleFunctions3| *6 *7 *8))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|Stream| *6))
       (|isDomain| *5 (|InfiniteTuple| *7)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|))
       (|isDomain| *2 (|Stream| *8))
       (|isDomain| *1 (|InfiniteTupleFunctions3| *6 *7 *8))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *8 *6 *7))
       (|isDomain| *4 (|InfiniteTuple| *6)) (|isDomain| *5 (|Stream| *7))
       (|ofCategory| *6 (|Type|)) (|ofCategory| *7 (|Type|))
       (|ofCategory| *8 (|Type|)) (|isDomain| *2 (|Stream| *8))
       (|isDomain| *1 (|InfiniteTupleFunctions3| *6 *7 *8))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|List| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|ListFunctions2| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|List| *6))
       (|isDomain| *5 (|List| *7)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|))
       (|isDomain| *2 (|List| *8))
       (|isDomain| *1 (|ListFunctions3| *6 *7 *8))))
 ((*1 *1 *2 *1 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3))
       (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *8 *5)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *8 (|Ring|))
       (|ofCategory| *6 (|FiniteLinearAggregate| *5))
       (|ofCategory| *7 (|FiniteLinearAggregate| *5))
       (|ofCategory| *2 (|MatrixCategory| *8 *9 *10))
       (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2))
       (|ofCategory| *4 (|MatrixCategory| *5 *6 *7))
       (|ofCategory| *9 (|FiniteLinearAggregate| *8))
       (|ofCategory| *10 (|FiniteLinearAggregate| *8))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *8 "failed") *5))
   (|ofCategory| *5 (|Ring|)) (|ofCategory| *8 (|Ring|))
   (|ofCategory| *6 (|FiniteLinearAggregate| *5))
   (|ofCategory| *7 (|FiniteLinearAggregate| *5))
   (|ofCategory| *2 (|MatrixCategory| *8 *9 *10))
   (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2))
   (|ofCategory| *4 (|MatrixCategory| *5 *6 *7))
   (|ofCategory| *9 (|FiniteLinearAggregate| *8))
   (|ofCategory| *10 (|FiniteLinearAggregate| *8))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *7 (|IntegralDomain|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Fraction| *8)))
       (|isDomain| *1 (|MultipleMap| *5 *6 *4 *7 *8 *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *6)))
       (|ofCategory| *8 (|UnivariatePolynomialCategory| *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *9 *8)) (|ofCategory| *8 (|Ring|))
       (|ofCategory| *9 (|Ring|)) (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|PolynomialCategory| *9 *7 *5))
       (|isDomain| *1 (|MPolyCatFunctions2| *5 *6 *7 *8 *9 *4 *2))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|PolynomialCategory| *8 *6 *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|Ring|))
       (|ofCategory| *2 (|PolynomialCategory| *9 *8 *6))
       (|isDomain| *1 (|MPolyCatFunctions3| *5 *6 *7 *8 *9 *4 *2))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|PolynomialCategory| *9 *7 *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|MonoidRing| *5 *7))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|))
       (|ofCategory| *7 (|Monoid|)) (|isDomain| *2 (|MonoidRing| *6 *7))
       (|isDomain| *1 (|MonoidRingFunctions2| *5 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|NewSparseUnivariatePolynomial| *5))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|NewSparseUnivariatePolynomial| *6))
       (|isDomain| *1 (|NewSparseUnivariatePolynomialFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|CommutativeRing|))
       (|ofCategory| *6 (|CommutativeRing|))
       (|ofCategory| *2 (|OctonionCategory| *6))
       (|isDomain| *1 (|OctonionCategoryFunctions2| *4 *5 *2 *6))
       (|ofCategory| *4 (|OctonionCategory| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|OnePointCompletion| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|OnePointCompletion| *6))
       (|isDomain| *1 (|OnePointCompletionFunctions2| *5 *6))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|OnePointCompletion| *6))
       (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|OnePointCompletion| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *1 (|OnePointCompletionFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|OrderedCompletion| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|OrderedCompletion| *6))
       (|isDomain| *1 (|OrderedCompletionFunctions2| *5 *6))))
 ((*1 *2 *3 *4 *2 *2)
  (AND (|isDomain| *2 (|OrderedCompletion| *6))
       (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|OrderedCompletion| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *1 (|OrderedCompletionFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|ParametricPlaneCurve| *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|ParametricPlaneCurve| *6))
       (|isDomain| *1 (|ParametricPlaneCurveFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|ParametricSpaceCurve| *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|ParametricSpaceCurve| *6))
       (|isDomain| *1 (|ParametricSpaceCurveFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|ParametricSurface| *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|ParametricSurface| *6))
       (|isDomain| *1 (|ParametricSurfaceFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *7 *6))
       (|isDomain| *4 (|PatternMatchResult| *5 *6))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|))
       (|isDomain| *2 (|PatternMatchResult| *5 *7))
       (|isDomain| *1 (|PatternMatchResultFunctions2| *5 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Pattern| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|Pattern| *6))
       (|isDomain| *1 (|PatternFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Polynomial| *5))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|Polynomial| *6))
       (|isDomain| *1 (|PolynomialFunctions2| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *2 *7)) (|isDomain| *4 (|Mapping| *2 *8))
       (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|Ring|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2
                     (|Join| (|SetCategory|)
                             (CATEGORY |domain| (SIGNATURE + ($ $ $))
                              (SIGNATURE * ($ $ $))
                              (SIGNATURE ** ($ $ (|NonNegativeInteger|))))))
       (|isDomain| *1 (|PolynomialCategoryLifting| *6 *7 *8 *5 *2))
       (|ofCategory| *5 (|PolynomialCategory| *8 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|PrimitiveArray| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|PrimitiveArray| *6))
       (|isDomain| *1 (|PrimitiveArrayFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|PropositionalFormula| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|PropositionalFormula| *6))
       (|isDomain| *1 (|PropositionalFormulaFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Point| *5))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|Point| *6)) (|isDomain| *1 (|PointFunctions2| *5 *6))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|Mapping| *2 (|Polynomial| *4)))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *6))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $))
                              (SIGNATURE |variable|
                               ((|Union| $ "failed") (|Symbol|))))))
       (|isDomain| *1 (|PushVariables| *4 *5 *6 *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *6 (|IntegralDomain|))
       (|ofCategory| *2 (|QuotientFieldCategory| *6))
       (|isDomain| *1 (|QuotientFieldCategoryFunctions2| *5 *6 *4 *2))
       (|ofCategory| *4 (|QuotientFieldCategory| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|CommutativeRing|))
       (|ofCategory| *6 (|CommutativeRing|))
       (|ofCategory| *2 (|QuaternionCategory| *6))
       (|isDomain| *1 (|QuaternionCategoryFunctions2| *4 *5 *2 *6))
       (|ofCategory| *4 (|QuaternionCategory| *5))))
 ((*1 *1 *2 *1 *1)
  (AND (|isDomain| *2 (|Mapping| *5 *5 *5))
       (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *10 *7)) (|ofCategory| *7 (|Ring|))
       (|ofCategory| *10 (|Ring|)) (|ofType| *5 (|NonNegativeInteger|))
       (|ofType| *6 (|NonNegativeInteger|))
       (|ofCategory| *8 (|DirectProductCategory| *6 *7))
       (|ofCategory| *9 (|DirectProductCategory| *5 *7))
       (|ofCategory| *2 (|RectangularMatrixCategory| *5 *6 *10 *11 *12))
       (|isDomain| *1
        (|RectangularMatrixCategoryFunctions2| *5 *6 *7 *8 *9 *4 *10 *11 *12
                                               *2))
       (|ofCategory| *4 (|RectangularMatrixCategory| *5 *6 *7 *8 *9))
       (|ofCategory| *11 (|DirectProductCategory| *6 *10))
       (|ofCategory| *12 (|DirectProductCategory| *5 *10))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Segment| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|Segment| *6))
       (|isDomain| *1 (|SegmentFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Segment| *5))
       (|ofCategory| *5 (|OrderedRing|)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|SegmentFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|SegmentBinding| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|SegmentBinding| *6))
       (|isDomain| *1 (|SegmentBindingFunctions2| *5 *6))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Mapping| *4 *4))
       (|ofCategory| *1 (|SegmentExpansionCategory| *4 *2))
       (|ofCategory| *4 (|OrderedRing|))
       (|ofCategory| *2 (|StreamAggregate| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Stream| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|Stream| *6))
       (|isDomain| *1 (|StreamFunctions2| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|Stream| *6))
       (|isDomain| *5 (|Stream| *7)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *7 (|Type|)) (|ofCategory| *8 (|Type|))
       (|isDomain| *2 (|Stream| *8))
       (|isDomain| *1 (|StreamFunctions3| *6 *7 *8))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|SparseUnivariatePolynomial| *5))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *6))
       (|isDomain| *1 (|SparseUnivariatePolynomialFunctions2| *5 *6))))
 ((*1 *1 *2 *1 *1)
  (AND (|isDomain| *2 (|Mapping| *4 *4 *4))
       (|ofCategory| *1 (|TableAggregate| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|UnivariateLaurentSeries| *5 *7 *9))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|))
       (|ofType| *7 (|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6)
       (|isDomain| *2 (|UnivariateLaurentSeries| *6 *8 *10))
       (|isDomain| *1 (|UnivariateLaurentSeriesFunctions2| *5 *6 *7 *8 *9 *10))
       (|ofType| *8 (|Symbol|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|UniversalSegment| *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|UniversalSegment| *6))
       (|isDomain| *1 (|UniversalSegmentFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|UniversalSegment| *5))
       (|ofCategory| *5 (|OrderedRing|)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|Stream| *6))
       (|isDomain| *1 (|UniversalSegmentFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *8 *6))
       (|isDomain| *4 (|UnivariatePolynomial| *5 *6)) (|ofType| *5 (|Symbol|))
       (|ofCategory| *6 (|Ring|)) (|ofCategory| *8 (|Ring|))
       (|isDomain| *2 (|UnivariatePolynomial| *7 *8))
       (|isDomain| *1 (|UnivariatePolynomialFunctions2| *5 *6 *7 *8))
       (|ofType| *7 (|Symbol|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|Ring|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *6))
       (|isDomain| *1 (|UnivariatePolynomialCategoryFunctions2| *5 *4 *6 *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5))
       (|isDomain| *4 (|UnivariatePuiseuxSeries| *5 *7 *9))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|Ring|))
       (|ofType| *7 (|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6)
       (|isDomain| *2 (|UnivariatePuiseuxSeries| *6 *8 *10))
       (|isDomain| *1 (|UnivariatePuiseuxSeriesFunctions2| *5 *6 *7 *8 *9 *10))
       (|ofType| *8 (|Symbol|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|Ring|))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *6))
       (|isDomain| *1 (|UnivariateTaylorSeriesFunctions2| *5 *6 *4 *2))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Vector| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|Vector| *6))
       (|isDomain| *1 (|VectorFunctions2| *5 *6))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *6 "failed") *5))
   (|isDomain| *4 (|Vector| *5)) (|ofCategory| *5 (|Type|))
   (|ofCategory| *6 (|Type|)) (|isDomain| *2 (|Vector| *6))
   (|isDomain| *1 (|VectorFunctions2| *5 *6))))) 
(((*1 *1 *1) (|isDomain| *1 (|AlgebraicNumber|)))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *5 *2))
       (|isDomain| *4 (|OneDimensionalArray| *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|OneDimensionalArrayFunctions2| *5 *2))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |pol| (|SparseUnivariatePolynomial| *4))
                  (|:| |deg| (|PositiveInteger|))))
       (|isDomain| *1 (|DegreeReductionPackage| *4 *5))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *5 (|IntegralDomain|))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *6 *2))
       (|isDomain| *4 (|DirectProduct| *5 *6))
       (|ofType| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|DirectProductFunctions2| *5 *6 *2))))
 ((*1 *1 *2 *3)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *1 (|EuclideanModularRing| *4 *2 *3 *5 *6 *7))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *2 *2 *3))
       (|ofType| *6 (|Mapping| (|Union| *3 "failed") *3 *3))
       (|ofType| *7 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|Expression| *2)) (|ofCategory| *2 (|IntegralDomain|))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5))
       (|ofCategory| *2 (|Field|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4))))
 ((*1 *2 *3 *1 *2 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *2 (|BasicType|))
       (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *3 *1 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *2 *2))
       (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Mapping| *2 *2 *2))
       (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *2 *6))
       (|ofCategory| *4 (|FiniteLinearAggregate| *5))
       (|ofCategory| *6 (|FiniteLinearAggregate| *2))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *2 *6))
       (|ofCategory| *4 (|FiniteSetAggregate| *5))
       (|ofCategory| *6 (|FiniteSetAggregate| *2))))
 ((*1 *1 *1) (|isDomain| *1 (|InnerAlgebraicNumber|)))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|isDomain| *4 (|List| *5))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|ListFunctions2| *5 *2))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *6 (|FiniteLinearAggregate| *5))
       (|ofCategory| *7 (|FiniteLinearAggregate| *5))
       (|ofCategory| *8 (|FiniteLinearAggregate| *2))
       (|ofCategory| *9 (|FiniteLinearAggregate| *2))
       (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *2 *8 *9 *10))
       (|ofCategory| *4 (|MatrixCategory| *5 *6 *7))
       (|ofCategory| *10 (|MatrixCategory| *2 *8 *9))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3))
       (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3))
       (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModMonic| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3))
       (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3))
       (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))
 ((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|Fraction| *4))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|CommutativeRing|))
   (|ofCategory| *1 (|MonogenicAlgebra| *3 *4))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *1 (|MonogenicAlgebra| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *5 *2))
       (|isDomain| *4 (|PrimitiveArray| *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|PrimitiveArrayFunctions2| *5 *2))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6))
       (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5))
       (|ofType| *6 (|List| *2))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *7 *2)) (|ofCategory| *7 (|Ring|))
       (|ofCategory| *2 (|Ring|)) (|ofType| *5 (|NonNegativeInteger|))
       (|ofType| *6 (|NonNegativeInteger|))
       (|ofCategory| *8 (|DirectProductCategory| *6 *7))
       (|ofCategory| *9 (|DirectProductCategory| *5 *7))
       (|ofCategory| *10 (|DirectProductCategory| *6 *2))
       (|ofCategory| *11 (|DirectProductCategory| *5 *2))
       (|isDomain| *1
        (|RectangularMatrixCategoryFunctions2| *5 *6 *7 *8 *9 *4 *2 *10 *11
                                               *12))
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       (|ofCategory| *12 (|RectangularMatrixCategory| *5 *6 *2 *10 *11))))
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       (|isDomain| *4 (|Mapping| (|Boolean|) *2 *2))
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       (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *5 *6 *7))))
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  (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) (|isDomain| *4 (|Vector| *5))
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       (|isDomain| *1 (|VectorFunctions2| *5 *2))))) 
(((*1 *2 *3 *4 *5)
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       (|isDomain| *4 (|OneDimensionalArray| *6)) (|ofCategory| *6 (|Type|))
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       (|isDomain| *4 (|DirectProduct| *6 *7))
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       (|isDomain| *1 (|VectorFunctions2| *6 *5))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|Vector| *3))))) 
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                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |elt| ((|String|) $ (|Symbol|)))
                              (SIGNATURE |display| ((|Void|) $))
                              (SIGNATURE |fullDisplay| ((|Void|) $)))))))
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       (|ofCategory| *3 (|CancellationAbelianMonoid|))))
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       (|ofCategory| *3 (|AbelianMonoid|))))
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       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))
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  (AND (|isDomain| *2 (|Point| (|DoubleFloat|)))
       (|isDomain| *1 (|TubePlotTools|))))
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  (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|))
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(((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Ring|))
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(((*1 *1 *1 *1) (|ofCategory| *1 (|AbelianGroup|)))
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       (|ofCategory| *2
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |elt| ((|String|) $ (|Symbol|)))
                              (SIGNATURE |display| ((|Void|) $))
                              (SIGNATURE |fullDisplay| ((|Void|) $)))))))
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  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|))
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  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|))
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 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|GradedModule| *2 *3))
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  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
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 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Point| (|DoubleFloat|)))
       (|isDomain| *1 (|TubePlotTools|))))
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  (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|))
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 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *2 (|AbelianGroup|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2))
       (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *2)
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 ((*1 *2 *3 *3)
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       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|VectorCategory| *3)) (|ofCategory| *3 (|Type|))
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(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|PointCategory| *2)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Point| (|DoubleFloat|)))
       (|isDomain| *1 (|TubePlotTools|))))
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  (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FreeMagma| *3))
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 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
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       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
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       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QueueAggregate| *3)) (|ofCategory| *3 (|Type|))
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 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Tuple| *3))
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 ((*1 *2 *1)
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(((*1 *2 *1)
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(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialVariableCategory| *2))
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 ((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|Symbol|))
   (|isDomain| *1 (|OrderedVariableList| *3)) (|ofType| *3 (|List| *2))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|QueryEquation|))))
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 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4))
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       (|isDomain| *2 (|Symbol|))))
 ((*1 *2)
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       (|ofType| *3 *2)))) 
(((*1 *2 *3)
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       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4))
       (|isDomain| *1 (|UTSodetools| *4 *5 *6 *2))
       (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
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       (|isDomain| *2 (|Mapping| *6 (|List| *6)))
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       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))
       (|ofCategory| *6 (|UnivariateTaylorSeriesCategory| *4))))) 
(((*1 *2 *3 *4)
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       (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
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       (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
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       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4))
       (|isDomain| *1 (|UTSodetools| *4 *3 *5 *2))
       (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *5))
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       (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *5 *6))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *2 (|List| *2))) (|isDomain| *4 (|List| *5))
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       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5))
       (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *5 *2))))) 
(((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|Mapping| *2 *2 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4))
       (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *2))
       (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|))))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *2 *2))
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       (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *2))
       (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|))))))) 
(((*1 *2 *2 *2)
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(((*1 *2 *3)
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(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *5 *5 *5))
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(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *5 *5))
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(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
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                             (|LinearlyExplicitRingOver| (|Integer|))))
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       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *5))
       (|ofCategory| *5
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                             (|TranscendentalFunctionCategory|)
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 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Any|))
   (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
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 ((*1 *2 *3 *4)
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                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
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 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
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       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))))
 ((*1 *2 *3 *4 *5)
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                             (|TranscendentalFunctionCategory|)
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       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *6 *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 (|Integer|)))
       (|isDomain| *4 (|Equation| *6))
       (|ofCategory| *6
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
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       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *7 (|Integer|)))
       (|isDomain| *4 (|Equation| *7))
       (|isDomain| *5 (|UniversalSegment| (|Integer|)))
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                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
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       (|ofCategory| *6
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3))
       (|isDomain| *6 (|UniversalSegment| (|Integer|)))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *7)))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *3 (|Mapping| *8 #1=(|Fraction| (|Integer|))))
       (|isDomain| *4 (|Equation| *8)) (|isDomain| *5 (|UniversalSegment| #1#))
       (|isDomain| *6 (|Fraction| (|Integer|)))
       (|ofCategory| *8
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *7)))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *8))))
 ((*1 *2 *3 *4 *5 *6 *7)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3))
       (|isDomain| *6 (|UniversalSegment| (|Fraction| (|Integer|))))
       (|isDomain| *7 (|Fraction| (|Integer|)))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *8)))
       (|ofCategory| *8
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *8 *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3))))
       (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|InnerTaylorSeries| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3))))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *3
        (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| *4))))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| *3))))
   (|ofCategory| *3 (|Ring|))
   (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|isDomain| *2 (|List| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|InnerTaylorSeries| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|MonoidRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Stream| *3))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 (|Integer|))) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 (|Integer|)))
       (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 (|Integer|)))
       (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|Polynomial| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|Polynomial| *4))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *4))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Polynomial| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *4))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Polynomial| *4))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Integer|)))
       (|ofCategory| *4 (|RetractableTo| (|Integer|)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicFunction| *4 *2))
       (|ofCategory| *2 (|FunctionSpace| *4))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|CardinalNumber|)))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|DoubleFloat|)))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|DivisionRing|)) (|isDomain| *2 (|Integer|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Field|))
       (|ofCategory| *4 (|Algebra| *3))
       (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *4 *5 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *4 *5))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Field|))
       (|ofCategory| *4 (|Algebra| *3))
       (|ofCategory| *5 (|UnivariateLaurentSeriesCategory| *4))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *4 *5 *2 *6))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *4 *5))
       (|ofCategory| *6 (|PartialTranscendentalFunctions| *5))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|)))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|FreeGroup| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|Float|)))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|FreeMonoidCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *3 (|SemiGroup|))))
 ((*1 *1 *1 *2) (AND (|ofCategory| *1 (|Group|)) (|isDomain| *2 (|Integer|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|InputForm|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|InputForm|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|MappingPackage1| *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Field|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|ModuleOperator| *3 *4))
       (|ofCategory| *4 (|LeftModule| *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *4 *5))
       (|ofCategory| *5 (|LeftModule| *4))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|MonadWithUnit|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Operator| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|Operator| *4)) (|ofCategory| *4 (|Ring|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RadicalCategory|))
       (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|SemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *6))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *5 (|DirectProductCategory| *3 *4))
       (|ofCategory| *6 (|DirectProductCategory| *3 *4))
       (|ofCategory| *4 (|Field|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| *3)))
       (|ofCategory| *3
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Union| (|:| |f1| (|OrderedCompletion| *3))
                 (|:| |f2| (|List| (|OrderedCompletion| *3)))
                 (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")))
       (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *5 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|SegmentBinding| (|OrderedCompletion| *3)))
       (|isDomain| *5 (|String|))
       (|ofCategory| *3
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Union| (|:| |f1| (|OrderedCompletion| *3))
                 (|:| |f2| (|List| (|OrderedCompletion| *3))) (|:| |fail| #1#)
                 (|:| |pole| #2#)))
       (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *6 *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4
        (|SegmentBinding| (|OrderedCompletion| (|Expression| *5))))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *5)))
                 (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *5))))
                 (|:| |fail| #3="failed") (|:| |pole| #4="potentialPole")))
       (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *5))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *6)))
       (|isDomain| *4
        (|SegmentBinding| (|OrderedCompletion| (|Expression| *6))))
       (|isDomain| *5 (|String|))
       (|ofCategory| *6
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *6)))
                 (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *6))))
                 (|:| |fail| #3#) (|:| |pole| #4#)))
       (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *6))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *4
    (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| *5)))))
   (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
   (|ofCategory| *5
                 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2
    (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *5)))
             (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *5))))
             (|:| |fail| #3#) (|:| |pole| #4#)))
   (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *5))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *4
    (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| *6)))))
   (|isDomain| *5 (|String|)) (|isDomain| *3 (|Fraction| (|Polynomial| *6)))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2
    (|Union| (|:| |f1| (|OrderedCompletion| (|Expression| *6)))
             (|:| |f2| (|List| (|OrderedCompletion| (|Expression| *6))))
             (|:| |fail| #3#) (|:| |pole| #4#)))
   (|isDomain| *1 (|RationalFunctionDefiniteIntegration| *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Union| *3 (|List| *3)))
       (|isDomain| *1 (|FunctionSpaceIntegration| *5 *3))
       (|ofCategory| *3
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *5)))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2 (|IntegrationResult| (|Fraction| *5)))
   (|isDomain| *1 (|RationalIntegration| *4 *5))
   (|isDomain| *3 (|Fraction| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|CharacteristicZero|))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Union| (|Expression| *5) (|List| (|Expression| *5))))
       (|isDomain| *1 (|IntegrationResultRFToFunction| *5))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Polynomial| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2 *3)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|))
       (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *2 *4))
       (|ofCategory| *4 (|PolynomialCategory| *3 (|IndexedExponents| *2) *2))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|SparseUnivariateLaurentSeries| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|SparseUnivariatePuiseuxSeries| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|SparseUnivariateTaylorSeries| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TaylorSeries| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|UnivariateLaurentSeries| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *1 *2)
  (OR
   (AND #5=(|isDomain| *2 (|Symbol|))
        #6=(|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3))
        #7=(|ofCategory| *3 (|Ring|))
        (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|)))
             (|ofCategory| *3 (|PrimitiveFunctionCategory|))
             (|ofCategory| *3 (|TranscendentalFunctionCategory|))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))
   (AND #5# #6# #7#
        (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3)))
             (|has| *3 (SIGNATURE |integrate| (*3 *3 *2)))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *2))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|UnivariatePuiseuxSeries| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *1 *2)
  (OR
   (AND #8=(|isDomain| *2 (|Symbol|))
        #9=(|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *3))
        #10=(|ofCategory| *3 (|Ring|))
        (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|)))
             (|ofCategory| *3 (|PrimitiveFunctionCategory|))
             (|ofCategory| *3 (|TranscendentalFunctionCategory|))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))
   (AND #8# #9# #10#
        (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3)))
             (|has| *3 (SIGNATURE |integrate| (*3 *3 *2)))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *2))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|))
       (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))
 ((*1 *1 *1 *2)
  (OR
   (AND #11=(|isDomain| *2 (|Symbol|))
        #12=(|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3))
        #13=(|ofCategory| *3 (|Ring|))
        (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|)))
             (|ofCategory| *3 (|PrimitiveFunctionCategory|))
             (|ofCategory| *3 (|TranscendentalFunctionCategory|))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))
   (AND #11# #12# #13#
        (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3)))
             (|has| *3 (SIGNATURE |integrate| (*3 *3 *2)))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|UnivariatePolynomial| *5 *4))
       (|isDomain| *1 (|SparseUnivariateTaylorSeries| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofType| *5 (|Symbol|)) (|ofType| *6 *4)))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|UnivariatePolynomial| *5 *4))
       (|isDomain| *1 (|UnivariateTaylorSeries| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofType| *5 (|Symbol|)) (|ofType| *6 *4)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2)))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))))
 ((*1 *1 *1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofType| *3 (|Symbol|)) (|ofType| *4 *2)))) 
(((*1 *2 *3 *3 *2)
  (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))))
 ((*1 *1 *2 *2 *1)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)))) 
(((*1 *2 *3 *3 *2)
  (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))))
 ((*1 *1 *2 *2 *1)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|LinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Stream| (|Stream| *4))) (|isDomain| *2 (|Stream| *4))
       (|isDomain| *1 (|StreamFunctions1| *4)) (|ofCategory| *4 (|Type|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedAggregate| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1)
  (AND (|isDomain| *1 (|OrderedFreeMonoid| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|Pair| *2 *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|LyndonWord| *3))
       (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
   (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1 *3 *3 *2)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5))
       (|ofCategory| *2 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 "right")
       (|ofCategory| *1 (|BinaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 "left") (|ofCategory| *1 (|BinaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 (|Integer|))
       (|ofType| *5 (|NonNegativeInteger|))))
 ((*1 *2 *1 *3 *3 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3)
       (|ofType| *5 (|NonNegativeInteger|))))
 ((*1 *2 *1 *3 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3)
       (|ofType| *5 (|NonNegativeInteger|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3)
       (|ofType| *5 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|CartesianTensor| *3 *4 *2)) (|ofType| *3 (|Integer|))
       (|ofType| *4 (|NonNegativeInteger|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|DataList| (|String|)))
       (|isDomain| *1 (|Database| *4))
       (|ofCategory| *4
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |elt| ((|String|) $ *3))
                              (SIGNATURE |display| ((|Void|) $))
                              (SIGNATURE |fullDisplay| ((|Void|) $)))))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|QueryEquation|)) (|isDomain| *1 (|Database| *3))
       (|ofCategory| *3
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |elt| ((|String|) $ (|Symbol|)))
                              (SIGNATURE |display| ((|Void|) $))
                              (SIGNATURE |fullDisplay| ((|Void|) $)))))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 "count") (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|DataList| *4)) (|ofCategory| *4 (|OrderedSet|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 "sort") (|isDomain| *1 (|DataList| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 "unique") (|isDomain| *1 (|DataList| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|Eltable| *3 *2)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3 *2)
  (AND (|ofCategory| *1 (|EltableAggregate| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *2 *1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|BasicOperator|))))
 ((*1 *1 *2 *1 *1 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|BasicOperator|))))
 ((*1 *1 *2 *1 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|BasicOperator|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|BasicOperator|))))
 ((*1 *2 *1 *2 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4))
       (|ofCategory| *2 (|UniqueFactorizationDomain|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3)))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|IndexCard|))))
 ((*1 *1 *1 *2 *2)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|))
       (|isDomain| *3 (|List| (|Pattern| *4))) (|isDomain| *1 (|Pattern| *4))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Permutation| *4))
       (|isDomain| *1 (|PermutationGroup| *4))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 "value") (|ofCategory| *1 (|RecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3 *3 *2)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *5 *2))
       (|ofCategory| *7 (|DirectProductCategory| *4 *2))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7))
       (|ofCategory| *6 (|DirectProductCategory| *5 *2))
       (|ofCategory| *7 (|DirectProductCategory| *4 *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5
                     (|Join| (|Ring|) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|isDomain| *1 (|RewriteRule| *4 *5 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))))
 ((*1 *2 *1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5
                     (|Join| (|Ring|) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|isDomain| *1 (|Ruleset| *4 *5 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|StringAggregate|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|Fraction| *1))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Fraction| *1))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 "last") (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 "rest") (|ofCategory| *1 (|UnaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 "first") (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|OrderedFreeMonoid| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *2 *3 *4 *5))
   (|ofCategory| *2 (|IntegralDomain|))
   (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *4 (|OrderedSet|))
   (|ofCategory| *5 (|RecursivePolynomialCategory| *2 *3 *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|SequenceAst|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
   (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|Pair| *3 *2))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1 *3 *3 *2)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5))
       (|ofCategory| *2 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))))
 ((*1 *1 *1 *2 *1)
  (AND (|isDomain| *2 "right")
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *1 (|BinaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2 *1)
  (AND (|isDomain| *2 "left")
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *1 (|BinaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
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  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|EltableAggregate| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3 *2)
  (AND (|isDomain| *2 (|Any|)) (|isDomain| *3 (|Symbol|))
       (|isDomain| *1 (|Library|))))
 ((*1 *2 *1 *3 *2)
  (AND (|isDomain| *3 (|UniversalSegment| (|Integer|)))
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))
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  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
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  (AND (|isDomain| *3 "value")
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3 *2)
  (AND (|isDomain| *3 "last")
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))
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  (AND (|isDomain| *2 "rest")
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1 *3 *2)
  (AND (|isDomain| *3 "first")
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Stream| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *1 (|UnaryRecursiveAggregate| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *1)
  (|partial| AND
   (|ofCategory| *3
                 (|Join| (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|GcdDomain|)))
   (|isDomain| *2 (|OrderedCompletion| *4))
   (|isDomain| *1 (|ExponentialExpansion| *3 *4 *5 *6))
   (|ofCategory| *4
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))
   (|ofType| *5 (|Symbol|)) (|ofType| *6 *4)))
 ((*1 *2 *1)
  (|partial| AND
   (|ofCategory| *3
                 (|Join| (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|GcdDomain|)))
   (|isDomain| *2 (|OrderedCompletion| *4))
   (|isDomain| *1
    (|UnivariatePuiseuxSeriesWithExponentialSingularity| *3 *4 *5 *6))
   (|ofCategory| *4
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))
   (|ofType| *5 (|Symbol|)) (|ofType| *6 *4)))) 
(((*1 *2 *1)
  (|partial| AND
   (|ofCategory| *3
                 (|Join| (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|GcdDomain|)))
   (|isDomain| *2
    (|Record|
     (|:| |%term|
          (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| *4 *5 *6))
                    (|:| |%expon|
                         (|ExponentialOfUnivariatePuiseuxSeries| *4 *5 *6))
                    (|:| |%expTerms|
                         (|List|
                          (|Record| (|:| |k| (|Fraction| (|Integer|)))
                                    (|:| |c| *4))))))
     (|:| |%type| (|String|))))
   (|isDomain| *1
    (|UnivariatePuiseuxSeriesWithExponentialSingularity| *3 *4 *5 *6))
   (|ofCategory| *4
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))
   (|ofType| *5 (|Symbol|)) (|ofType| *6 *4)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *5))
       (|ofCategory| *5
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Any|))
   (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *4)))))
 ((*1 *2 *3 *4)
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       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))))
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  (AND (|isDomain| *4 (|Equation| *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))))
 ((*1 *2 *3 *4 *5)
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       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *6 *3))))
 ((*1 *2 *3 *4 *5 *6)
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       (|isDomain| *4 (|Equation| *8)) (|isDomain| *5 (|UniversalSegment| #1#))
       (|isDomain| *6 (|Fraction| (|Integer|)))
       (|ofCategory| *8
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *7)))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *8))))
 ((*1 *2 *3 *4 *5 *6 *7)
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       (|isDomain| *6 (|UniversalSegment| (|Fraction| (|Integer|))))
       (|isDomain| *7 (|Fraction| (|Integer|)))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *8)))
       (|ofCategory| *8
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *8 *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *4 *3))
       (|ofCategory| *3 (|UnivariateLaurentSeriesCategory| *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *2 (|Fraction| (|Integer|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *5))
       (|ofCategory| *5
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Any|))
   (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *4)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Integer|))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| *4)
                             (|LinearlyExplicitRingOver| *4)))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Equation| *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| *5)
                             (|LinearlyExplicitRingOver| *5)))
       (|isDomain| *5 (|Integer|)) (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *6 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *7 (|Integer|)))
       (|isDomain| *4 (|Equation| *7))
       (|isDomain| *5 (|UniversalSegment| (|Integer|)))
       (|ofCategory| *7
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3))
       (|isDomain| *6 (|UniversalSegment| (|Integer|)))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *7)))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *4 *3))
       (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3))))) 
(((*1 *2 *1)
  (|partial| AND
   (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2))
   (|ofCategory| *3 (|Ring|))
   (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *2)
  (AND
   (|isDomain| *2
    (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime"))
              (|:| |fctr| *4) (|:| |xpnt| (|Integer|))))
   (|ofCategory| *4
                 (|Join| (|UnivariatePolynomialCategory| *3) (|IntegralDomain|)
                         (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)))))
   (|ofCategory| *3 (|IntegralDomain|))
   (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *4))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|PolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *1))))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|UniqueFactorizationDomain|)))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *2))
       (|ofCategory| *2
                     (|Join| (|UnivariatePolynomialCategory| *3)
                             (|IntegralDomain|)
                             (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)))))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4 (|CancellationAbelianMonoid|))
       (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4))))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *4))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|OrderedType|))
       (|isDomain| *2 (|List| (|IndexedProductTerm| *3 *4)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Record| (|:| |coef| *3) (|:| |monom| *4))))
       (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|Monoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|isDomain| *2 (|Stream| (|Record| (|:| |k| *4) (|:| |c| *3))))))) 
(((*1 *2 *2 *3 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|DisplayPackage|))))
 ((*1 *2 *2 *3 *4)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *3 (|Integer|))
       (|isDomain| *4 (|String|)) (|isDomain| *1 (|DisplayPackage|))))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3))
       (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *4))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *3))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteFieldCategory|))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|FiniteDivisor| *4 *5 *6 *7))
       (|ofCategory| *4 (|Join| (|Finite|) (|Field|)))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|ofCategory| *7 (|FunctionFieldCategory| *4 *5 *6))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FindOrderFinite| *4 *5 *6 *7))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|))
       (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|InnerTaylorSeries| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|InnerTaylorSeries| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|LaurentPolynomial| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *1 *3 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *3))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *3))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8))
   (|ofCategory| *5 (|FunctionSpace| *4))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
   (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7))
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2 (|NonNegativeInteger|))
   (|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8))))
 ((*1 *2 *3)
  (|partial| AND
   (|isDomain| *3 (|FiniteDivisor| (|Fraction| (|Integer|)) *4 *5 *6))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
   (|ofCategory| *6 (|FunctionFieldCategory| (|Fraction| (|Integer|)) *4 *5))
   (|isDomain| *2 (|NonNegativeInteger|))
   (|isDomain| *1 (|PointsOfFiniteOrderRational| *4 *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|FiniteDivisor| *6 *7 *4 *8))
       (|isDomain| *5 (|Mapping| *9 *6)) (|ofCategory| *6 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *7)))
       (|ofCategory| *8 (|FunctionFieldCategory| *6 *7 *4))
       (|ofCategory| *9 (|Join| (|Finite|) (|Field|)))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|ReducedDivisor| *6 *7 *4 *8 *9))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))) 
(((*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))
 ((*1 *1 *1 *2 *2)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|BalancedPAdicRational| *4)) (|ofType| *4 *3)
       (|isDomain| *3 (|Integer|))))
 ((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|PAdicRational| *4)) (|ofType| *4 *3)
       (|isDomain| *3 (|Integer|))))
 ((*1 *2 *1 *3)
  (AND (|ofType| *4 *3) (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|PAdicRationalConstructor| *4 *5))
       (|isDomain| *3 (|Integer|))
       (|ofCategory| *5 (|PAdicIntegerCategory| *4))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RealClosedField|))
       (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *3 *1 *2)
  (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *2 *3))
       (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3))
       (|ofCategory| *3 (|OrderedAbelianMonoid|))
       (|has| *2 (SIGNATURE ** (*2 *2 *3)))
       (|has| *2 (SIGNATURE |coerce| (*2 (|Symbol|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LazyStreamAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PointCategory| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *3 (|Fraction| *5))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|ChangeOfVariable| *4 *5 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|CycleIndicators|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Equation| *3)))
       (|ofCategory| *3 (|Evalable| *3)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Equation| *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *2 (|Evalable| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|Equation| *2))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *1 *1))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|))
       (|isDomain| *3 (|Mapping| *1 (|List| *1)))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|BasicOperator|)))
       (|isDomain| *3 (|List| (|Mapping| *1 (|List| *1))))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|BasicOperator|)))
       (|isDomain| *3 (|List| (|Mapping| *1 *1)))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Mapping| *1 *1))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Mapping| *1 (|List| *1)))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Symbol|)))
       (|isDomain| *3 (|List| (|Mapping| *1 (|List| *1))))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Symbol|)))
       (|isDomain| *3 (|List| (|Mapping| *1 *1)))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Equation| *3)))
       (|ofCategory| *1 (|Evalable| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Equation| *3)) (|ofCategory| *1 (|Evalable| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *2 (|Integer|)))
       (|isDomain| *4 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|EvaluateCycleIndicators| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|FreeLieAlgebra| *4 *5))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|CommutativeRing|))))
 ((*1 *1 *1 *2 *1)
  (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|))))
 ((*1 *1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *4 (|Mapping| *1 *1)) (|ofCategory| *1 (|FunctionSpace| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *5 (|Ring|))))
 ((*1 *1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *4 (|Mapping| *1 (|List| *1)))
       (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *5 (|Ring|))))
 ((*1 *1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|List| (|Symbol|)))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|isDomain| *4 (|List| (|Mapping| *1 (|List| *1))))
       (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *5 (|Ring|))))
 ((*1 *1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|List| (|Symbol|)))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|isDomain| *4 (|List| (|Mapping| *1 *1)))
       (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *5 (|Ring|))))
 ((*1 *1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|List| (|BasicOperator|))) (|isDomain| *3 (|List| *1))
       (|isDomain| *4 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *5))
       (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *5 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *1 *1 *2 *1 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Symbol|))
       (|ofCategory| *1 (|FunctionSpace| *4)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *4 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Symbol|)))
       (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *1 *1 *2 *3)
  (AND (|ofCategory| *1 (|InnerEvalable| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *5))
       (|ofCategory| *1 (|InnerEvalable| *4 *5))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|OnePointCompletion| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|MoebiusTransform| *3))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *2 *3 *2)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *4)))
       (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|RationalFunction| *4))))
 ((*1 *2 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Symbol|)))
       (|isDomain| *4 (|List| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *2 (|Fraction| (|Polynomial| *5)))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *1 (|RationalFunction| *5))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *4))))
       (|isDomain| *2 (|Fraction| (|Polynomial| *4)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|RationalFunction| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))
       (|isDomain| *2 (|Fraction| (|Polynomial| *4)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|RationalFunction| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|has| *3 (SIGNATURE ** (*3 *3 *4))) (|isDomain| *2 (|Stream| *3))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Vector| *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *1 *1 *2)
  (|partial| AND (|isDomain| *2 (|NonNegativeInteger|))
   (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1 *1 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialDomain| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|DifferentialSpace|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|DifferentialSpaceExtension| *4))
       (|ofCategory| *4 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|ofCategory| *1 (|DifferentialSpaceExtension| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *4 *4))
       (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *2 (|Field|))
       (|ofCategory| *2 (|PartialDifferentialRing| *3))
       (|isDomain| *1 (|IntegrationResult| *2)) (|isDomain| *3 (|Symbol|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Mapping| *2 *2))
       (|isDomain| *1 (|IntegrationResult| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|PartialDifferentialDomain| *2 *3))
       (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *4))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|ofCategory| *1 (|PartialDifferentialSpace| *4))
       (|ofCategory| *4 (|BasicType|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|PartialDifferentialSpace| *2))
       (|ofCategory| *2 (|BasicType|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| *3))
       (|ofCategory| *1 (|PartialDifferentialSpace| *3))
       (|ofCategory| *3 (|BasicType|))))
 ((*1 *1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2)
  (AND (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|ComplexCategory&| *3 *2))
       (|ofCategory| *3 (|ComplexCategory| *2))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankAlgebra| *2 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|FramedAlgebra&| *3 *2 *4))
       (|ofCategory| *3 (|FramedAlgebra| *2 *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedAlgebra| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|NumberFieldIntegralBasis| *3 *4))
       (|ofCategory| *4 (|FramedAlgebra| *2 *3))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ThreeSpaceCategory| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *2 *1)
  (|partial| AND (|isDomain| *2 (|Fraction| *1))
   (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef| *4) (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |coef| *3) (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2
        (|Record| (|:| |polyPart| (|LaurentPolynomial| *4 *5))
                  (|:| |fracPart| (|Fraction| *5))))
       (|isDomain| *1 (|LaurentPolynomial| *4 *5))
       (|isDomain| *3 (|Fraction| *5))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SubSpace| *3 *4)))
       (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|Ring|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |primePart| *1) (|:| |commonPart| *1)))
       (|ofCategory| *1 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *2 *2 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3 *3)
  (|partial| AND (|ofCategory| *4 (|IntegralDomain|))
   (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
   (|isDomain| *1 (|UnivariatePolynomialDivisionPackage| *4 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (|partial| AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
   (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3)))
   (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *2)
  (|partial| AND
   (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
   (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *3 *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
   (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
   (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|QuotientFieldCategory| *4))
       (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4)))
       (|isDomain| *1 (|CommonDenominator| *4 *5 *3))
       (|ofCategory| *3 (|FiniteLinearAggregate| *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|QuotientFieldCategory| *4))
       (|isDomain| *2 (|Record| (|:| |num| *6) (|:| |den| *4)))
       (|isDomain| *1 (|InnerCommonDenominator| *4 *5 *6 *3))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|ofCategory| *3 (|FiniteLinearAggregate| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *5))
       (|ofCategory| *5 (|QuotientFieldCategory| *4))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |num| (|Matrix| *4)) (|:| |den| *4)))
       (|isDomain| *1 (|MatrixCommonDenominator| *4 *5))))
 ((*1 *2 *3 *4)
  (AND
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *2 (|Record| (|:| |eq| *7) (|:| |rh| (|List| (|Fraction| *6)))))
   (|isDomain| *1 (|PrimitiveRatDE| *5 *6 *7 *3))
   (|isDomain| *4 (|List| (|Fraction| *6)))
   (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| *6))
   (|ofCategory| *3
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *6)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|QuotientFieldCategory| *4))
       (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4)))
       (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *4 *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|isDomain| *1 (|CommonDenominator| *3 *4 *2))
       (|ofCategory| *2 (|FiniteLinearAggregate| *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|QuotientFieldCategory| *4))
       (|ofCategory| *2 (|FiniteLinearAggregate| *4))
       (|isDomain| *1 (|InnerCommonDenominator| *4 *5 *2 *3))
       (|ofCategory| *3 (|FiniteLinearAggregate| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *5))
       (|ofCategory| *5 (|QuotientFieldCategory| *4))
       (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Matrix| *4))
       (|isDomain| *1 (|MatrixCommonDenominator| *4 *5))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *3 *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|CommonDenominator| *2 *4 *3))
       (|ofCategory| *3 (|FiniteLinearAggregate| *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|InnerCommonDenominator| *2 *4 *5 *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *3 (|FiniteLinearAggregate| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *4))
       (|ofCategory| *4 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|MatrixCommonDenominator| *2 *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *2 *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2 *3 *1)
  (AND (|isDomain| *1 (|PolynomialRing| *3 *2))
       (|ofCategory| *2 (|CancellationAbelianMonoid|))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|OrderedAbelianMonoid|))))
 ((*1 *1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|Partition|))
       (|ofCategory| *2 (|CancellationAbelianMonoid|))
       (|isDomain| *1 (|SymmetricPolynomial| *3))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|UnivariatePolynomial| *4 *3)) (|ofType| *4 (|Symbol|))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *2 *2)
  (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|UniversalSegment| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|SegmentCategory| *3))
       (|isDomain| *1 (|RangeBinding| *2 *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Segment| *3)) (|isDomain| *1 (|SegmentBinding| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2 *2)
  (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|UniversalSegment| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|UniversalSegment| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|isDomain| *2
        (|Record| (|:| |contp| (|Integer|))
                  (|:| |factors|
                       (|List|
                        (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|)))))))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|isDomain| *2
        (|Record| (|:| |contp| (|Integer|))
                  (|:| |factors|
                       (|List|
                        (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|)))))))
       (|isDomain| *1 (|UnivariateFactorize| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|NonNegativeInteger|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|List| (|NonNegativeInteger|)))
       (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|RationalFactorize| *3))
       (|ofCategory| *3
                     (|UnivariatePolynomialCategory|
                      (|Fraction| (|Integer|))))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|UnivariateFactorize| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|AlgebraicNumber|)))
       (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgFactor| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgFactor| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|AlgebraicNumber|)))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| (|AlgebraicNumber|) *6 *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|AlgebraicNumber|)))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|PolynomialCategory| (|AlgebraicNumber|) *6 *5))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7)))
       (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *7))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|ComplexFactorization| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Boolean|))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|NonNegativeInteger|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|List| (|NonNegativeInteger|)))
       (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| (|Complex| (|Integer|))))
       (|isDomain| *1 (|GaussianFactorizationPackage|))
       (|isDomain| *3 (|Complex| (|Integer|)))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|OrderedSet|)
                         (CATEGORY |domain|
                          (SIGNATURE |convert| ((|Symbol|) $))
                          (SIGNATURE |variable|
                           ((|Union| $ "failed") (|Symbol|))))))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *3))
   (|isDomain| *1 (|GeneralizedMultivariateFactorize| *4 *5 *6 *7 *3))
   (|ofCategory| *6 (|IntegralDomain|))
   (|ofCategory| *3 (|PolynomialCategory| *7 *5 *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|EuclideanDomain|))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *4)))
       (|isDomain| *1 (|GenUFactorize| *4))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|ofCategory| *7
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|MonogenicAlgebra| *5 *6)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|InnerAlgFactor| *5 *6 *7 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *7))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *4
    (|Mapping| (|Factored| (|SparseUnivariatePolynomial| *7))
               (|SparseUnivariatePolynomial| *7)))
   (|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|isDomain| *2 (|Factored| *3))
   (|isDomain| *1 (|InnerMultFact| *5 *6 *7 *3))
   (|ofCategory| *3 (|PolynomialCategory| *7 *6 *5))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *4
    (|Mapping| (|Factored| (|SparseUnivariatePolynomial| *7))
               (|SparseUnivariatePolynomial| *7)))
   (|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *8 (|PolynomialCategory| *7 *6 *5))
   (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *8)))
   (|isDomain| *1 (|InnerMultFact| *5 *6 *7 *8))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *8))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|IntegerFactorizationPackage| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|List| *5) *6))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2
        (|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6))))
       (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *5 *6))
       (|isDomain| *3
        (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|AlgebraicallyClosedField|))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2
        (|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5))))
       (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *4 *5))
       (|isDomain| *3
        (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|OrderedFreeMonoid| *4))
       (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *2 (|List| (|LyndonWord| *4)))
       (|isDomain| *1 (|LyndonWord| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|FiniteFieldCategory|))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|FiniteFieldCategory|))
       (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7)))
       (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *7))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $))
                              (SIGNATURE |variable|
                               ((|Union| $ "failed") (|Symbol|))))))
       (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MPolyCatPolyFactorizer| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| (|Polynomial| *6) *4 *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $)))))
       (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3))
       (|ofCategory| *3
                     (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *4
                                           *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MRationalFactorize| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| (|Fraction| *6) *4 *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7)))
       (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *7))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|RationalFactorize| *3))
       (|ofCategory| *3
                     (|UnivariatePolynomialCategory|
                      (|Fraction| (|Integer|))))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|RationalFunctionFactor| *3))
       (|ofCategory| *3
                     (|UnivariatePolynomialCategory|
                      (|Fraction| (|Polynomial| (|Integer|)))))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|MonogenicAlgebra| (|Fraction| (|Integer|)) *4)))
   (|isDomain| *2 (|Factored| *3))
   (|isDomain| *1 (|SimpleAlgebraicExtensionAlgFactor| *4 *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|UnivariatePolynomialCategory|
                  (|Fraction| (|Polynomial| (|Integer|)))))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|MonogenicAlgebra|
                          (|Fraction| (|Polynomial| (|Integer|))) *4)))
   (|isDomain| *2 (|Factored| *3))
   (|isDomain| *1 (|SAERationalFunctionAlgFactor| *4 *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
       (|isDomain| *2
        (|Factored| (|SparseUnivariatePolynomial| (|Fraction| *7))))
       (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| *7)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Factored| *1))
       (|ofCategory| *1 (|UniqueFactorizationDomain|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|UnivariateFactorize| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|BalancedPAdicRational| *3))
       (|ofType| *3 *2)))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|BalancedPAdicRational| *2)) (|ofType| *2 (|Integer|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PAdicRational| *3))
       (|ofType| *3 *2)))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|PAdicRational| *2)) (|ofType| *2 (|Integer|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|ofType| *3 *2)
       (|isDomain| *1 (|PAdicRationalConstructor| *3 *4))
       (|ofCategory| *4 (|PAdicIntegerCategory| *3))))
 ((*1 *1 *1)
  (AND (|ofType| *2 (|Integer|))
       (|isDomain| *1 (|PAdicRationalConstructor| *2 *3))
       (|ofCategory| *3 (|PAdicIntegerCategory| *2))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *2 *3))
       (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *2))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *5))
       (|ofCategory| *5
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Any|))
   (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *4)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Equation| *3)) (|isDomain| *5 (|NonNegativeInteger|))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *6 *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 (|Integer|)))
       (|isDomain| *4 (|Equation| *6))
       (|ofCategory| *6
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *7 (|Integer|)))
       (|isDomain| *4 (|Equation| *7))
       (|isDomain| *5 (|UniversalSegment| (|NonNegativeInteger|)))
       (|ofCategory| *7
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Equation| *3))
       (|isDomain| *6 (|UniversalSegment| (|NonNegativeInteger|)))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *7)))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2))
       (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(((*1 *2 *1)
  (|partial| AND
   (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2))
   (|ofCategory| *3 (|Ring|))
   (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *4))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Fraction| (|Polynomial| *4)))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *4))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Fraction| (|Polynomial| *4)))))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|Byte|)))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|SystemNonNegativeInteger| *2))
       (|ofType| *2 (|PositiveInteger|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt16|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt32|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt64|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt8|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|Byte|)))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|SystemNonNegativeInteger| *2))
       (|ofType| *2 (|PositiveInteger|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt16|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt32|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt64|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|UInt8|)))) 
(((*1 *1) (|ofCategory| *1 (|AbelianMonoid|)))
 ((*1 *1) (|ofCategory| *1 (|Aggregate|))) ((*1 *1) (|isDomain| *1 (|Byte|)))
 ((*1 *1)
  (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1) (|isDomain| *1 (|Int16|))) ((*1 *1) (|isDomain| *1 (|Int32|)))
 ((*1 *1) (|isDomain| *1 (|Int64|))) ((*1 *1) (|isDomain| *1 (|Int8|)))
 ((*1 *1) (|ofCategory| *1 (|Monoid|))) ((*1 *1) (|isDomain| *1 (|Symbol|)))
 ((*1 *1)
  (AND (|isDomain| *1 (|SystemInteger| *2)) (|ofType| *2 (|PositiveInteger|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|SystemNonNegativeInteger| *2))
       (|ofType| *2 (|PositiveInteger|))))
 ((*1 *1) (|isDomain| *1 (|UInt16|))) ((*1 *1) (|isDomain| *1 (|UInt32|)))
 ((*1 *1) (|isDomain| *1 (|UInt64|))) ((*1 *1) (|isDomain| *1 (|UInt8|)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Complex| (|Integer|))) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|GaussianFactorizationPackage|))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|PolynomialIdeals| (|Fraction| (|Integer|))
                        (|DirectProduct| *5 (|NonNegativeInteger|))
                        (|OrderedVariableList| *4)
                        (|DistributedMultivariatePolynomial| *4
                                                             (|Fraction|
                                                              (|Integer|)))))
   (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|IdealDecompositionPackage| *4 *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerPrimesPackage| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UniqueFactorizationDomain|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|UserDefinedVariableOrdering|))))) 
(((*1 *2)
  (AND
   (|isDomain| *2
    (|Record| (|:| |high| (|List| (|Symbol|)))
              (|:| |low| (|List| (|Symbol|)))))
   (|isDomain| *1 (|UserDefinedVariableOrdering|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|UserDefinedVariableOrdering|))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|UserDefinedVariableOrdering|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|StreamAggregate| *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|UserDefinedPartialOrdering| *3))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *2))
       (|isDomain| *4 (|Mapping| (|Boolean|) *2 *2))
       (|isDomain| *1 (|UserDefinedPartialOrdering| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|OrderedSet|))
       (|isDomain| *1 (|UserDefinedPartialOrdering| *2))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|UserDefinedPartialOrdering| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|StreamAggregate| *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *3)
  (|partial| AND (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|UserDefinedPartialOrdering| *3))
   (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|Boolean|) *3 *3))
       (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|UserDefinedPartialOrdering| *3))))) 
(((*1 *2)
  (AND
   (|isDomain| *2 (|Record| (|:| |low| (|List| *3)) (|:| |high| (|List| *3))))
   (|isDomain| *1 (|UserDefinedPartialOrdering| *3))
   (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|UserDefinedPartialOrdering| *4))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|UserDefinedPartialOrdering| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|Factored|
         (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *5))))
       (|isDomain| *1 (|TwoFactorize| *5))
       (|isDomain| *3
        (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *5)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|Factored|
         (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))))
       (|isDomain| *1 (|TwoFactorize| *4))
       (|isDomain| *3
        (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|Factored|
         (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))))
       (|isDomain| *1 (|TwoFactorize| *4))
       (|isDomain| *3
        (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|FiniteAggregate| *3))
       (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|InfiniteTuple| *3))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|LazyStreamAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1 *3)
  (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *2))
   (|ofCategory| *4 (|IntegralDomain|))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *3 (|OrderedSet|))
   (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *3))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *1 (|Tuple| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *3 *3 *3 *4 *5)
  (AND (|isDomain| *5 (|List| (|List| (|DoubleFloat|))))
       (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *2 (|List| (|Point| *4)))
       (|isDomain| *1 (|TubePlotTools|)) (|isDomain| *3 (|Point| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|isDomain| *2 (|List| (|List| (|DoubleFloat|))))
       (|isDomain| *1 (|TubePlotTools|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|ofCategory| *1 (|DirectProductCategory| *3 *4))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|Type|))))
 ((*1 *1 *2)
  (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5
                     (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))
       (|ofType| *6
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *5))
                   (|Record| (|:| |index| *2) (|:| |exponent| *5))))
       (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *2 *5 *6 *7))
       (|ofCategory| *2 (|OrderedSet|))
       (|ofCategory| *7
                     (|PolynomialCategory| *4 *5 (|OrderedVariableList| *3)))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| (|DoubleFloat|)))
       (|isDomain| *1 (|TubePlotTools|))))) 
(((*1 *2 *1 *3 *4)
  (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *4 (|Palette|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GraphImage|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|PointCategory| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Point| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|ThreeSpaceCategory| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *1 (|ThreeSpaceCategory| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *3 *3 *3 *3)
  (AND (|isDomain| *2 (|Point| (|DoubleFloat|)))
       (|isDomain| *1 (|TubePlotTools|)) (|isDomain| *3 (|DoubleFloat|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|DoubleFloat|)) (|isDomain| *5 (|Integer|))
       (|isDomain| *2 (|TubePlot| *3)) (|isDomain| *1 (|NumericTubePlot| *3))
       (|ofCategory| *3 (|PlottableSpaceCurveCategory|))))
 ((*1 *1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *4 (|Boolean|)) (|isDomain| *1 (|TubePlot| *2))
       (|ofCategory| *2 (|PlottableSpaceCurveCategory|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TubePlot| *3))
       (|ofCategory| *3 (|PlottableSpaceCurveCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TubePlot| *3))
       (|ofCategory| *3 (|PlottableSpaceCurveCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SubSpaceComponentProperty|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TubePlot| *3))
       (|ofCategory| *3 (|PlottableSpaceCurveCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *1 (|TubePlot| *3))
       (|ofCategory| *3 (|PlottableSpaceCurveCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *1 (|TubePlot| *2))
       (|ofCategory| *2 (|PlottableSpaceCurveCategory|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Mapping| (|Boolean|) *9))
   (|isDomain| *5 (|Mapping| (|Boolean|) *9 *9))
   (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8))
   (|ofCategory| *6 (|IntegralDomain|))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *8 (|OrderedSet|))
   (|isDomain| *2 (|Record| (|:| |bas| *1) (|:| |top| (|List| *9))))
   (|isDomain| *3 (|List| *9))
   (|ofCategory| *1 (|TriangularSetCategory| *6 *7 *8 *9))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|Mapping| (|Boolean|) *8 *8))
   (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
   (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|OrderedSet|))
   (|isDomain| *2 (|Record| (|:| |bas| *1) (|:| |top| (|List| *8))))
   (|isDomain| *3 (|List| *8))
   (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *8))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|List| *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2
        (|Record| (|:| |close| (|List| *6)) (|:| |open| (|List| *6))))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1 *4)
  (AND (|isDomain| *4 (|Mapping| (|Boolean|) *3 *3))
       (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *3))
       (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *7 (|List| *7)))
       (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *2 *1 *3 *4)
  (AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| *8 *8 *8))
       (|isDomain| *4 (|Mapping| (|Boolean|) *8 *8))
       (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))))) 
(((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))
 ((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))
 ((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *2 *3 *4 *5))
       (|ofCategory| *2 (|IntegralDomain|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|RecursivePolynomialCategory| *2 *3 *4))))) 
(((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| *10))
       (|isDomain| *1 (|LazardSetSolvingPackage| *5 *6 *7 *8 *9 *10))
       (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *10
                     (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6))))
   (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
   (|ofType| *6 (|List| (|Symbol|)))
   (|isDomain| *2 (|List| (|RegularChain| *5 *6)))
   (|isDomain| *1 (|LexTriangularPackage| *5 *6))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6))))
   (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
   (|ofType| *6 (|List| (|Symbol|)))
   (|isDomain| *2
    (|List|
     (|SquareFreeRegularTriangularSet| *5
                                       (|IndexedExponents|
                                        (|OrderedVariableList| *6))
                                       (|OrderedVariableList| *6)
                                       (|NewSparseMultivariatePolynomial| *5
                                                                          (|OrderedVariableList|
                                                                           *6)))))
   (|isDomain| *1 (|LexTriangularPackage| *5 *6))))
 ((*1 *2 *3 *4 *4 *4 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *8)))
       (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *8)))
       (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8))))
 ((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3
    (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6))))
   (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
   (|ofType| *6 (|List| (|Symbol|)))
   (|isDomain| *2 (|List| (|RegularChain| *5 *6)))
   (|isDomain| *1 (|RegularChain| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *5 *6 *7 *8))))
 ((*1 *2 *3 *4 *4 *4 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)))
       (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)))
       (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2
        (|List| (|Record| (|:| |close| *1) (|:| |open| (|List| *7)))))
       (|isDomain| *3 (|List| *7))
       (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|List| *5))))) 
(((*1 *1 *1 *2)
  (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2))
   (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *5 (|Finite|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3))
       (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|AntiSymm| *2 *3))
       (|ofType| *3 (|List| (|Symbol|)))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|))) (|ofCategory| *2 (|Field|))
       (|isDomain| *1 (|CliffordAlgebra| *4 *2 *5))
       (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|QuadraticForm| *4 *2))))
 ((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Expression| *3))
       (|isDomain| *1 (|DeRhamComplex| *3 *4))
       (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *2 (|CancellationAbelianMonoid|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|BasicType|))
       (|isDomain| *1 (|IndexedProductTerm| *2 *3))
       (|ofCategory| *3 (|OrderedType|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|LaurentPolynomial| *2 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MonogenicLinearOperator| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|MonoidRing| *2 *3))
       (|ofCategory| *3 (|Monoid|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *5))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *2))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *6))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *2))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *2 (|PolynomialCategory| *4 (|IndexedExponents| *5) *5))
       (|isDomain| *1 (|SparseMultivariateTaylorSeries| *4 *5 *2))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Polynomial| *4))
       (|isDomain| *1 (|TaylorSeries| *4)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|Mapping| (|SparseMultivariateTaylorSeries| *4 *3 *5)))
       (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|SparseMultivariateTaylorSeries| *4 *3 *5))
       (|ofCategory| *5 (|PolynomialCategory| *4 (|IndexedExponents| *3) *3))))
 ((*1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|Mapping| (|TaylorSeries| *4)))
       (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|TaylorSeries| *4))
       (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|ConvertibleTo| (|Pattern| *3)))
       (|ofCategory| *3 (|PatternMatchable| *3))
       (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2 (|ConvertibleTo| (|Pattern| *3)))
       (|ofCategory| *2 (|PatternMatchable| *3))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|PropositionalFormulaFunctions1| *3))))
 ((*1 *1 *1)
  (AND (|ofCategory| *2 (|CharacteristicZero|))
       (|ofCategory| *2 (|EuclideanDomain|)) (|ofCategory| *2 (|GcdDomain|))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|QuasiAlgebraicSet| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|AlgebraicNumber|))
       (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|SimplifyAlgebraicNumberConvertPackage|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|TranscendentalManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|TriangularMatrixOperations| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|TriangularMatrixOperations| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2 (|Complex| (|Expression| *4)))
   (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| (|Complex| *4))))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Complex| *3))
   (|isDomain| *1 (|TrigonometricManipulations| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *4)))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| (|Complex| *4))))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|TrigonometricManipulations| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *4)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2 (|Expression| *4))
   (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| (|Complex| *4))))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|TrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2 (|Expression| *4))
   (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| (|Complex| *4))))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|TrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))))) 
(((*1 *2 *2)
  (AND
   (|ofCategory| *3 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *1 (|ComplexTrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| (|Complex| *3))))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|TrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))))) 
(((*1 *2 *2)
  (AND
   (|ofCategory| *3 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *1 (|ComplexTrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| (|Complex| *3))))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| (|Complex| *4))))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|TrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|TrigonometricManipulations| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))) 
(((*1 *2 *2)
  (AND
   (|ofCategory| *3 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *1 (|ComplexTrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| (|Complex| *3))))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| (|Complex| *4))))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|TrigonometricManipulations| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|TrigonometricManipulations| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|FourierComponent| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|FourierComponent| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Tree| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *1 (|Tree| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Tree| *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Tree| *2))) (|isDomain| *1 (|Tree| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|Tree| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Tree| *3))) (|isDomain| *1 (|Tree| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Tree| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Tree| *3))) (|isDomain| *1 (|Tree| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2)
  (AND (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *1) (|isDomain| *1 (|Pi|)))
 ((*1 *1) (|ofCategory| *1 (|TranscendentalFunctionCategory|)))) 
(((*1 *2)
  (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelThreeSpace|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ToolsForSign| *4)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|ToolsForSign| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Permutation| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *3)
  (|partial| AND
   (|ofCategory| *4
                 (|Join| (|IntegralDomain|) (|RetractableTo| *2)
                         (|LinearlyExplicitRingOver| *2) (|GcdDomain|)))
   (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ElementaryFunctionSign| *4 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *4)))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|isDomain| *5 (|OrderedCompletion| *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *6)))
   (|ofCategory| *6
                 (|Join| (|IntegralDomain|) (|RetractableTo| *2)
                         (|LinearlyExplicitRingOver| *2) (|GcdDomain|)))
   (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|ElementaryFunctionSign| *6 *3))))
 ((*1 *2 *3 *4 *3 *5)
  (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|String|))
   (|ofCategory| *6
                 (|Join| (|IntegralDomain|) (|RetractableTo| *2)
                         (|LinearlyExplicitRingOver| *2) (|GcdDomain|)))
   (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ElementaryFunctionSign| *6 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *6)))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
   (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|RationalFunctionSign| *4))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|isDomain| *5 (|OrderedCompletion| (|Fraction| (|Polynomial| *6))))
   (|isDomain| *3 (|Fraction| (|Polynomial| *6)))
   (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|RationalFunctionSign| *6))))
 ((*1 *2 *3 *4 *3 *5)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *6)))
   (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|String|))
   (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|RationalFunctionSign| *6))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|ToolsForSign| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|))))
 ((*1 *2 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *1 (|File| *2))
   (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|TextFile|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|TextFile|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|OutputForm|) (|OutputForm|)))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|OutputForm|) (|List| (|OutputForm|))))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2 (|Maybe| (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))))
   (|isDomain| *1 (|BasicOperator|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Database| *3))
       (|ofCategory| *3
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |elt| ((|String|) $ (|Symbol|)))
                              (SIGNATURE |display| (*2 $))
                              (SIGNATURE |fullDisplay| (*2 $)))))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|IndexCard|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|MathMLFormat|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TexFormat|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TexFormat|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|))))) 
(((*1 *1 *2 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1) (|isDomain| *1 (|SubSpaceComponentProperty|)))
 ((*1 *1)
  (AND (|isDomain| *1 (|DataArray| *2 *3)) (|ofType| *2 (|PositiveInteger|))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *2 *2)
  (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileNameCategory|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|PatternMatchListResult| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *4 (|ListAggregate| *3))))
 ((*1 *1)
  (AND (|isDomain| *1 (|PatternMatchResult| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|SquareMatrix| *3 *2))
       (|ofType| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1) (|isDomain| *1 (|Symbol|))) ((*1 *1) (|isDomain| *1 (|Symbol|)))
 ((*1 *1) (|isDomain| *1 (|TexFormat|)))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|TexFormat|))))) 
(((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *1 (|BinarySearchTree| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *1 (|BinaryTournament| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|ExtensibleLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|ExtensibleLinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MultiDictionary| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TabulatedComputationPackage| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2 *3)
  (|partial| AND (|ofCategory| *2 (|SetCategory|))
   (|isDomain| *1 (|TabulatedComputationPackage| *3 *2))
   (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|TabulatedComputationPackage| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|TabulatedComputationPackage| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|TabulatedComputationPackage| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TabulatedComputationPackage| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TabulatedComputationPackage| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TabulatedComputationPackage| *4 *5))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TabulatedComputationPackage| *4 *5))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TabulatedComputationPackage| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Record| (|:| |key| *3) (|:| |entry| *4))))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *1 (|TableAggregate| *3 *4))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|TableAggregate| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|TangentExpansions| *2))
       (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
       (|isDomain| *1 (|TangentExpansions| *3)) (|ofCategory| *3 (|Field|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|TangentExpansions| *2))
       (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicFunction| *3 *4))
       (|ofCategory| *4 (|FunctionSpace| *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Arity|))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|BasicOperator|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *3 *4))
       (|ofCategory| *4 (|FunctionSpace| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|BasicOperator|))
       (|isDomain| *1 (|CommonOperators|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *4))
       (|ofCategory| *4 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|BasicOperator|))
       (|isDomain| *1 (|ExpressionSpace&| *3))
       (|ofCategory| *3 (|ExpressionSpace|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|BasicOperator|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|FunctionSpace&| *3 *4))
       (|ofCategory| *3 (|FunctionSpace| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *4))
       (|ofCategory| *4 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *1 (|Kernel| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|BasicOperator|)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *3 *4))
       (|ofCategory| *4
                     (|Join| (|FunctionSpace| *3) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ReduceAst|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Arity|)) (|isDomain| *1 (|TermAlgebraOperator| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Tableau| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|List| (|List| *3)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|List| (|List| *5)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|Tableau| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *2
        (|Record| (|:| |f1| (|List| *4))
                  (|:| |f2| #1=(|List| (|List| (|List| *4))))
                  (|:| |f3| (|List| (|List| *4))) (|:| |f4| #1#)))
       (|isDomain| *1 (|TableauxBumpers| *4))
       (|isDomain| *3 (|List| (|List| (|List| *4))))))) 
(((*1 *2 *3 *4 *5 *4 *4 *4)
  (AND (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *3 (|List| *6))
       (|isDomain| *5 (|List| *3))
       (|isDomain| *2
        (|Record| (|:| |f1| *3) (|:| |f2| #1=(|List| *5)) (|:| |f3| *5)
                  (|:| |f4| #1#)))
       (|isDomain| *1 (|TableauxBumpers| *6)) (|isDomain| *4 (|List| *5))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *3 (|Field|))
   (|ofCategory| *4 (|FiniteLinearAggregate| *3))
   (|ofCategory| *5 (|FiniteLinearAggregate| *3))
   (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *3 *4 *5 *2))
   (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))
 ((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|IntegralDomain|))
   (|ofCategory| *5 (|FiniteLinearAggregate| *4))
   (|ofCategory| *6 (|FiniteLinearAggregate| *4))
   (|ofCategory| *7 (|QuotientFieldCategory| *4))
   (|ofCategory| *2 (|MatrixCategory| *7 *8 *9))
   (|isDomain| *1
    (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *2))
   (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))
   (|ofCategory| *8 (|FiniteLinearAggregate| *7))
   (|ofCategory| *9 (|FiniteLinearAggregate| *7))))
 ((*1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2))
   (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *2)
  (|partial| AND (|ofCategory| *3 (|Field|))
   (|ofCategory| *3 (|CommutativeRing|))
   (|ofCategory| *4 (|FiniteLinearAggregate| *3))
   (|ofCategory| *5 (|FiniteLinearAggregate| *3))
   (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2))
   (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))
 ((*1 *1 *1)
  (|partial| AND (|isDomain| *1 (|Matrix| *2)) (|ofCategory| *2 (|Field|))
   (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|SquareMatrixCategory| *2 *3 *4 *5))
   (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|DirectProductCategory| *2 *3))
   (|ofCategory| *5 (|DirectProductCategory| *2 *3))
   (|ofCategory| *3 (|Field|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|TableauxBumpers| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|List| (|List| *4)))
       (|isDomain| *1 (|TableauxBumpers| *4)) (|isDomain| *3 (|List| *4))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|TableauxBumpers| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Tableau| (|List| *4)))
       (|isDomain| *1 (|TableauxBumpers| *4)) (|isDomain| *3 (|List| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *2 (|List| (|List| (|List| *4))))
       (|isDomain| *1 (|TableauxBumpers| *4))
       (|isDomain| *3 (|List| (|List| *4)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Tableau| (|List| *4))) (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *2 (|List| (|List| *4)))
       (|isDomain| *1 (|TableauxBumpers| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|List| (|List| *4))))
       (|isDomain| *2 (|List| (|List| *4)))
       (|isDomain| *1 (|TableauxBumpers| *4))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| (|List| (|List| *4))))
       (|isDomain| *2 (|List| (|List| *4))) (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|TableauxBumpers| *4))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| (|List| (|List| *4))))
       (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|TableauxBumpers| *4))))) 
(((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|List| (|List| (|List| *5))))
       (|isDomain| *3 (|Mapping| (|Boolean|) *5 *5))
       (|isDomain| *4 (|List| *5)) (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|TableauxBumpers| *5))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *6 *6))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *4 (|List| *6))
       (|isDomain| *2
        (|Record| (|:| |fs| (|Boolean|)) (|:| |sd| *4) (|:| |td| (|List| *4))))
       (|isDomain| *1 (|TableauxBumpers| *6)) (|isDomain| *5 (|List| *4))))) 
(((*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|System|))))) 
(((*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|System|))))) 
(((*1 *2) (AND (|isDomain| *2 (|ByteOrder|)) (|isDomain| *1 (|System|))))) 
(((*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|System|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|System|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|List| (|Polynomial| *5))))
       (|isDomain| *1 (|SystemSolvePackage| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|)))))
       (|isDomain| *2 (|List| (|List| (|Equation| (|Polynomial| *4)))))
       (|isDomain| *1 (|FloatingRealPackage| *4))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))))
   (|isDomain| *2 (|List| (|List| (|Equation| (|Polynomial| *4)))))
   (|isDomain| *1 (|FloatingRealPackage| *4))
   (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Integer|))))
       (|isDomain| *2 (|List| (|Equation| (|Polynomial| *4))))
       (|isDomain| *1 (|FloatingRealPackage| *4))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| (|Integer|)))))
       (|isDomain| *2 (|List| (|Equation| (|Polynomial| *4))))
       (|isDomain| *1 (|FloatingRealPackage| *4))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *5 (|Symbol|))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|ofCategory| *4
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|isDomain| *2 (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4))))
   (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *4 *3))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))
 ((*1 *2 *3 *2 *4 *2 *5)
  (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|List| *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *2 *3))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|ofCategory| *6
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|ofCategory| *4
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| *4 #1="failed"))
                  (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *4 *3))
       (|ofCategory| *3 (|MatrixCategory| *5 *6 *4))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|ofCategory| *6
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|ofCategory| *7
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |particular| (|Union| *7 #1#))
                   (|:| |basis| (|List| *7)))))
       (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *7 *3))
       (|isDomain| *4 (|List| *7))
       (|ofCategory| *3 (|MatrixCategory| *5 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *5)) (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| #2=(|Vector| *5) #3="failed"))
                  (|:| |basis| (|List| #2#))))
       (|isDomain| *1 (|LinearSystemMatrixPackage1| *5))
       (|isDomain| *4 (|Vector| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|List| *5))) (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| #4=(|Vector| *5) #3#))
                  (|:| |basis| (|List| #4#))))
       (|isDomain| *1 (|LinearSystemMatrixPackage1| *5))
       (|isDomain| *4 (|Vector| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *5)) (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |particular| (|Union| (|Vector| *5) #3#))
                   (|:| |basis| (|List| (|Vector| *5))))))
       (|isDomain| *1 (|LinearSystemMatrixPackage1| *5))
       (|isDomain| *4 (|List| (|Vector| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|List| *5))) (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |particular| (|Union| (|Vector| *5) #3#))
                   (|:| |basis| (|List| (|Vector| *5))))))
       (|isDomain| *1 (|LinearSystemMatrixPackage1| *5))
       (|isDomain| *4 (|List| (|Vector| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5))))))
       (|isDomain| *1 (|NonLinearSolvePackage| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4))))))
       (|isDomain| *1 (|NonLinearSolvePackage| *4))))
 ((*1 *2 *2 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|Symbol|))
   (|ofCategory| *5
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *1 (|NonLinearFirstOrderODESolver| *5 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *5)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *3 (|Matrix| *7)) (|isDomain| *5 (|Symbol|))
   (|ofCategory| *7
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2
    (|Record| (|:| |particular| #5=(|Vector| *7)) (|:| |basis| (|List| #5#))))
   (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7))
   (|isDomain| *4 (|Vector| *7))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Matrix| *6)) (|isDomain| *4 (|Symbol|))
   (|ofCategory| *6
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *5)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|ofCategory| *5
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2 (|List| (|Vector| *6)))
   (|isDomain| *1 (|ElementaryFunctionODESolver| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *3 (|List| (|Equation| *7)))
   (|isDomain| *4 (|List| (|BasicOperator|))) (|isDomain| *5 (|Symbol|))
   (|ofCategory| *7
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2
    (|Record| (|:| |particular| (|Vector| *7))
              (|:| |basis| (|List| (|Vector| *7)))))
   (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *3 (|List| *7))
   (|isDomain| *4 (|List| (|BasicOperator|))) (|isDomain| *5 (|Symbol|))
   (|ofCategory| *7
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2
    (|Record| (|:| |particular| (|Vector| *7))
              (|:| |basis| (|List| (|Vector| *7)))))
   (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Equation| *7)) (|isDomain| *4 (|BasicOperator|))
       (|isDomain| *5 (|Symbol|))
       (|ofCategory| *7
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                             (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)))
       (|ofCategory| *6
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *2
        (|Union| (|Record| (|:| |particular| *7) (|:| |basis| (|List| *7))) *7
                 #6="failed"))
       (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|Symbol|))
       (|ofCategory| *6
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *2
        (|Union| (|Record| (|:| |particular| *3) (|:| |basis| (|List| *3))) *3
                 #6#))
       (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                             (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)))))
 ((*1 *2 *3 *4 *3 *5)
  (|partial| AND (|isDomain| *3 (|Equation| *2))
   (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|List| *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *2))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))))
 ((*1 *2 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *3 (|BasicOperator|))
   (|isDomain| *4 (|Equation| *2)) (|isDomain| *5 (|List| *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                         (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *2))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND
   (|isDomain| *5
    (|Mapping|
     (|Union| (|Record| (|:| |particular| *6) (|:| |basis| (|List| *6)))
              "failed")
     *7 *6))
   (|ofCategory| *6 (|Field|))
   (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| *6))
   (|isDomain| *2
    (|Record| (|:| |particular| (|Vector| *6)) (|:| |basis| (|Matrix| *6))))
   (|isDomain| *1 (|SystemODESolver| *6 *7)) (|isDomain| *3 (|Matrix| *6))
   (|isDomain| *4 (|Vector| *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Polynomial| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|RealSolvePackage|))
       (|isDomain| *4 (|Float|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Polynomial| (|Integer|)))
       (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|RealSolvePackage|))
       (|isDomain| *4 (|Float|))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *4))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2 (|List| (|Equation| (|Expression| *4))))
   (|isDomain| *1 (|TransSolvePackage| *4)) (|isDomain| *3 (|Expression| *4))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2 (|List| (|Equation| (|Expression| *4))))
   (|isDomain| *1 (|TransSolvePackage| *4))
   (|isDomain| *3 (|Equation| (|Expression| *4)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|Equation| (|Expression| *5))))
       (|isDomain| *1 (|TransSolvePackage| *5))
       (|isDomain| *3 (|Equation| (|Expression| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|Equation| (|Expression| *5))))
       (|isDomain| *1 (|TransSolvePackage| *5))
       (|isDomain| *3 (|Expression| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *5)))))
       (|isDomain| *1 (|TransSolvePackage| *5))
       (|isDomain| *3 (|List| (|Equation| (|Expression| *5))))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5))))))
       (|isDomain| *1 (|SystemSolvePackage| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5))))))
       (|isDomain| *1 (|SystemSolvePackage| *5))
       (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *4))))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4))))))
       (|isDomain| *1 (|SystemSolvePackage| *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4))))))
       (|isDomain| *1 (|SystemSolvePackage| *4))
       (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))
       (|isDomain| *1 (|SystemSolvePackage| *5))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))
       (|isDomain| *1 (|SystemSolvePackage| *5))
       (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *5))))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))
       (|isDomain| *1 (|SystemSolvePackage| *4))
       (|isDomain| *3 (|Fraction| (|Polynomial| *4)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))
       (|isDomain| *1 (|SystemSolvePackage| *4))
       (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *4))))))) 
(((*1 *2 *1) (AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|ParameterAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|ParameterAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|String|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|Identifier|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|IsAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|HasAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|CaseAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|ColonAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|SuchThatAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|LetAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|SequenceAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|SegmentAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|RestrictAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|PretendAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|CoerceAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|ReturnAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|ExitAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|ConstructAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|CollectAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|StepAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|InAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|WhileAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|RepeatAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|IfAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|MappingAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|AttributeAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|SignatureAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|CapsuleAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|JoinAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|CategoryAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|WhereAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|MacroAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|DefinitionAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|ImportAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Syntax|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Syntax|))) (|isDomain| *1 (|Syntax|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|List| (|Syntax|)))
       (|isDomain| *1 (|Syntax|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Syntax|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|Identifier|))
   (|isDomain| *1 (|ElaboratedExpression|))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) (|Syntax|)))
   (|isDomain| *1 (|Syntax|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|List| (|ElaboratedExpression|)))
   (|isDomain| *1 (|ElaboratedExpression|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Syntax|))) (|isDomain| *1 (|Syntax|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Syntax|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| |true|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|KleeneTrivalentLogic|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| |unknown|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|KleeneTrivalentLogic|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| |false|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|KleeneTrivalentLogic|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| |nothing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Maybe| *4)) (|ofCategory| *4 (|Type|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Maybe| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| (|String|))) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|ParameterAst|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| (|Identifier|))) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|ParameterAst|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|Integer|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|String|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|Identifier|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|IsAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|HasAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|CaseAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|ColonAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|SuchThatAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|LetAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|SequenceAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|SegmentAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|RestrictAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|PretendAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|CoerceAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|ExitAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|ConstructAst|)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|CollectAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|StepAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|JoinAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
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 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|WhereAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|MacroAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|DefinitionAst|)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|SpadAstExports|))
       (|isDomain| *3 (|[\|\|]| (|ImportAst|))) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| (|String|))) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| (|Identifier|))) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| (|DoubleFloat|))) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Syntax|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|[\|\|]| (|Integer|))) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Syntax|))))) 
(((*1 *1) (|ofCategory| *1 (|Aggregate|)))
 ((*1 *1) (|isDomain| *1 (|Environment|)))
 ((*1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1)
  (AND (|ofCategory| *2 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|))
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       (|isDomain| *1 (|QuasiAlgebraicSet| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3))))
 ((*1 *1) (|isDomain| *1 (|Scope|)))
 ((*1 *1)
  (AND (|isDomain| *1 (|SplittingNode| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))
 ((*1 *1) (|isDomain| *1 (|TheSymbolTable|)))
 ((*1 *1) (|isDomain| *1 (|SymbolTable|)))) 
(((*1 *2 *3 *2 *3)
  (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|Symbol|))
       (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|Symbol|))
       (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *2 *4 *1)
  (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|List| (|Symbol|)))
       (|isDomain| *4 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *2 *3 *1)
  (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|Symbol|))
       (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *2 *1)
  (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|Symbol|))
       (|isDomain| *1 (|SymbolTable|))))
 ((*1 *2 *3 *2 *1)
  (AND (|isDomain| *2 (|FortranType|)) (|isDomain| *3 (|List| (|Symbol|)))
       (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|FortranType|))
       (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|FortranScalarType|))
       (|isDomain| *2
        (|List|
         (|Union| (|:| |name| (|Symbol|))
                  (|:| |bounds|
                       (|List|
                        (|Union| (|:| S (|Symbol|))
                                 (|:| P (|Polynomial| (|Integer|)))))))))
       (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|List|
     (|List|
      (|Union| (|:| |name| (|Symbol|))
               (|:| |bounds|
                    (|List|
                     (|Union| (|:| S (|Symbol|))
                              (|:| P (|Polynomial| (|Integer|))))))))))
   (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|)))))
   (|isDomain| *1 (|SymbolTable|))))) 
(((*1 *1) (|isDomain| *1 (|TheSymbolTable|)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *4 *1)
  (AND (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")))
   (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Symbol|))
       (|isDomain| *4
        (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *4 *1)
  (AND (|isDomain| *3 (|Symbol|))
       (|isDomain| *4
        (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TheSymbolTable|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Symbol|))
       (|isDomain| *2
        (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")))
       (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|TheSymbolTable|))
       (|isDomain| *3 (|Symbol|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|SymbolTable|))
       (|isDomain| *1 (|TheSymbolTable|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|Vector| *4))
       (|isDomain| *1 (|SymmetricFunctions| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *3))
       (|isDomain| *1 (|SymmetricFunctions| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Symbol|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|AttributeAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|Binding|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileCategory| *2 *3))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FunctionCalled| *3))
       (|ofType| *3 *2)))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|HeadAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OperatorCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|OverloadSet|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|Property|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|RuleCalled| *3))
       (|ofType| *3 *2)))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|SignatureAst|))))
 ((*1 *1 *1) (|isDomain| *1 (|Symbol|)))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Symbol|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |sub| (|List| (|OutputForm|)))
              (|:| |sup| (|List| (|OutputForm|)))
              (|:| |presup| (|List| (|OutputForm|)))
              (|:| |presub| (|List| (|OutputForm|)))
              (|:| |args| (|List| (|OutputForm|)))))
   (|isDomain| *1 (|Symbol|))))) 
(((*1 *1 *1 *2)
  (AND
   (|isDomain| *2
    (|Record| (|:| |sub| (|List| (|OutputForm|)))
              (|:| |sup| (|List| (|OutputForm|)))
              (|:| |presup| (|List| (|OutputForm|)))
              (|:| |presub| (|List| (|OutputForm|)))
              (|:| |args| (|List| (|OutputForm|)))))
   (|isDomain| *1 (|Symbol|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| (|OutputForm|))))
       (|isDomain| *1 (|Symbol|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|Symbol|))))) 
(((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|String|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|String|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|String|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Symbol|))))) 
(((*1 *1 *2)
  (AND (|ofCategory| *1 (|ListAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|Symbol|))))) 
(((*1 *2 *1 *3 *3 *4)
  (AND (|isDomain| *3 (|Mapping| #1=(|OutputForm|) #1# #1#))
       (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|OutputForm|))
       (|isDomain| *1 (|ListMonoidOps| *5 *6 *7))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|AbelianMonoid|))
       (|ofType| *7 *6)))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|OutputForm|))
       (|isDomain| *1 (|SparseUnivariateSkewPolynomial| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Automorphism| *3))
       (|ofType| *5 (|Mapping| *3 *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|OutputForm|))
       (|isDomain| *1 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Segment| *3))
       (|ofCategory| *3 (|PolynomialCategory| *7 *6 *4))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| (|Integer|))))
       (|isDomain| *1 (|InnerPolySum| *6 *4 *7 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| (|Integer|))))
       (|isDomain| *1 (|InnerPolySum| *5 *4 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))
 ((*1 *1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|FunctionSpaceSum| *4 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|CombinatorialOpsCategory|)
                             (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|SegmentBinding| *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|CombinatorialOpsCategory|)
                             (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|FunctionSpaceSum| *4 *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *2 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *1 (|RationalFunctionSum| *5))
       (|isDomain| *3 (|Polynomial| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *2
        (|Union| (|Fraction| (|Polynomial| *5)) (|Expression| *5)))
       (|isDomain| *1 (|RationalFunctionSum| *5))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|SegmentBinding| (|Polynomial| *5)))
       (|isDomain| *3 (|Polynomial| *5))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *2 (|Fraction| *3))
       (|isDomain| *1 (|RationalFunctionSum| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|SegmentBinding| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *2 (|Union| *3 (|Expression| *5)))
       (|isDomain| *1 (|RationalFunctionSum| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Mapping| (|Boolean|) *5))
       (|isDomain| *1 (|PatternFunctions1| *4 *5)) (|ofCategory| *5 (|Type|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|SuchThatAst|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *1 (|Collection| *3))))
 ((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| *4)
               (|:| |num| *4))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|)))
   (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4))))
 ((*1 *1 *2 *3 *4)
  (AND
   (|isDomain| *2
    (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")))
   (|isDomain| *3 (|List| (|Polynomial| (|Integer|))))
   (|isDomain| *4 (|Boolean|)) (|isDomain| *1 (|FortranType|))))
 ((*1 *1 *2 *3 *4)
  (AND
   (|isDomain| *2 (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)))
   (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *4 (|Boolean|))
   (|isDomain| *1 (|FortranType|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|InfiniteTuple| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|LieAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|LiePolynomial| *3 *4))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|LiePolynomial| *3 *4))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|LiePolynomial| *3 *4))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|ModuleMonomial| *2 *3 *4))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|SetCategory|))
       (|ofType| *4
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *3))
                   (|Record| (|:| |index| *2) (|:| |exponent| *3))))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|Signature|))
       (|isDomain| *1 (|OperatorSignature|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|Pair| *2 *3)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2)
  (AND
   (|isDomain| *2 (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| *4))))
   (|ofCategory| *4 (|SetCategory|))
   (|isDomain| *1 (|PatternMatchResult| *3 *4))
   (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *5))
       (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *2 (|List| (|SplittingNode| *3 *5)))
       (|isDomain| *1 (|SplittingNode| *3 *5))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Record| (|:| |val| *4) (|:| |tower| *5))))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *2 (|List| (|SplittingNode| *4 *5)))
       (|isDomain| *1 (|SplittingNode| *4 *5))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Record| (|:| |val| *3) (|:| |tower| *4)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingNode| *3 *4))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|SplittingNode| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))
 ((*1 *1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))
 ((*1 *1 *2 *3 *2 *4)
  (AND (|isDomain| *4 (|List| *3))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingTree| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))))
 ((*1 *1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|SplittingNode| *2 *3)))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingTree| *2 *3))))
 ((*1 *1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|SplittingTree| *2 *3)))
       (|isDomain| *1 (|SplittingTree| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|SplittingNode| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingTree| *3 *4))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|SuchThat| *2 *3)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|CaseAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ColonAst|))))
 ((*1 *2 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|HasAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IsAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|LetAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))
       (|isDomain| *1 (|RewriteRule| *3 *4 *2))
       (|ofCategory| *4
                     (|Join| (|Ring|) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|SuchThat| *2 *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|CaseAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|TypeAst|)) (|isDomain| *1 (|ColonAst|))))
 ((*1 *2 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|HasAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IsAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|LetAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))
       (|isDomain| *1 (|RewriteRule| *3 *4 *2))
       (|ofCategory| *4
                     (|Join| (|Ring|) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|SuchThat| *3 *2))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpace| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpace| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SubSpace| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RecursiveAggregate| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SubSpace| *3 *4)))
       (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|SubSpace| *3 *4)) (|ofType| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 (|PositiveInteger|))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2 *1 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3))
       (|ofCategory| *1 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
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       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|)))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
(((*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
(((*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
(((*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
(((*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|DoubleFloat|)))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|Float|)))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
(((*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
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 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
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 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
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 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3))
       (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2))
       (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3))
       (|isDomain| *1
        (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5))
       (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4))
       (|ofCategory| *5 (|PartialTranscendentalFunctions| *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctions| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *2
        (|Record| (|:| |sinh| #1=(|Stream| *4)) (|:| |cosh| #1#)))
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       (|isDomain| *3 (|Stream| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|Record| (|:| |sin| #1=(|Stream| *4)) (|:| |cos| #1#)))
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       (|isDomain| *3 (|Stream| *4))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Field|))
       (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *4 (|Integer|)))
       (|isDomain| *5 (|Mapping| (|Stream| *4))) (|ofCategory| *4 (|Field|))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Stream| *4))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Field|))
       (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Stream| *4)) (|ofCategory| *4 (|Algebra| *3))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *3 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Stream| (|Stream| *4))) (|isDomain| *2 (|Stream| *4))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))
       (|ofCategory| *4 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|Stream| *3))) (|isDomain| *2 (|Stream| *3))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Stream| (|Stream| *4))) (|isDomain| *2 (|Stream| *4))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|PolynomialComposition| *2 *3))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Mapping| *4 (|Integer|)))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *1 (|ODEIntegration| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *4)
                             (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)))))
 ((*1 *1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Stream| *3))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Stream| (|Integer|)))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Stream| (|Integer|)))
       (|isDomain| *1 (|StreamTaylorSeriesOperations| *4))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *3 (|Integer|))))) 
(((*1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
   (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|)))
 ((*1 *1 *1) (|partial| |ofCategory| *1 (|Monoid|)))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *3)))
       (|isDomain| *1 (|NormalizationPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))
 ((*1 *2 *2 *1)
  (|partial| AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *3 *2))
   (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|)))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
   (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(((*1 *1 *1 *2)
  (|partial| AND (|ofCategory| *1 (|ComplexCategory| *2))
   (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *2)
  (|partial| AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))
   (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *1) (|partial| |ofCategory| *1 (|IntegralDomain|)))
 ((*1 *1 *1 *2)
  (|partial| AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2))
   (|ofCategory| *4 (|FiniteLinearAggregate| *2))
   (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *1) (|partial| |isDomain| *1 (|NonNegativeInteger|)))
 ((*1 *1 *1 *2)
  (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *2 *3)
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       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *3 *4))))
 ((*1 *1 *1 *2)
  (|partial| AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *2 *5 *6))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *4 *2))
   (|ofCategory| *6 (|DirectProductCategory| *3 *2))
   (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *2 *2 *2)
  (|partial| AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|))
   (|isDomain| *1 (|StreamTaylorSeriesOperations| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|Stream| *3))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Stream| *4))))) 
(((*1 *2 *3 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |cycle?| (|Boolean|))
              (|:| |prefix| #1=(|NonNegativeInteger|)) (|:| |period| #1#)))
   (|isDomain| *1 (|Stream| *4)) (|ofCategory| *4 (|Type|))
   (|isDomain| *3 (|NonNegativeInteger|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|Stream| *3))) (|isDomain| *1 (|Stream| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *1 *2 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *1) (AND (|isDomain| *1 (|Stream| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *1) (|isDomain| *1 (|IOMode|)))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|OutputPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|OutputPackage|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *4 (|OutputForm|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OutputPackage|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|Stream| *4)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *4 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Stream| *3))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|Type|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stream| *3))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Vector| (|List| (|Integer|))))
       (|isDomain| *1 (|HallBasis|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|InfiniteTuple| *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|Stream| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|Stream| *3))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|InfiniteTuple| *3))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|Stream| *3))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|InfiniteTuple| *3))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|Stream| *3))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|InfiniteProductCharacteristicZero| *4 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4))))
 ((*1 *2 *2 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| *3)))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|MonogenicAlgebra| *4 *5))
       (|isDomain| *1 (|InfiniteProductFiniteField| *4 *5 *6 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *6))))
 ((*1 *2 *2 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| *3)))
       (|isDomain| *1 (|InfiniteProductPrimeField| *4 *2))
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 ((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|StreamInfiniteProduct| *4))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|InfiniteProductCharacteristicZero| *3 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *5 (|MonogenicAlgebra| *3 *4))
   (|isDomain| *1 (|InfiniteProductFiniteField| *3 *4 *5 *2))
   (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))))
   (|isDomain| *1 (|InfiniteProductPrimeField| *3 *2))
   (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|StreamInfiniteProduct| *3))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|InfiniteProductCharacteristicZero| *3 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *5 (|MonogenicAlgebra| *3 *4))
   (|isDomain| *1 (|InfiniteProductFiniteField| *3 *4 *5 *2))
   (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))))
   (|isDomain| *1 (|InfiniteProductPrimeField| *3 *2))
   (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|StreamInfiniteProduct| *3))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|InfiniteProductCharacteristicZero| *3 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *5 (|MonogenicAlgebra| *3 *4))
   (|isDomain| *1 (|InfiniteProductFiniteField| *3 *4 *5 *2))
   (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5))))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|) (|Finite|) (|ConvertibleTo| (|Integer|))))
   (|isDomain| *1 (|InfiniteProductPrimeField| *3 *2))
   (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| *3))
       (|ofCategory| *3 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *1 (|StreamInfiniteProduct| *3))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|InAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|StepAst|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|StepAst|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| (|SpadAst|))) (|isDomain| *1 (|StepAst|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|StepAst|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))
 ((*1 *1) (|ofCategory| *1 (|StepThrough|)))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|StepThrough|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|StreamAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|StreamAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|StreamAggregate| *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|Stack| *3))))) 
(((*1 *2 *3 *1 *4 *4 *4 *4 *4)
  (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *3)))
       (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *3))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *2))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5))))
 ((*1 *2 *3 *1 *4 *4 *4 *4 *4)
  (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *3)))
       (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *3))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))))) 
(((*1 *2 *3 *4 *4 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|RegularTriangularSet| *5 *6 *7 *8)))
       (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8))))
 ((*1 *2 *3 *4 *4 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)))
       (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))))) 
(((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |val| (|List| *8))
                  (|:| |towers|
                       (|List| (|RegularTriangularSet| *5 *6 *7 *8)))))
       (|isDomain| *1 (|RegularTriangularSet| *5 *6 *7 *8))
       (|isDomain| *3 (|List| *8))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |val| (|List| *8))
                  (|:| |towers|
                       (|List|
                        (|SquareFreeRegularTriangularSet| *5 *6 *7 *8)))))
       (|isDomain| *1 (|SquareFreeRegularTriangularSet| *5 *6 *7 *8))
       (|isDomain| *3 (|List| *8))))) 
(((*1 *2 *3 *4)
  (AND
   (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9))))
   (|isDomain| *4 (|NonNegativeInteger|))
   (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
   (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8))
   (|ofCategory| *5 (|GcdDomain|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Void|))
   (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9))))
   (|isDomain| *4 (|NonNegativeInteger|))
   (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
   (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))
   (|ofCategory| *5 (|GcdDomain|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Void|))
   (|isDomain| *1
    (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9))))) 
(((*1 *2 *3 *4 *2 *5 *6)
  (AND
   (|isDomain| *5
    (|Record| (|:| |done| (|List| *11))
              (|:| |todo|
                   (|List| (|Record| (|:| |val| *3) (|:| |tower| *11))))))
   (|isDomain| *6 (|NonNegativeInteger|))
   (|isDomain| *2
    (|List| (|Record| (|:| |val| (|List| *10)) (|:| |tower| *11))))
   (|isDomain| *3 (|List| *10)) (|isDomain| *4 (|List| *11))
   (|ofCategory| *10 (|RecursivePolynomialCategory| *7 *8 *9))
   (|ofCategory| *11 (|RegularTriangularSetCategory| *7 *8 *9 *10))
   (|ofCategory| *7 (|GcdDomain|))
   (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *9 (|OrderedSet|))
   (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *10 *11))))
 ((*1 *2 *3 *4 *2 *5 *6)
  (AND
   (|isDomain| *5
    (|Record| (|:| |done| (|List| *11))
              (|:| |todo|
                   (|List| (|Record| (|:| |val| *3) (|:| |tower| *11))))))
   (|isDomain| *6 (|NonNegativeInteger|))
   (|isDomain| *2
    (|List| (|Record| (|:| |val| (|List| *10)) (|:| |tower| *11))))
   (|isDomain| *3 (|List| *10)) (|isDomain| *4 (|List| *11))
   (|ofCategory| *10 (|RecursivePolynomialCategory| *7 *8 *9))
   (|ofCategory| *11 (|SquareFreeRegularTriangularSetCategory| *7 *8 *9 *10))
   (|ofCategory| *7 (|GcdDomain|))
   (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *9 (|OrderedSet|))
   (|isDomain| *1
    (|SquareFreeRegularSetDecompositionPackage| *7 *8 *9 *10 *11))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5))
       (|isDomain| *2
        (|Record| (|:| |id| (|FractionalIdeal| *4 (|Fraction| *4) *5 *6))
                  (|:| |principalPart| *6)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *6 *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|Record| (|:| |poly| *6) (|:| |normal| #1=(|Fraction| *6))
                  (|:| |special| #1#)))
       (|isDomain| *1 (|MonomialExtensionTools| *5 *6))
       (|isDomain| *3 (|Fraction| *6))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|PolynomialDecomposition| *3 *4))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *4 *4)
  (|partial| AND (|isDomain| *4 (|NonNegativeInteger|))
   (|ofCategory| *5 (|Field|))
   (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3)))
   (|isDomain| *1 (|PolynomialDecomposition| *3 *5))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))
 ((*1 *2 *3 *2 *4 *4)
  (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8))
       (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9))))
 ((*1 *2 *3 *2 *4 *4 *4 *4 *4)
  (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8))
       (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9))))
 ((*1 *2 *3 *2 *4 *4)
  (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8))
       (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9))))
 ((*1 *2 *3 *2 *4 *4 *4 *4 *4)
  (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|List| *8))
       (|isDomain| *4 (|Boolean|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9))))) 
(((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|Boolean|))
       (|ofCategory| *7 (|GcdDomain|))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *9 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *7 *8 *9))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *7 *8 *9 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|Boolean|))
       (|ofCategory| *7 (|GcdDomain|))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *9 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *7 *8 *9))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *7 *8 *9 *3 *4))
       (|ofCategory| *4
                     (|SquareFreeRegularTriangularSetCategory| *7 *8 *9 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *6 *7 *8 *3 *4))
       (|ofCategory| *4
                     (|SquareFreeRegularTriangularSetCategory| *6 *7 *8 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4
                     (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *6 *7 *8 *3 *4))
       (|ofCategory| *4
                     (|SquareFreeRegularTriangularSetCategory| *6 *7 *8 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4
                     (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |done| (|List| *4))
                  (|:| |todo|
                       (|List|
                        (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4
                     (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *9))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1
        (|SquareFreeRegularSetDecompositionPackage| *5 *6 *7 *8 *9))))) 
(((*1 *1) (|isDomain| *1 (|CharacterClass|)))
 ((*1 *1 *1) (|isDomain| *1 (|Character|)))
 ((*1 *1 *1) (|ofCategory| *1 (|StringAggregate|)))) 
(((*1 *1 *1) (|ofCategory| *1 (|StringAggregate|)))) 
(((*1 *1) (|isDomain| *1 (|CharacterClass|)))
 ((*1 *1 *1) (|isDomain| *1 (|Character|)))
 ((*1 *1 *1) (|ofCategory| *1 (|StringAggregate|)))) 
(((*1 *1 *1) (|ofCategory| *1 (|StringAggregate|)))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *1 *3)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *3 (|Integer|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *6))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *1 (|ListToMap| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *2))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|ListToMap| *5 *2))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| *5))
       (|ofCategory| *6 (|SetCategory|)) (|ofCategory| *5 (|Type|))
       (|isDomain| *2 (|Mapping| *5 *6)) (|isDomain| *1 (|ListToMap| *6 *5))))
 ((*1 *2 *3 *4 *5 *2)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *2))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *2 (|Type|))
       (|isDomain| *1 (|ListToMap| *5 *2))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *3 (|List| *5))
       (|isDomain| *4 (|List| *6)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|Type|)) (|isDomain| *1 (|ListToMap| *5 *6))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|List| *2))
       (|isDomain| *6 (|Mapping| *2 *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|ListToMap| *5 *2))))
 ((*1 *2 *1 *1 *3)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *3 (|Character|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1 *1 *3)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *3 (|Character|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1 *2 *1)
  (AND (|ofCategory| *1 (|StringAggregate|))
       (|isDomain| *2 (|UniversalSegment| (|Integer|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|CachableSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *3 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|BasicType|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|BasicType|))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4))
       (|ofCategory| *1 (|FiniteLinearAggregate| *4))
       (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|InputBinaryFile|))))
 ((*1 *2 *3 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *3 (|CharacterClass|))))
 ((*1 *2 *1 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgFactor| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|)))))
 ((*1 *2 *3 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |less| #1=(|BinarySearchTree| *3)) (|:| |greater| #1#)))
   (|isDomain| *1 (|BinarySearchTree| *3)) (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|IntegrationResult| *4))
       (|ofCategory| *4
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *3)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *3
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|IntegrationResultToFunction| *3 *4))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|IntegrationResult| (|Fraction| (|Polynomial| *3))))
       (|ofCategory| *3
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|IntegrationResultRFToFunction| *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *3 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|Record| (|:| |normal| *3) (|:| |special| *3)))
       (|isDomain| *1 (|MonomialExtensionTools| *5 *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Vector| *5)) (|ofCategory| *5 (|Field|))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|Matrix| *5))))
       (|isDomain| *1 (|RepresentationPackage2| *5))
       (|isDomain| *3 (|List| (|Matrix| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Vector| (|Vector| *5))) (|ofCategory| *5 (|Field|))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|Matrix| *5))))
       (|isDomain| *1 (|RepresentationPackage2| *5))
       (|isDomain| *3 (|List| (|Matrix| *5)))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|CharacterClass|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|StringAggregate|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Character|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|StringAggregate|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|))
       (|isDomain| *2 (|CharacterClass|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Character|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|))
       (|isDomain| *2 (|CharacterClass|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Character|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|))
       (|isDomain| *2 (|CharacterClass|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|StringAggregate|)) (|isDomain| *2 (|Character|))))) 
(((*1 *1 *1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5))
       (|ofType| *3 *2) (|ofType| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|CommutativeRing|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|CommutativeRing|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *3 *2 *4))
       (|ofCategory| *2 (|FiniteLinearAggregate| *3))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|SquareMatrix| *2 *3))
       (|ofType| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Matrix| *4)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|SquareMatrix| *3 *4))
       (|ofType| *3 (|NonNegativeInteger|))))) 
(((*1 *1 *1)
  (|partial| AND (|isDomain| *1 (|SplittingTree| *2 *3))
   (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
   (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|SplittingTree| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|SplittingTree| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1 (|SplittingTree| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|SplittingNode| *4 *5))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingTree| *4 *5))))) 
(((*1 *2 *3 *1 *4)
  (AND (|isDomain| *3 (|SplittingNode| *5 *6))
       (|isDomain| *4 (|Mapping| (|Boolean|) *6 *6))
       (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *6 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingTree| *5 *6))))) 
(((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *2))
       (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *2 (|BasicType|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|FiniteAggregate| *3))
       (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|LazyStreamAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2 *1 *3)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|Multiset| *4))))
 ((*1 *1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Multiset| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|SplittingNode| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingTree| *3 *4))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|FiniteAggregate| *3))
       (|ofCategory| *1 (|DictionaryOperations| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *2))
       (|ofCategory| *1 (|DictionaryOperations| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2))
       (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|ExtensibleLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *3 *1)
  (|partial| AND (|ofCategory| *1 (|KeyedDictionary| *3 *2))
   (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *1 *3)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|SetCategory|)) (|isDomain| *1 (|Multiset| *4))))
 ((*1 *1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Multiset| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|SplittingNode| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingTree| *3 *4))))) 
(((*1 *1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|SplittingNode| *4 *5)))
       (|isDomain| *3 (|Mapping| (|Boolean|) *5 *5))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingTree| *4 *5))))
 ((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|SplittingNode| *3 *4)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingTree| *3 *4))))) 
(((*1 *2 *1) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OrdSetInts|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|Property|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|QueryEquation|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *1 (|SplittingNode| *2 *3))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|GcdDomain|))
   (|ofCategory| *4 (|OrderedSet|))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6))
   (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *1 *1) (|ofCategory| *1 (|Aggregate|)))
 ((*1 *1 *1) (|isDomain| *1 (|BasicOperator|)))
 ((*1 *1 *1) (|isDomain| *1 (|SubSpaceComponentProperty|)))
 ((*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *2)) (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|SplittingNode| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|SplittingNode| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|SplittingNode| *3 *2))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *3 *4))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|SplittingNode| *2 *3))
       (|ofCategory| *2 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *3 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *2 *1 *1 *3 *4)
  (AND (|isDomain| *3 (|Mapping| #1=(|Boolean|) *5 *5))
       (|isDomain| *4 (|Mapping| #1# *6 *6))
       (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|)))
       (|ofCategory| *6 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *5 *6))))) 
(((*1 *2 *1 *1 *3)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *5 *5))
       (|ofCategory| *5 (|Join| (|SetCategory|) (|Aggregate|)))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|SplittingNode| *4 *5))
       (|ofCategory| *4 (|Join| (|SetCategory|) (|Aggregate|)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
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  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
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  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *1 *1) (|isDomain| *1 (|DoubleFloat|)))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
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  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
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  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|DoubleFloat|)))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Mapping| (|Float|)))
       (|isDomain| *1 (|RandomFloatDistributions|))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *2 (|RealNumberSystem|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *1 *1) (|ofCategory| *1 (|OrderedAbelianGroup|)))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *2 (|RealNumberSystem|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *2 (|RealNumberSystem|))))
 ((*1 *1 *1) (|ofCategory| *1 (|SpecialFunctionCategory|)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SpecialOutputPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|OutputForm|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SpecialOutputPackage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SpecialOutputPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|OutputForm|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SpecialOutputPackage|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *4 (|OutputForm|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SpecialOutputPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SpecialOutputPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|OutputForm|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SpecialOutputPackage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|List| (|Syntax|)))
       (|isDomain| *1 (|SpadParser|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|SubSpace| 3 *3)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *2)) (|ofCategory| *2 (|Ring|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6))
       (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| (|Point| *4)))
       (|ofCategory| *1 (|ThreeSpaceCategory| *4)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *2 *2)
  (AND (|isDomain| *1 (|ParametricPlaneCurve| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *2 *2)
  (AND (|isDomain| *1 (|ParametricSpaceCurve| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|Point| *3)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3)))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Point| *3)))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|Point| *3)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3)))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Point| *3)))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|Point| *3)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Point| *3))) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3)))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Point| *3)))
       (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|Point| *3))))))
 ((*1 *1 *2 *3 *3)
  (AND (|isDomain| *2 (|List| (|List| (|Point| *4))))
       (|isDomain| *3 (|Boolean|)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| (|Point| *3))))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|ThreeSpaceCategory| *3))))
 ((*1 *1 *1 *2 *3 *3)
  (AND (|isDomain| *2 (|List| (|List| (|List| *4))))
       (|isDomain| *3 (|Boolean|)) (|ofCategory| *1 (|ThreeSpaceCategory| *4))
       (|ofCategory| *4 (|Ring|))))
 ((*1 *1 *1 *2 *3 *3)
  (AND (|isDomain| *2 (|List| (|List| (|Point| *4))))
       (|isDomain| *3 (|Boolean|)) (|ofCategory| *1 (|ThreeSpaceCategory| *4))
       (|ofCategory| *4 (|Ring|))))
 ((*1 *1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|List| (|List| (|List| *5))))
       (|isDomain| *3 (|List| (|SubSpaceComponentProperty|)))
       (|isDomain| *4 (|SubSpaceComponentProperty|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *5)) (|ofCategory| *5 (|Ring|))))
 ((*1 *1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|List| (|List| (|Point| *5))))
       (|isDomain| *3 (|List| (|SubSpaceComponentProperty|)))
       (|isDomain| *4 (|SubSpaceComponentProperty|))
       (|ofCategory| *1 (|ThreeSpaceCategory| *5)) (|ofCategory| *5 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|Point| *3)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|List| (|NonNegativeInteger|)))))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|List| (|Point| *3)))))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|SubSpaceComponentProperty|))))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|List| (|SubSpaceComponentProperty|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |points| (|NonNegativeInteger|))
                  (|:| |curves| (|NonNegativeInteger|))
                  (|:| |polygons| (|NonNegativeInteger|))
                  (|:| |constructs| (|NonNegativeInteger|))))))) 
(((*1 *2 *3 *3)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |factor| (|SparseUnivariatePolynomial| *6))
               (|:| |exponent| (|Integer|)))))
   (|ofCategory| *6 (|EuclideanDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7))
   (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|ThreeSpaceCategory| *2)) (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *1 (|SortPackage| *4 *2))
       (|ofCategory| *2
                     (|Join| (|IndexedAggregate| (|Integer|) *4)
                             (|FiniteAggregate| *4)
                             (|ShallowlyMutableAggregate| *4)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|SortPackage| *3 *2))
       (|ofCategory| *2
                     (|Join| (|IndexedAggregate| (|Integer|) *3)
                             (|FiniteAggregate| *3)
                             (|ShallowlyMutableAggregate| *3)))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *1 (|SortPackage| *4 *2))
       (|ofCategory| *2
                     (|Join| (|IndexedAggregate| (|Integer|) *4)
                             (|FiniteAggregate| *4)
                             (|ShallowlyMutableAggregate| *4)))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|SortPackage| *3 *2))
       (|ofCategory| *2
                     (|Join| (|IndexedAggregate| (|Integer|) *3)
                             (|FiniteAggregate| *3)
                             (|ShallowlyMutableAggregate| *3)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *2))))
 ((*1 *2 *3 *2 *4)
  (AND
   (|isDomain| *2
    (|Fraction| (|SparseUnivariatePolynomial| (|Expression| *5))))
   (|isDomain| *3 (|Vector| (|Expression| *5))) (|isDomain| *4 (|Integer|))
   (|ofCategory| *5 (|IntegralDomain|))
   (|isDomain| *1 (|TransSolvePackageService| *5))))) 
(((*1 *2 *2 *2 *2)
  (AND
   (|isDomain| *2
    (|Fraction| (|SparseUnivariatePolynomial| (|Expression| *3))))
   (|ofCategory| *3 (|IntegralDomain|))
   (|isDomain| *1 (|TransSolvePackageService| *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|SuchThat| (|List| (|Expression| *5))
                    (|List| (|Equation| (|Expression| *5)))))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|SuchThat| (|List| (|Expression| *5))
                    (|List| (|Equation| (|Expression| *5)))))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|Expression| *5)))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|List| (|Expression| *5))))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|Equation| (|Expression| *5))))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|Equation| (|Expression| *4))))
       (|isDomain| *1 (|RadicalSolvePackage| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|Equation| (|Expression| *5))))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *4))))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|Equation| (|Expression| *4))))
       (|isDomain| *1 (|RadicalSolvePackage| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *5)))))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| *4))))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *4)))))
       (|isDomain| *1 (|RadicalSolvePackage| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *5)))))
       (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *5)))))
       (|isDomain| *1 (|RadicalSolvePackage| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Equation| (|Fraction| (|Polynomial| *4)))))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|List| (|List| (|Equation| (|Expression| *4)))))
       (|isDomain| *1 (|RadicalSolvePackage| *4))))) 
(((*1 *2 *2 *2 *2 *2 *2)
  (AND
   (|ofCategory| *2
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *2 *2 *2 *2)
  (AND
   (|ofCategory| *2
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *2 *2 *2)
  (AND
   (|ofCategory| *2
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *2 *2)
  (AND
   (|ofCategory| *2
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *4))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *3 *3 *3 *3)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *3))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *4))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *3 *3 *3)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *3))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *4))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *3 *3)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *3))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *4))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *3)
  (AND
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *2 (|List| *3))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *5 *5))
       (|ofCategory| *5
                     (|Join| (|Field|)
                             (CATEGORY |domain|
                              (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
       (|isDomain| *2
        (|Record| (|:| |solns| (|List| *5))
                  (|:| |maps|
                       (|List| (|Record| (|:| |arg| *5) (|:| |res| *5))))))
       (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *5))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3 *2)
  (|partial| AND (|ofCategory| *4 (|Field|))
   (|ofCategory| *5
                 (|Join| (|FiniteLinearAggregate| *4)
                         (|ShallowlyMutableAggregate| *4)))
   (|ofCategory| *2
                 (|Join| (|FiniteLinearAggregate| *4)
                         (|ShallowlyMutableAggregate| *4)))
   (|isDomain| *1 (|LinearSystemMatrixPackage| *4 *5 *2 *3))
   (|ofCategory| *3 (|MatrixCategory| *4 *5 *2))))
 ((*1 *2 *3 *2)
  (|partial| AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Matrix| *4))
   (|ofCategory| *4 (|Field|))
   (|isDomain| *1 (|LinearSystemMatrixPackage1| *4))))
 ((*1 *2 *3 *2 *4 *5)
  (|partial| AND (|isDomain| *4 (|List| *2)) (|isDomain| *5 (|Mapping| *2 *2))
   (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|ODETools| *2 *3))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *2
                 (|Join| (|Field|)
                         (CATEGORY |domain|
                          (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))))
   (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| (|Stream| *7)))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|PolynomialCategory| *5 (|IndexedExponents| *6) *6))
       (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Mapping| (|Stream| *7) *7))
       (|isDomain| *1 (|SparseMultivariateTaylorSeries| *5 *6 *7))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|EuclideanDomain|))
       (|ofCategory| *6 (|FiniteLinearAggregate| *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *5))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| *4 "failed"))
                  (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|SmithNormalForm| *5 *6 *4 *3))
       (|ofCategory| *3 (|MatrixCategory| *5 *6 *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|EuclideanDomain|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2
        (|Record| (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3)))
       (|isDomain| *1 (|SmithNormalForm| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|SmithNormalForm| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|EuclideanDomain|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|Record| (|:| |Hermite| *3) (|:| |eqMat| *3)))
       (|isDomain| *1 (|SmithNormalForm| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|SmithNormalForm| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *2)
  (AND (|ofCategory| *2 (|Ring|))
       (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5))
       (|ofCategory| *4 (|DirectProductCategory| *3 *2))
       (|ofCategory| *5 (|DirectProductCategory| *3 *2))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|Matrix| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *4)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *6))
       (|ofCategory| *5 (|DirectProductCategory| *3 *4))
       (|ofCategory| *6 (|DirectProductCategory| *3 *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *2 *5))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *5 (|DirectProductCategory| *3 *4))
       (|ofCategory| *2 (|DirectProductCategory| *3 *4))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2))
       (|ofCategory| *2 (|Field|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankAlgebra| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5))
       (|ofCategory| *4 (|DirectProductCategory| *3 *2))
       (|ofCategory| *5 (|DirectProductCategory| *3 *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2
                     (|Join| (|EuclideanDomain|)
                             (CATEGORY |domain|
                              (SIGNATURE |squareFree| ((|Factored| $) $)))))
       (|isDomain| *1 (|IntegralBasisTools| *2 *4 *5))
       (|ofCategory| *5 (|FramedAlgebra| *2 *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5))
       (|ofCategory| *4 (|DirectProductCategory| *3 *2))
       (|ofCategory| *5 (|DirectProductCategory| *3 *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Field|))
       (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *2 *4 *5 *3))
       (|ofCategory| *3 (|MatrixCategory| *2 *4 *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *2 *4 *5 *3))
       (|ofCategory| *3 (|MatrixCategory| *2 *4 *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5))
       (|ofCategory| *4 (|DirectProductCategory| *3 *2))
       (|ofCategory| *5 (|DirectProductCategory| *3 *2))
       (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *2 *4 *5 *3))
       (|ofCategory| *3 (|MatrixCategory| *2 *4 *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5))
       (|ofCategory| *4 (|DirectProductCategory| *3 *2))
       (|ofCategory| *5 (|DirectProductCategory| *3 *2))
       (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|StackAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|StackAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|StackAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|StackAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|Boolean|)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|)))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|Signature|))
       (|isDomain| *1 (|SignatureAst|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|DefinitionAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|FunctionDescriptor|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|OperatorSignature|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Syntax|))) (|isDomain| *3 (|Syntax|))
       (|isDomain| *1 (|Signature|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|SignatureAst|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|TypeAst|)) (|isDomain| *1 (|CoerceAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|TypeAst|)) (|isDomain| *1 (|MappingAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|TypeAst|)) (|isDomain| *1 (|PretendAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|TypeAst|)) (|isDomain| *1 (|RestrictAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Syntax|)) (|isDomain| *1 (|Signature|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|MappingAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Syntax|))) (|isDomain| *1 (|Signature|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|SturmHabichtPackage| *4 *5))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|SturmHabichtPackage| *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4))
       (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|SturmHabichtPackage| *4 *5))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4))
       (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|SturmHabichtPackage| *4 *5))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|UnivariatePolynomial| *5 *4))
       (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|))
       (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|SturmHabichtPackage| *4 *5))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|))
       (|isDomain| *2 (|List| (|UnivariatePolynomial| *5 *4)))
       (|isDomain| *1 (|SturmHabichtPackage| *4 *5))
       (|isDomain| *3 (|UnivariatePolynomial| *5 *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|OrderedIntegralDomain|)) (|ofType| *5 (|Symbol|))
       (|isDomain| *2 (|List| (|UnivariatePolynomial| *5 *4)))
       (|isDomain| *1 (|SturmHabichtPackage| *4 *5))
       (|isDomain| *3 (|UnivariatePolynomial| *5 *4))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|))
       (|isDomain| *1 (|SemiGroupOperation| *3))))) 
(((*1 *2 *3 *3 *3)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *3 *3)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *3 *3)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *2 *2 *3)
  (AND (|isDomain| *2 (|Vector| (|Integer|))) (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))
 ((*1 *2 *3 *2 *4)
  (AND (|isDomain| *2 (|Vector| #1=(|Integer|))) (|isDomain| *3 (|List| #1#))
       (|isDomain| *4 (|Integer|))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *3 *2 *4)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *3 (|List| (|PositiveInteger|))) (|isDomain| *4 (|Boolean|))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *3 *3 *2)
  (AND (|isDomain| *2 (|Matrix| (|Integer|)))
       (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *4 (|List| (|Integer|)))
       (|isDomain| *2 (|Matrix| (|Integer|)))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *2 (|List| (|Matrix| (|Integer|))))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *2 *2 *3)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *3 (|Matrix| (|Integer|)))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|Matrix| (|Integer|)))
       (|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| *4))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| *4))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| *4))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *3 *4 *5 *5)
  (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *8 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9))))
   (|isDomain| *5 (|Boolean|))
   (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4))
   (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8))
   (|ofCategory| *6 (|GcdDomain|))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *4 (|OrderedSet|))
   (|isDomain| *2 (|List| (|Record| (|:| |val| *8) (|:| |tower| *9))))
   (|isDomain| *1
    (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *4 *8 *9))))) 
(((*1 *2 *3 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *3 *4 *5 *6 *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *3 *4 *5 *6 *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))))) 
(((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *3 *4 *5 *6 *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *3 *4 *5 *6 *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))))) 
(((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1
        (|SquareFreeRegularTriangularSetGcdPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
  (|partial| AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *8 (|OrderedSet|))
   (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8))
   (|isDomain| *2
    (|Record| (|:| |eq| #1=(|List| *9)) (|:| |tower| *4) (|:| |ineq| #1#)))
   (|isDomain| *1 (|QuasiComponentPackage| *6 *7 *8 *9 *4))
   (|isDomain| *3 (|List| *9))
   (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *9))))
 ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
  (|partial| AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *8 (|OrderedSet|))
   (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8))
   (|isDomain| *2
    (|Record| (|:| |eq| #2=(|List| *9)) (|:| |tower| *4) (|:| |ineq| #2#)))
   (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *4))
   (|isDomain| *3 (|List| *9))
   (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *9))))) 
(((*1 *2 *3 *4 *5 *5)
  (AND (|isDomain| *4 (|List| *10)) (|isDomain| *5 (|Boolean|))
       (|ofCategory| *10 (|RegularTriangularSetCategory| *6 *7 *8 *9))
       (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eq| #1=(|List| *9)) (|:| |tower| *10)
                   (|:| |ineq| #1#))))
       (|isDomain| *1 (|QuasiComponentPackage| *6 *7 *8 *9 *10))
       (|isDomain| *3 (|List| *9))))
 ((*1 *2 *3 *4 *5 *5)
  (AND (|isDomain| *4 (|List| *10)) (|isDomain| *5 (|Boolean|))
       (|ofCategory| *10 (|RegularTriangularSetCategory| *6 *7 *8 *9))
       (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eq| #2=(|List| *9)) (|:| |tower| *10)
                   (|:| |ineq| #2#))))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *10))
       (|isDomain| *3 (|List| *9))))) 
(((*1 *2 *2)
  (AND
   (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *6)) (|:| |tower| *7))))
   (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
   (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))
   (|ofCategory| *3 (|GcdDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7))))
 ((*1 *2 *2)
  (AND
   (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *6)) (|:| |tower| *7))))
   (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
   (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))
   (|ofCategory| *3 (|GcdDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8)))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8)))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *5 *6 *7 *8 *3))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *5 *6 *7 *8 *3))))) 
(((*1 *2 *3 *3)
  (|partial| AND (|ofCategory| *4 (|GcdDomain|))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *6 (|OrderedSet|))
   (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3))
   (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3)
  (|partial| AND (|ofCategory| *4 (|GcdDomain|))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *6 (|OrderedSet|))
   (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3))
   (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))))) 
(((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8))
       (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RuntimeValue|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerRetractions| *3))
       (|ofCategory| *3 (|RetractableTo| (|Integer|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2 (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| *4))))
   (|isDomain| *1 (|PatternMatchResult| *3 *4))
   (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *7 (|SetCategory|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *2 *4 *5 *6))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerRetractions| *3))
       (|ofCategory| *3 (|RetractableTo| *2))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *2 *5 *6))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *2 *2 *3)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|PositiveInteger|))
       (|ofCategory| *1 (|FloatingPointSystem|))))
 ((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|FloatingPointSystem|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *2 *6))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *2))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|SetCategory|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|SetCategory|))))) 
(((*1 *1 *1 *2)
  (|partial| AND (|isDomain| *2 (|PositiveInteger|))
   (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 *2)
   (|ofType| *4 *2)))) 
(((*1 *1 *1 *2 *2)
  (|partial| AND (|isDomain| *2 (|PositiveInteger|))
   (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 *2)
   (|ofType| *4 *2)))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|ConstructAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Vector| (|SetOfMIntegersInOneToN| *3 *4)))
       (|isDomain| *1 (|SetOfMIntegersInOneToN| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *3 (|BasicType|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Permutation| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PermutationGroup| *4))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SetOfMIntegersInOneToN| *4 *5)) (|ofType| *4 *3)
       (|ofType| *5 *3)))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|SetOfMIntegersInOneToN| *4 *5)) (|ofType| *4 *3)
       (|ofType| *5 *3)))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SetCategory|)) (|isDomain| *2 (|SingleInteger|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SetCategory|)) (|isDomain| *2 (|String|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|SetAggregate| *3))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|SetAggregate| *3))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|PolynomialIdeals| *3 *4 *5 *6)))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *2 (|Field|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|List| (|Kernel| *4)))
       (|ofCategory| *4 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|IntegrationTools| *3 *4))))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|PatternMatchResult| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|SetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|AddAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Syntax|)) (|isDomain| *1 (|AnonymousFunction|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|CapsuleAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|CategoryAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|CollectAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|CommaAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|DefinitionAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|MacroAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ReduceAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|RepeatAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|SequenceAst|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|SegmentCategory| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|SegmentCategory| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *1 *2 *2)
  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|String|))
       (|isDomain| *1 (|QueryEquation|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *4 (|Type|))
       (|isDomain| *1 (|RangeBinding| *3 *4))
       (|ofCategory| *3 (|SegmentCategory| *4))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Segment| *4))
       (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|SegmentBinding| *4))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|SegmentAst|))))) 
(((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))))
   (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4))
       (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *3))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *4))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Vector| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FramedAlgebra| *4 *5))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2 (|Vector| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Vector| *3)) (|isDomain| *1 (|LinearElement| *3 *4))
       (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Vector| *3)) (|isDomain| *1 (|LinearForm| *3 *4))
       (|ofCategory| *3 (|Field|)) (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|Matrix| *5))) (|isDomain| *3 (|Matrix| *5))
       (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Vector| *5))
       (|isDomain| *1 (|StructuralConstantsPackage| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|Vector| (|Matrix| *4)))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|Vector| (|Matrix| *4)))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *2 (|Vector| (|Matrix| *3)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|Vector| (|Matrix| (|Fraction| (|Polynomial| *5)))))
       (|isDomain| *1 (|StructuralConstantsPackage| *5))
       (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *5))))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|Vector| (|Matrix| (|Polynomial| *5))))
       (|isDomain| *1 (|StructuralConstantsPackage| *5))
       (|isDomain| *4 (|Matrix| (|Polynomial| *5)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|ofCategory| *4 (|Field|))
       (|isDomain| *2 (|Vector| (|Matrix| *4)))
       (|isDomain| *1 (|StructuralConstantsPackage| *4))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Contour|))) (|isDomain| *1 (|Scope|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| (|Binding|)))
       (|isDomain| *1 (|Contour|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| (|Binding|)))
       (|isDomain| *1 (|Scope|))))) 
(((*1 *1 *2 *1) (AND (|isDomain| *2 (|Binding|)) (|isDomain| *1 (|Scope|))))) 
(((*1 *1) (|isDomain| *1 (|Scope|)))) 
(((*1 *1) (|isDomain| *1 (|Scope|)))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *2))
       (|ofCategory| *2 (|CachableSet|)) (|isDomain| *1 (|SortedCache| *2))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|Integer|) *2 *2))
       (|ofCategory| *2 (|CachableSet|)) (|isDomain| *1 (|SortedCache| *2))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|SortedCache| *3))
       (|ofCategory| *3 (|CachableSet|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|SortedCache| *3))
       (|ofCategory| *3 (|CachableSet|))))) 
(((*1 *1) (|isDomain| *1 (|SingletonAsOrderedSet|)))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| *3))
       (|isDomain| *1
        (|InternalRationalUnivariateRepresentationPackage| *5 *6 *7 *8 *3))
       (|ofCategory| *3
                     (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5))
                   (|:| |coordinates| (|List| (|Polynomial| *5))))))
       (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *5 *6))
       (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|ofType| *6 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4))
                   (|:| |coordinates| (|List| (|Polynomial| *4))))))
       (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *4 *5))
       (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofType| *5 (|List| (|Symbol|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5))
                   (|:| |coordinates| (|List| (|Polynomial| *5))))))
       (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *5 *6))
       (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|ofType| *6 (|List| (|Symbol|)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|RewriteRule| *3 *4 *5)))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4
                     (|Join| (|Ring|) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))
       (|ofCategory| *5
                     (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))
       (|isDomain| *1 (|Ruleset| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4
                     (|Join| (|Ring|) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))
       (|isDomain| *2 (|List| (|RewriteRule| *3 *4 *5)))
       (|isDomain| *1 (|Ruleset| *3 *4 *5))
       (|ofCategory| *5
                     (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))))) 
(((*1 *1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5
                     (|Join| (|Ring|) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|isDomain| *1 (|RewriteRule| *4 *5 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))))
 ((*1 *1 *2 *2)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4
                     (|Join| (|Ring|) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))
       (|isDomain| *1 (|RewriteRule| *3 *4 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Pattern| *4))
       (|isDomain| *3 (|Mapping| (|Boolean|) *5))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|))
       (|isDomain| *1 (|PatternFunctions1| *4 *5))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Pattern| *4))
       (|isDomain| *3 (|List| (|Mapping| (|Boolean|) *5)))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|))
       (|isDomain| *1 (|PatternFunctions1| *4 *5))))
 ((*1 *2 *2 *3 *4)
  (AND (|isDomain| *2 (|Pattern| *5)) (|isDomain| *3 (|List| (|Symbol|)))
       (|isDomain| *4 (|Mapping| (|Boolean|) (|List| *6)))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *1 (|PatternFunctions1| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Mapping| (|Boolean|) *5))
       (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|AttachPredicates| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Symbol|))
       (|isDomain| *4 (|List| (|Mapping| (|Boolean|) *5)))
       (|ofCategory| *5 (|Type|)) (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|AttachPredicates| *5))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *5)) (|ofCategory| *5 (|Type|))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|FunctionSpaceAttachPredicates| *4 *2 *5))
       (|ofCategory| *2 (|FunctionSpace| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| (|Mapping| (|Boolean|) *5)))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|FunctionSpaceAttachPredicates| *4 *2 *5))
       (|ofCategory| *2 (|FunctionSpace| *4))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Symbol|)))
       (|isDomain| *3 (|Mapping| (|Boolean|) (|List| *6)))
       (|ofCategory| *6
                     (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5
                     (|Join| (|Ring|) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|isDomain| *1 (|RewriteRule| *4 *5 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4
                     (|Join| (|Ring|) (|PatternMatchable| *3)
                             (|ConvertibleTo| *2)))
       (|isDomain| *2 (|Pattern| *3)) (|isDomain| *1 (|RewriteRule| *3 *4 *5))
       (|ofCategory| *5
                     (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3)
                             (|ConvertibleTo| *2)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4
                     (|Join| (|Ring|) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))
       (|isDomain| *2 (|List| (|Symbol|)))
       (|isDomain| *1 (|RewriteRule| *3 *4 *5))
       (|ofCategory| *5
                     (|Join| (|FunctionSpace| *4) (|PatternMatchable| *3)
                             (|ConvertibleTo| (|Pattern| *3))))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|CoerceAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ExitAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|PretendAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|QuasiquoteAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ReturnAst|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|RestrictAst|))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4))))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *3 *4 *5 *5)
  (AND (|isDomain| *5 (|Boolean|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *8 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) (|:| |tower| *9))))
   (|isDomain| *5 (|Boolean|))
   (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4))
   (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8))
   (|ofCategory| *6 (|GcdDomain|))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *4 (|OrderedSet|))
   (|isDomain| *2 (|List| (|Record| (|:| |val| *8) (|:| |tower| *9))))
   (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *4 *8 *9))))) 
(((*1 *2 *3 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4))))
       (|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Union| (|Boolean|) (|List| *1)))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *1))))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))) 
(((*1 *2 *3 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Union| *3 (|List| *1)))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2))
       (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *2 *3 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *1))))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Arity|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntervalCategory| *3))
       (|ofCategory| *3
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntervalCategory| *3))
       (|ofCategory| *3
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|RetractableTo| (|Integer|)))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|ComplexCategory&| *3 *4))
       (|ofCategory| *3 (|ComplexCategory| *4))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|Ring|)) (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *3 *2))
       (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| (|Integer|))) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|RealClosedField|))
       (|isDomain| *2 (|List| *1))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|List| *1))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *3))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|isDomain| *3 (|Symbol|))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Polynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|))
       (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2))
       (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2))
       (|isDomain| *4 (|Symbol|)) (|ofCategory| *2 (|FunctionSpace| *5))
       (|isDomain| *1 (|AlgebraicFunction| *5 *2))
       (|ofCategory| *5 (|IntegralDomain|))))
 ((*1 *1 *2 *3)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
   (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *1 *2 *3 *4)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
   (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|OutputForm|))
   (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *1 *2 *3)
  (|partial| AND (|isDomain| *3 (|PositiveInteger|))
   (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))
   (|ofCategory| *1 (|RealRootCharacterizationCategory| *4 *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|RealClosure| *3))
       (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|) (|RealConstant|)))))
 ((*1 *2 *3 *1 *2)
  (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))
 ((*1 *2 *3 *1 *2)
  (AND (|ofCategory| *1 (|RealRootCharacterizationCategory| *2 *3))
       (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|CollectAst|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|RepeatAst|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|HeadAst|)) (|isDomain| *1 (|DefinitionAst|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|HeadAst|)) (|isDomain| *1 (|MacroAst|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3))
       (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|AntiSymm| *2 *3))
       (|ofType| *3 (|List| (|Symbol|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Expression| *3))
       (|isDomain| *1 (|DeRhamComplex| *3 *4))
       (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofType| *3 (|List| (|Symbol|)))
       (|ofCategory| *5
                     (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))
       (|ofType| *6
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *4) (|:| |exponent| *5))
                   (|Record| (|:| |index| *4) (|:| |exponent| *5))))
       (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|GeneralModulePolynomial| *3 *2 *4 *5 *6 *7))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *7
                     (|PolynomialCategory| *2 *5 (|OrderedVariableList| *3)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3))
       (|ofCategory| *3 (|OrderedType|)) (|ofCategory| *2 (|BasicType|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|LaurentPolynomial| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|MonoidRing| *2 *3))
       (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 (|Monoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4))
       (|ofCategory| *3 (|OrderedAbelianMonoid|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1 *1)
  (|partial| AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *2 *1 *1 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2
        (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|))
                  (|:| |remainder| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2
        (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|))
                  (|:| |remainder| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |coef| *3) (|:| |gap| (|NonNegativeInteger|))
              (|:| |quotient| #1=(|NewSparseUnivariatePolynomial| *3))
              (|:| |remainder| #1#)))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1 *1 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2
        (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|))
                  (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2
        (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|))
                  (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |polnum| (|NewSparseUnivariatePolynomial| *3))
              (|:| |polden| *3) (|:| |power| (|NonNegativeInteger|))))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2
        (|Record| (|:| |polnum| *1) (|:| |polden| *1)
                  (|:| |power| (|NonNegativeInteger|))))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Any|)) (|isDomain| *1 (|AnyFunctions1| *2))
   (|ofCategory| *2 (|Type|))))
 ((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|FiniteFieldCategory|))
   (|ofCategory| *5 (|FiniteAlgebraicExtensionField| *4))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *2
    (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))
   (|isDomain| *1 (|NormRetractPackage| *4 *5 *6 *3 *7))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *6))
   (|ofType| *7 (|PositiveInteger|))))
 ((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|List| *6))
   (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|RetractableTo| *2))
   (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (|partial| OR
   (AND #1=(|isDomain| *2 (|Polynomial| *3))
        (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))
             (|not| (|ofCategory| *3 (|Algebra| (|Integer|))))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #2=((|ofCategory| *3 (|Ring|))
              (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
              (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
              (|ofCategory| *5 (|OrderedSet|))))
   (AND #1#
        (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|)))
             (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))
             (|ofCategory| *3 (|Algebra| (|Integer|)))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #2#)
   (AND #1#
        (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|))))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #2#)))
 ((*1 *1 *2)
  (|partial| OR
   (AND #3=(|isDomain| *2 (|Polynomial| (|Integer|)))
        #4=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
        (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))
             (|ofCategory| *3 (|Algebra| (|Integer|)))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #5=((|ofCategory| *3 (|Ring|))
              (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
              (|ofCategory| *5 (|OrderedSet|))))
   (AND #3# #4#
        (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #5#)))
 ((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|))))
   (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
   (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Any|)) (|isDomain| *1 (|AnyFunctions1| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *2)
  (OR
   (AND #1=(|isDomain| *2 (|Polynomial| *3))
        (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))
             (|not| (|ofCategory| *3 (|Algebra| (|Integer|))))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #2=((|ofCategory| *3 (|Ring|))
              (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
              (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
              (|ofCategory| *5 (|OrderedSet|))))
   (AND #1#
        (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|)))
             (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))
             (|ofCategory| *3 (|Algebra| (|Integer|)))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #2#)
   (AND #1#
        (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|))))
             (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #2#)))
 ((*1 *1 *2)
  (OR
   (AND #3=(|isDomain| *2 (|Polynomial| (|Integer|)))
        #4=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
        (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))
             (|ofCategory| *3 (|Algebra| (|Integer|)))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #5=((|ofCategory| *3 (|Ring|))
              (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
              (|ofCategory| *5 (|OrderedSet|))))
   (AND #3# #4#
        (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
             (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))))
        . #5#)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|))))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |gcd| #1=(|NewSparseUnivariatePolynomial| *3))
              (|:| |coef1| #1#) (|:| |coef2| #1#)))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2
        (|Record| (|:| |gcd| *1) (|:| |coef1| *1) (|:| |coef2| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |gcd| #1=(|NewSparseUnivariatePolynomial| *3))
              (|:| |coef1| #1#)))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef1| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |gcd| #1=(|NewSparseUnivariatePolynomial| *3))
              (|:| |coef2| #1#)))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef2| *1)))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *1 *1 *1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|)))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|HeuGcd| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *2 *2 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|)))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|))
       (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *2))
       (|ofCategory| *2 (|PolynomialCategory| *5 *3 *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2 (|PolynomialCategory| *6 *4 *5))
       (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *2))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6))
       (|ofCategory| *6 (|PolynomialCategory| *5 *3 *4))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|))
       (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *6))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|SparseUnivariatePolynomial| *7)))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *7))
       (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|PositiveInteger|)))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RomanNumeral|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|RomanNumeral|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2)
  (AND (|ofType| *4 *2) (|ofCategory| *5 (|Type|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|DirectProductCategory&| *3 *4 *5))
       (|ofCategory| *3 (|DirectProductCategory| *4 *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4 (|CancellationAbelianMonoid|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4))
       (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FreeGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeMonoidCategory| *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FiniteSetAggregate&| *3 *4))
       (|ofCategory| *3 (|FiniteSetAggregate| *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|ListMonoidOps| *3 *4 *5))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|))
       (|ofType| *5 *4)))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|MonogenicAlgebra&| *3 *4 *5))
       (|ofCategory| *3 (|MonogenicAlgebra| *4 *5))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|PlaneAlgebraicCurvePlot|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|Factored| *4) *4))
       (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Factored| *4))
       (|isDomain| *1 (|FactoredFunctionUtilities| *4))))
 ((*1 *1 *1) (|isDomain| *1 (|Plot|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *1) (|isDomain| *1 (|Plot3D|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))
 ((*1 *2 *3 *2 *4)
  (AND
   (|isDomain| *2
    (|Record| (|:| |left| #1=(|Fraction| (|Integer|))) (|:| |right| #1#)))
   (|isDomain| *4 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|RealZeroPackage| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *2 *2)
  (|partial| AND
   (|isDomain| *2
    (|Record| (|:| |left| (|Fraction| (|Integer|)))
              (|:| |right| (|Fraction| (|Integer|)))))
   (|isDomain| *1 (|RealZeroPackage| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *2 *4)
  (AND
   (|isDomain| *2
    (|Record| (|:| |left| #2=(|Fraction| (|Integer|))) (|:| |right| #2#)))
   (|isDomain| *4 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|RealZeroPackageQ| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *2 *2)
  (|partial| AND
   (|isDomain| *2
    (|Record| (|:| |left| (|Fraction| (|Integer|)))
              (|:| |right| (|Fraction| (|Integer|)))))
   (|isDomain| *1 (|RealZeroPackageQ| *3))
   (|ofCategory| *3
                 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))))
 ((*1 *1 *1)
  (AND (|ofCategory| *2 (|Join| (|OrderedRing|) (|Field|)))
       (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Kernel| (|AlgebraicNumber|))))
       (|isDomain| *1 (|AlgebraicNumber|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Kernel| (|AlgebraicNumber|)))
       (|isDomain| *1 (|AlgebraicNumber|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| #1=(|AlgebraicNumber|)))
       (|isDomain| *3 (|List| (|Kernel| #1#)))
       (|isDomain| *1 (|AlgebraicNumber|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| #2=(|AlgebraicNumber|)))
       (|isDomain| *3 (|Kernel| #2#)) (|isDomain| *1 (|AlgebraicNumber|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2)))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2))
       (|ofCategory| *2 (|Field|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankAlgebra| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|QuotientFieldCategory| *3))
       (|isDomain| *1 (|FractionalIdeal| *3 *2 *4 *5))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *5
                     (|Join| (|FramedAlgebra| *2 *4) (|RetractableTo| *2)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|QuotientFieldCategory| *3))
       (|isDomain| *1 (|FramedModule| *3 *2 *4 *5 *6))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *5 (|FramedAlgebra| *2 *4)) (|ofType| *6 (|Vector| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *5)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *2))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Kernel| (|InnerAlgebraicNumber|))))
       (|isDomain| *1 (|InnerAlgebraicNumber|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Kernel| (|InnerAlgebraicNumber|)))
       (|isDomain| *1 (|InnerAlgebraicNumber|))))
 ((*1 *2 *2 *3)
  (AND
   (|isDomain| *2 (|SparseUnivariatePolynomial| #3=(|InnerAlgebraicNumber|)))
   (|isDomain| *3 (|List| (|Kernel| #3#)))
   (|isDomain| *1 (|InnerAlgebraicNumber|))))
 ((*1 *2 *2 *3)
  (AND
   (|isDomain| *2 (|SparseUnivariatePolynomial| #4=(|InnerAlgebraicNumber|)))
   (|isDomain| *3 (|Kernel| #4#)) (|isDomain| *1 (|InnerAlgebraicNumber|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|MonogenicAlgebra| *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|NormInMonogenicAlgebra| *4 *2 *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|ofCategory| *2 (|IntegerNumberSystem|))))
 ((*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|ofCategory| *2 (|IntegerNumberSystem|))))
 ((*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) 
(((*1 *2 *1)
  (AND (|isDomain| *1 (|ContinuedFraction| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))
 ((*1 *2 *1)
  (AND (|isDomain| *1 (|PartialFraction| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|ofCategory| *2 (|EuclideanDomain|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RealNumberSystem|)) (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|BinaryExpansion|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|DecimalExpansion|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|HexadecimalExpansion|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))
       (|ofCategory| *2 (|EuclideanDomain|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))
 ((*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) 
(((*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|ComplexCategory&| *3 *4))
       (|ofCategory| *3 (|ComplexCategory| *4))))
 ((*1 *2)
  (AND (|ofType| *4 *2) (|ofCategory| *5 (|Type|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|DirectProductCategory&| *3 *4 *5))
       (|ofCategory| *3 (|DirectProductCategory| *4 *5))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FunctionSpace&| *3 *4))
       (|ofCategory| *3 (|FunctionSpace| *4))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|IntegerNumberSystem&| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|NonAssociativeRing|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|OctonionCategory&| *3 *4))
       (|ofCategory| *3 (|OctonionCategory| *4))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|QuotientFieldCategory&| *3 *4))
       (|ofCategory| *3 (|QuotientFieldCategory| *4))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|QuaternionCategory&| *3 *4))
       (|ofCategory| *3 (|QuaternionCategory| *4))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|RealClosedField&| *3))
       (|ofCategory| *3 (|RealClosedField|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|RealNumberSystem&| *3))
       (|ofCategory| *3 (|RealNumberSystem|))))) 
(((*1 *2 *1 *1) (AND (|ofCategory| *1 (|Rng|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Matrix| *5)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *1 (|RectangularMatrix| *3 *4 *5))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofType| *4 (|NonNegativeInteger|))))) 
(((*1 *1 *2 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *3 (|Mapping| *4 (|Integer|) (|Integer|)))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|MatrixCategory| *4 *5 *6))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| (|OutputForm|))))
       (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|SquareMatrix| *3 *4))
       (|isDomain| *1 (|QuadraticForm| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *5))) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5))
       (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|DataArray| *4 *2)) (|ofType| *4 (|PositiveInteger|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|EltableAggregate| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7))
       (|ofCategory| *6 (|DirectProductCategory| *5 *2))
       (|ofCategory| *7 (|DirectProductCategory| *4 *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *2 *5))
       (|ofCategory| *4 (|Type|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *2 (|FiniteLinearAggregate| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *6 *2 *7))
       (|ofCategory| *6 (|Ring|))
       (|ofCategory| *7 (|DirectProductCategory| *4 *6))
       (|ofCategory| *2 (|DirectProductCategory| *5 *6))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *5 *2))
       (|ofCategory| *4 (|Type|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *2 (|FiniteLinearAggregate| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *6 *7 *2))
       (|ofCategory| *6 (|Ring|))
       (|ofCategory| *7 (|DirectProductCategory| *5 *6))
       (|ofCategory| *2 (|DirectProductCategory| *4 *6))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|ofCategory| *7 (|QuotientFieldCategory| *4))
       (|ofCategory| *2 (|MatrixCategory| *7 *8 *9))
       (|isDomain| *1
        (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *2))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))
       (|ofCategory| *8 (|FiniteLinearAggregate| *7))
       (|ofCategory| *9 (|FiniteLinearAggregate| *7))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|ModularHermitianRowReduction| *3))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *2 *3 *4 *5 *6))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *5 (|DirectProductCategory| *3 *4))
       (|ofCategory| *6 (|DirectProductCategory| *2 *4))
       (|ofCategory| *4 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|))
       (|ofType| *4 *2) (|ofCategory| *5 (|CommutativeRing|))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|ComplexCategory&| *3 *4))
       (|ofCategory| *3 (|ComplexCategory| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *4))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|ofCategory| *6
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|ofCategory| *4
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *4 *3))
       (|ofCategory| *3 (|MatrixCategory| *5 *6 *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *5)) (|isDomain| *4 (|Vector| *5))
       (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|LinearSystemMatrixPackage1| *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *6 (|ShallowlyMutableAggregate| *4))
       (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))
 ((*1 *2 *3)
  (AND (|ofCategory| *9 (|ShallowlyMutableAggregate| *7))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|ofCategory| *7 (|QuotientFieldCategory| *4))
       (|ofCategory| *8 (|FiniteLinearAggregate| *7))
       (|ofCategory| *9 (|FiniteLinearAggregate| *7))
       (|isDomain| *2 (|List| *6))
       (|isDomain| *1
        (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *10))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))
       (|ofCategory| *10 (|MatrixCategory| *7 *8 *9))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7))
       (|ofCategory| *5 (|Ring|))
       (|ofCategory| *6 (|DirectProductCategory| *4 *5))
       (|ofCategory| *7 (|DirectProductCategory| *3 *5))
       (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| *7))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *5))
       (|isDomain| *3 (|List| *5)) (|ofType| *4 (|Symbol|))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *1 (|PolynomialInterpolation| *4 *5))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *5))
       (|isDomain| *1 (|PolynomialInterpolation| *4 *5))
       (|ofType| *4 (|Symbol|))))
 ((*1 *2 *3 *3 *4 *4)
  (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *6 (|Field|))
       (|isDomain| *2 (|Fraction| (|Polynomial| *6)))
       (|isDomain| *1 (|RationalInterpolation| *5 *6))
       (|ofType| *5 (|Symbol|))))) 
(((*1 *2 *2 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|RandomIntegerDistributions|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 |RationalNumber|) (|isDomain| *2 (|Mapping| (|Integer|)))
       (|isDomain| *1 (|RandomIntegerDistributions|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 |RationalNumber|) (|isDomain| *2 (|Mapping| (|Integer|)))
       (|isDomain| *1 (|RandomIntegerDistributions|))))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|)))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 |RationalNumber|) (|isDomain| *2 (|Mapping| (|Integer|)))
       (|isDomain| *1 (|RandomIntegerDistributions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Set| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Mapping| *4))
       (|isDomain| *1 (|RandomDistributions| *4))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|Float|)))
       (|isDomain| *1 (|RandomFloatDistributions|)) (|isDomain| *3 (|Float|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Segment| (|Integer|)))
       (|isDomain| *2 (|Mapping| (|Integer|)))
       (|isDomain| *1 (|RandomIntegerDistributions|))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|RGBColorSpace| *2))
       (|ofCategory| *2 (|AbelianMonoid|))))) 
(((*1 *1) (|isDomain| *1 (|Color|)))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RGBColorModel| *2))
       (|ofCategory| *2 (|AbelianMonoid|))))) 
(((*1 *1) (|isDomain| *1 (|Color|)))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RGBColorModel| *2))
       (|ofCategory| *2 (|AbelianMonoid|))))) 
(((*1 *1) (|isDomain| *1 (|Color|)))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|RGBColorModel| *2))
       (|ofCategory| *2 (|AbelianMonoid|))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|RGBColorModel| *2))
       (|ofCategory| *2 (|AbelianMonoid|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
       (|ofCategory| *4 (|EuclideanDomain|))
       (|isDomain| *2 (|Fraction| (|Factored| (|Polynomial| *4))))
       (|isDomain| *1 (|RationalFunctionFactorizer| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Mapping| (|Float|)))
       (|isDomain| *1 (|RandomFloatDistributions|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Mapping| (|Float|)))
       (|isDomain| *1 (|RandomFloatDistributions|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Mapping| (|Float|)))
       (|isDomain| *1 (|RandomFloatDistributions|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5))
       (|ofCategory| *3 (|Field|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)
       (|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Float|)))
       (|isDomain| *1 (|RandomFloatDistributions|)) (|isDomain| *3 (|Float|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|Float|)))
       (|isDomain| *1 (|RandomFloatDistributions|)) (|isDomain| *3 (|Float|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Float|))
       (|isDomain| *1 (|RandomFloatDistributions|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|RandomFloatDistributions|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|RandomFloatDistributions|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|RandomFloatDistributions|))))) 
(((*1 *2 *3 *4 *2)
  (AND
   (|isDomain| *3
    (|SparseUnivariatePolynomial|
     (|Fraction| (|SparseUnivariatePolynomial| *2))))
   (|isDomain| *4 (|Kernel| *2))
   (|ofCategory| *2
                 (|Join| (|FunctionSpace| *5) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *5
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|GenusZeroIntegration| *5 *2 *6))
   (|ofCategory| *6 (|SetCategory|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|SparseUnivariatePolynomial| *2)))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                              (SIGNATURE |numer| (*7 $))
                              (SIGNATURE |denom| (*7 $)))))
       (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *2))
       (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *5)))))
   (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Fraction| (|Polynomial| *5)))
   (|isDomain| *1 (|RationalFunction| *5))
   (|ofCategory| *5 (|IntegralDomain|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Kernel| *1)) (|ofCategory| *1 (|FunctionSpace| *4))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *1)))))
 ((*1 *2 *3 *4 *4 *5)
  (AND (|isDomain| *4 (|Kernel| *3))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|SparseUnivariatePolynomial|
         (|Fraction| (|SparseUnivariatePolynomial| *3))))
       (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7))
       (|isDomain| *5 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *7 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Variable| *5)) (|ofType| *5 (|Symbol|))
       (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|UnivariatePolynomial| *5 (|Polynomial| *6)))
       (|isDomain| *1 (|PolynomialToUnivariatePolynomial| *5 *6))
       (|isDomain| *3 (|Polynomial| *6))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
       (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4))
       (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *3)))
       (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *3))
       (|ofCategory| *3
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                              (SIGNATURE |numer| (*7 $))
                              (SIGNATURE |denom| (*7 $)))))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *3
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                              (SIGNATURE |numer| (*7 $))
                              (SIGNATURE |denom| (*7 $)))))
       (|ofCategory| *7 (|PolynomialCategory| *6 *5 *4))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|Fraction|
         (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *5)))))
       (|isDomain| *1 (|RationalFunction| *5))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2))
   (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|PolynomialCategory| *5 *4 *2))
   (|ofCategory| *2 (|OrderedSet|))
   (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *2 *5 *6 *3))
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain| (SIGNATURE |coerce| ($ *6))
                          (SIGNATURE |numer| (*6 $))
                          (SIGNATURE |denom| (*6 $)))))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
   (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Symbol|))
   (|isDomain| *1 (|RationalFunction| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *7))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|List| *5))
       (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|List| (|Symbol|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Pattern| *3))) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *5))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
       (|isDomain| *2 (|List| *5))
       (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3))
       (|ofCategory| *3
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                              (SIGNATURE |numer| (*7 $))
                              (SIGNATURE |denom| (*7 $)))))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|List| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
       (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Symbol|)))
       (|isDomain| *1 (|RationalFunction| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *6)))
       (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *6 (|Join| (|IntegralDomain|) (|RetractableTo| *5)))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *6))))))
       (|isDomain| *1 (|RetractSolvePackage| *5 *6))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Kernel| *6))
       (|ofCategory| *6
                     (|Join| (|FunctionSpace| *5) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|SparseUnivariatePolynomial|
         (|Fraction| (|SparseUnivariatePolynomial| *6))))
       (|isDomain| *1 (|GenusZeroIntegration| *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *6))
       (|ofCategory| *7 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|ModMonic| *3 *2)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *3 *4 *4 *5 *6 *7 *8)
  (|partial| AND (|isDomain| *4 (|SparseUnivariatePolynomial| *11))
   (|isDomain| *6 (|List| *10)) (|isDomain| *7 (|List| (|NonNegativeInteger|)))
   (|isDomain| *8 (|List| *11)) (|ofCategory| *10 (|OrderedSet|))
   (|ofCategory| *11 (|EuclideanDomain|))
   (|ofCategory| *9 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|PolynomialCategory| *11 *9 *10))
   (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *5)))
   (|isDomain| *1 (|MultivariateSquareFree| *9 *10 *11 *5))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5))
       (|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofType| *6 (|List| *2))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *1 (|RepeatedSquaring| *2))
       (|ofCategory| *2
                     (|Join| (|SetCategory|)
                             (CATEGORY |domain| (SIGNATURE * ($ $ $)))))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *1 (|RepeatedDoubling| *2))
       (|ofCategory| *2
                     (|Join| (|SetCategory|)
                             (CATEGORY |domain| (SIGNATURE + ($ $ $)))))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Vector| *5))) (|isDomain| *4 (|Integer|))
       (|isDomain| *2 (|Vector| *5))
       (|isDomain| *1 (|RepresentationPackage2| *5))
       (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Finite|))
       (|ofCategory| *5 (|Ring|))))) 
(((*1 *2 *3 *4 *5 *5)
  (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *5 (|Integer|))
       (|ofCategory| *6 (|Field|)) (|ofCategory| *6 (|Finite|))
       (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|Matrix| *6))))
       (|isDomain| *1 (|RepresentationPackage2| *6))
       (|isDomain| *3 (|List| (|Matrix| *6)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|Finite|))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|Matrix| *4))))
       (|isDomain| *1 (|RepresentationPackage2| *4))
       (|isDomain| *3 (|List| (|Matrix| *4)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|Field|))
       (|ofCategory| *5 (|Finite|)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|Matrix| *5))))
       (|isDomain| *1 (|RepresentationPackage2| *5))
       (|isDomain| *3 (|List| (|Matrix| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Field|))
       (|ofCategory| *5 (|Finite|)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|List| (|List| (|Matrix| *5))))
       (|isDomain| *1 (|RepresentationPackage2| *5))
       (|isDomain| *3 (|List| (|Matrix| *5)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Matrix| *5))) (|isDomain| *4 (|Integer|))
       (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|RepresentationPackage2| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|ofCategory| *4 (|Field|))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|RepresentationPackage2| *4))))) 
(((*1 *2 *3 *3 *4 *5)
  (AND (|isDomain| *3 (|List| (|Matrix| *6))) (|isDomain| *4 (|Boolean|))
       (|isDomain| *5 (|Integer|)) (|isDomain| *2 (|Matrix| *6))
       (|isDomain| *1 (|RepresentationPackage2| *6))
       (|ofCategory| *6 (|Field|)) (|ofCategory| *6 (|Ring|))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|isDomain| *2 (|Matrix| *4))
       (|isDomain| *1 (|RepresentationPackage2| *4))
       (|ofCategory| *4 (|Field|)) (|ofCategory| *4 (|Ring|))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *3 (|List| (|Matrix| *5))) (|isDomain| *4 (|Integer|))
       (|isDomain| *2 (|Matrix| *5))
       (|isDomain| *1 (|RepresentationPackage2| *5))
       (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|Ring|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Matrix| *5))) (|isDomain| *4 (|Vector| *5))
       (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Matrix| *5))
       (|isDomain| *1 (|RepresentationPackage2| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Matrix| *5)))
       (|ofCategory| *5 (|EuclideanDomain|)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Vector| (|Vector| *5)))
       (|isDomain| *1 (|RepresentationPackage2| *5))
       (|isDomain| *4 (|Vector| *5))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|List| (|Matrix| *4))) (|isDomain| *2 (|Matrix| *4))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage2| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| (|Vector| *4))) (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|Matrix| *4))
       (|isDomain| *1 (|RepresentationPackage2| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Permutation| (|Integer|))) (|isDomain| *4 (|Integer|))
       (|isDomain| *2 (|Matrix| *4))
       (|isDomain| *1 (|RepresentationPackage1| *5))
       (|ofCategory| *5 (|Ring|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|Matrix| (|Integer|)))
       (|isDomain| *1 (|RepresentationPackage1| *4))
       (|ofCategory| *4 (|Ring|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Permutation| (|Integer|))))
       (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| (|Matrix| *4)))
       (|isDomain| *1 (|RepresentationPackage1| *5))
       (|ofCategory| *5 (|Ring|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|List| (|Integer|))))
       (|isDomain| *2 (|List| (|Matrix| (|Integer|))))
       (|isDomain| *1 (|RepresentationPackage1| *4))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *3))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|List| (|Matrix| *3))) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|Matrix| *3))) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *3))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| (|Matrix| *4)))
       (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Matrix| (|Polynomial| *4)))
       (|isDomain| *1 (|RepresentationPackage1| *4))
       (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|PositiveInteger|))
       (|has| *4 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| (|Matrix| *4)))
       (|isDomain| *3 (|PositiveInteger|))
       (|has| *4 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|RepresentationPackage1| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))
       (|isDomain| *2 (|List| (|Matrix| (|Expression| (|Integer|)))))
       (|isDomain| *1 (|RadicalEigenPackage|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|Matrix| (|Expression| (|Integer|)))))
       (|isDomain| *1 (|RadicalEigenPackage|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Matrix| (|Expression| (|Integer|))))
       (|isDomain| *1 (|RadicalEigenPackage|))))) 
(((*1 *2 *3)
  (|partial| AND
   (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))
   (|isDomain| *2 (|Matrix| (|Expression| (|Integer|))))
   (|isDomain| *1 (|RadicalEigenPackage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))
       (|isDomain| *2 (|List| (|Expression| (|Integer|))))
       (|isDomain| *1 (|RadicalEigenPackage|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))
       (|isDomain| *2 (|List| (|Matrix| (|Expression| (|Integer|)))))
       (|isDomain| *1 (|RadicalEigenPackage|))
       (|isDomain| *3 (|Expression| (|Integer|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| (|Integer|)))))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |radval| (|Expression| (|Integer|)))
                   (|:| |radmult| (|Integer|))
                   (|:| |radvect|
                        (|List| (|Matrix| (|Expression| (|Integer|))))))))
       (|isDomain| *1 (|RadicalEigenPackage|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *1 *2 *2)
  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Reference| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *1 *2) (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1) (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|Field|)) (|isDomain| *1 (|ReductionOfOrder| *3 *2))
       (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *3))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|Record| (|:| |eq| *3) (|:| |op| (|List| *5))))
       (|isDomain| *1 (|ReductionOfOrder| *5 *3)) (|isDomain| *4 (|List| *5))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(((*1 *1 *2 *3)
  (AND
   (|isDomain| *2
    (|RightOpenIntervalRootCharacterization| #1=(|RealClosure| *4)
                                             (|SparseUnivariatePolynomial|
                                              #1#)))
   (|isDomain| *3 (|OutputForm|)) (|isDomain| *1 (|RealClosure| *4))
   (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|) (|RealConstant|)))))) 
(((*1 *2 *1)
  (|partial| AND
   (|isDomain| *2
    (|RightOpenIntervalRootCharacterization| #1=(|RealClosure| *3)
                                             (|SparseUnivariatePolynomial|
                                              #1#)))
   (|isDomain| *1 (|RealClosure| *3))
   (|ofCategory| *3 (|Join| (|OrderedRing|) (|Field|) (|RealConstant|)))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |left| (|Fraction| (|Integer|)))
               (|:| |right| (|Fraction| (|Integer|))))))
   (|isDomain| *1 (|RealZeroPackage| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |left| (|Fraction| (|Integer|)))
               (|:| |right| (|Fraction| (|Integer|))))))
   (|isDomain| *1 (|RealZeroPackage| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))
   (|isDomain| *4
    (|Record| (|:| |left| (|Fraction| (|Integer|)))
              (|:| |right| (|Fraction| (|Integer|)))))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |left| #1=(|Fraction| (|Integer|))) (|:| |right| #1#))))
   (|isDomain| *1 (|RealZeroPackage| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))
   (|isDomain| *4 (|Fraction| (|Integer|)))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Fraction| (|Integer|)))
       (|isDomain| *2 (|List| (|Record| (|:| |left| *5) (|:| |right| *5))))
       (|isDomain| *1 (|RealZeroPackage| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))
       (|isDomain| *4 (|Record| (|:| |left| *5) (|:| |right| *5)))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |left| (|Fraction| (|Integer|)))
               (|:| |right| (|Fraction| (|Integer|))))))
   (|isDomain| *1 (|RealZeroPackageQ| *3))
   (|ofCategory| *3
                 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |left| (|Fraction| (|Integer|)))
               (|:| |right| (|Fraction| (|Integer|))))))
   (|isDomain| *1 (|RealZeroPackageQ| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))
   (|isDomain| *4
    (|Record| (|:| |left| (|Fraction| (|Integer|)))
              (|:| |right| (|Fraction| (|Integer|)))))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Fraction| (|Integer|)))
       (|isDomain| *2 (|List| (|Record| (|:| |left| *4) (|:| |right| *4))))
       (|isDomain| *1 (|RealZeroPackageQ| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Fraction| (|Integer|)))
       (|isDomain| *2 (|List| (|Record| (|:| |left| *5) (|:| |right| *5))))
       (|isDomain| *1 (|RealZeroPackageQ| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *4 (|Record| (|:| |left| *5) (|:| |right| *5)))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |left| (|Fraction| (|Integer|)))
               (|:| |right| (|Fraction| (|Integer|))))))
   (|isDomain| *2 (|List| (|Fraction| (|Integer|))))
   (|isDomain| *1 (|RealZeroPackage| *4))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Record| (|:| |left| #1=(|Fraction| (|Integer|))) (|:| |right| #1#)))
   (|isDomain| *2 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|RealZeroPackage| *4))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Vector| *6)) (|isDomain| *4 (|Vector| (|Integer|)))
       (|isDomain| *5 (|Integer|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|Mapping| *6))
       (|isDomain| *1 (|RandomDistributions| *6))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|Record| (|:| |value| *4) (|:| |weight| (|Integer|)))))
   (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Mapping| *4))
   (|isDomain| *1 (|RandomDistributions| *4))))) 
(((*1 *2 *3 *3 *3)
  (|partial| AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2 (|List| (|Fraction| *5)))
   (|isDomain| *1 (|TranscendentalRischDESystem| *4 *5))
   (|isDomain| *3 (|Fraction| *5))))) 
(((*1 *2 *3 *3 *3 *4)
  (|partial| AND (|isDomain| *4 (|Mapping| *6 *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |a| *6) (|:| |b| #1=(|Fraction| *6)) (|:| |h| *6)
              (|:| |c1| #1#) (|:| |c2| #1#) (|:| |t| *6)))
   (|isDomain| *1 (|TranscendentalRischDESystem| *5 *6))
   (|isDomain| *3 (|Fraction| *6))))) 
(((*1 *2 *3 *3 *3 *4 *5)
  (AND (|isDomain| *5 (|Mapping| *3 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *6))
       (|ofCategory| *6
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| *4)))
       (|isDomain| *4 (|Integer|))
       (|isDomain| *2
        (|Union|
         (|:| |ans| (|Record| (|:| |ans| *3) (|:| |nosol| (|Boolean|))))
         (|:| |eq|
              (|Record| (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3)
                        (|:| |beta| *3)))))
       (|isDomain| *1 (|TranscendentalRischDE| *6 *3))))) 
(((*1 *2 *3 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2
    (|Record| (|:| |ans| (|Fraction| *5)) (|:| |nosol| (|Boolean|))))
   (|isDomain| *1 (|TranscendentalRischDE| *4 *5))
   (|isDomain| *3 (|Fraction| *5))))) 
(((*1 *2 *3 *3 *4)
  (|partial| AND (|isDomain| *4 (|Mapping| *6 *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |a| *6) (|:| |b| #1=(|Fraction| *6)) (|:| |c| #1#)
              (|:| |t| *6)))
   (|isDomain| *1 (|TranscendentalRischDE| *5 *6))
   (|isDomain| *3 (|Fraction| *6))))) 
(((*1 *2 *3 *4 *4 *4 *5 *6 *7)
  (|partial| AND (|isDomain| *5 (|Symbol|))
   (|isDomain| *6
    (|Mapping|
     (|Union|
      (|Record| (|:| |mainpart| *4)
                (|:| |limitedlogs|
                     (|List| (|Record| (|:| |coeff| *4) (|:| |logand| *4)))))
      "failed")
     *4 (|List| *4)))
   (|isDomain| *7
    (|Mapping|
     (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) "failed") *4 *4))
   (|ofCategory| *4
                 (|Join| (|TranscendentalFunctionCategory|)
                         (|AlgebraicallyClosedField|) (|FunctionSpace| *8)))
   (|ofCategory| *8
                 (|Join| (|GcdDomain|) (|CharacteristicZero|)
                         (|RetractableTo| *3) (|LinearlyExplicitRingOver| *3)))
   (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|List| *4))
   (|isDomain| *1 (|ElementaryRischDESystem| *8 *4))))) 
(((*1 *2 *3 *4 *4 *5 *6 *7)
  (AND (|isDomain| *5 (|Symbol|))
       (|isDomain| *6
        (|Mapping|
         (|Union|
          (|Record| (|:| |mainpart| *4)
                    (|:| |limitedlogs|
                         (|List|
                          (|Record| (|:| |coeff| *4) (|:| |logand| *4)))))
          "failed")
         *4 (|List| *4)))
       (|isDomain| *7
        (|Mapping|
         (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) "failed") *4
         *4))
       (|ofCategory| *4
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|AlgebraicallyClosedField|)
                             (|FunctionSpace| *8)))
       (|ofCategory| *8
                     (|Join| (|GcdDomain|) (|CharacteristicZero|)
                             (|RetractableTo| *3)
                             (|LinearlyExplicitRingOver| *3)))
       (|isDomain| *3 (|Integer|))
       (|isDomain| *2
        (|Record| (|:| |ans| *4) (|:| |right| *4) (|:| |sol?| (|Boolean|))))
       (|isDomain| *1 (|ElementaryRischDE| *8 *4))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3))
       (|isDomain| *2 (|Integer|))))
 ((*1 *1 *1) (|ofCategory| *1 (|RadicalCategory|)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|ofCategory| *1 (|RealClosedField|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RealClosedField|))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *1 *1) (|ofCategory| *1 (|RealClosedField|)))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|RealClosedField|))
   (|isDomain| *2 (|OutputForm|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
   (|ofCategory| *1 (|RealClosedField|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
   (|ofCategory| *1 (|RealClosedField|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|RecursiveAggregate| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|List| *3))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *3 (|BasicType|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *3 (|BasicType|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|ComplexCategory| *3))
   (|ofCategory| *3 (|CommutativeRing|))
   (|ofCategory| *3 (|IntegerNumberSystem|))
   (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegerNumberSystem|))
   (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|IntegerNumberSystem|))
   (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|OctonionCategory| *3))
   (|ofCategory| *3 (|CommutativeRing|))
   (|ofCategory| *3 (|IntegerNumberSystem|))
   (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|OnePointCompletion| *3))
   (|ofCategory| *3 (|IntegerNumberSystem|))
   (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|OrderedCompletion| *3))
   (|ofCategory| *3 (|IntegerNumberSystem|))
   (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|QuaternionCategory| *3))
   (|ofCategory| *3 (|CommutativeRing|))
   (|ofCategory| *3 (|IntegerNumberSystem|))
   (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *2 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|RationalRetractions| *3))
   (|ofCategory| *3 (|RetractableTo| *2))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Factored| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OnePointCompletion| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedCompletion| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RationalRetractions| *3))
       (|ofCategory| *3 (|RetractableTo| (|Fraction| (|Integer|))))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|Factored| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntegerNumberSystem|))
       (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|OnePointCompletion| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|OrderedCompletion| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|isDomain| *2 (|Fraction| (|Integer|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|RationalRetractions| *3))
       (|ofCategory| *3 (|RetractableTo| *2))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|RandomNumberSource|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|RandomNumberSource|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Integer|))) (|isDomain| *4 (|Integer|))
       (|isDomain| *2 (|Any|)) (|isDomain| *1 (|RadixUtilities|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| (|Integer|)))
       (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))) 
(((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|RadixExpansion| *3)) (|ofType| *3 (|Integer|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Factored| *5)) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *5)
                  (|:| |radicand| (|List| *5))))
       (|isDomain| *1 (|FactoredFunctions| *5))
       (|isDomain| *4 (|NonNegativeInteger|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Integer|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Queue| *3))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|Group|)))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|PartitionsAndPermutations|))))
 ((*1 *1 *1) (|isDomain| *1 (|Partition|)))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *1 *2 *2 *2 *2)
  (AND (|ofCategory| *1 (|QuaternionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|SquareMatrix| *3 *4)) (|ofType| *3 (|PositiveInteger|))
       (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|QuadraticForm| *3 *4))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|SparseMultivariatePolynomial| (|Integer|)
                                    (|Kernel| (|AlgebraicNumber|))))
   (|isDomain| *1 (|AlgebraicNumber|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Vector| *6))
       (|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6))
       (|ofCategory| *6
                     (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
       (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|SparseMultivariatePolynomial| (|Integer|)
                                    (|Kernel| (|InnerAlgebraicNumber|))))
   (|isDomain| *1 (|InnerAlgebraicNumber|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|Algebra| *3))
       (|isDomain| *1 (|LocalAlgebra| *2 *3 *4))
       (|ofCategory| *4 (|SubsetCategory| (|Monoid|) *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|Module| *3))
       (|isDomain| *1 (|Localize| *2 *3 *4))
       (|ofCategory| *4 (|SubsetCategory| (|Monoid|) *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|SparseMultivariatePolynomial| (|Integer|)
                                    (|Kernel| (|AlgebraicNumber|))))
   (|isDomain| *1 (|AlgebraicNumber|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|QuotientFieldCategory| *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *2 (|EuclideanDomain|))
       (|isDomain| *1 (|FractionalIdeal| *2 *3 *4 *5))
       (|ofCategory| *5
                     (|Join| (|FramedAlgebra| *3 *4) (|RetractableTo| *3)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1)))
       (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|SparseMultivariatePolynomial| (|Integer|)
                                    (|Kernel| (|InnerAlgebraicNumber|))))
   (|isDomain| *1 (|InnerAlgebraicNumber|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4))
       (|isDomain| *1 (|LocalAlgebra| *3 *4 *2))
       (|ofCategory| *3 (|Algebra| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *2 (|SubsetCategory| (|Monoid|) *4))
       (|isDomain| *1 (|Localize| *3 *4 *2)) (|ofCategory| *3 (|Module| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))
 ((*1 *1) (|ofCategory| *1 (|Finite|)))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *4))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))
 ((*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))
 ((*1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))
 ((*1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|)))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Permutation| *3))
       (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Permutation| *4))
       (|isDomain| *1 (|PermutationGroup| *4))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|QuotientFieldCategory| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *2)
  (AND
   (|isDomain| *2
    (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| *3)
                         (|DirectProduct| *4 (|NonNegativeInteger|))
                         (|DistributedMultivariatePolynomial| *3
                                                              (|Fraction|
                                                               (|Integer|)))))
   (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|NonNegativeInteger|))
   (|isDomain| *1 (|QuasiAlgebraicSet2| *3 *4))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *6 *5))
       (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|QuasiAlgebraicSet| *4 *5 *6 *3))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Union| (|Boolean|) "failed"))
       (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4))
       (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *2))
       (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *2 (|GcdDomain|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|QuasiAlgebraicSet| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *4 *2 *3 *5))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|ofCategory| *5 (|MonogenicAlgebra| *2 *3))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $)))))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *3 *5 *2))
       (|ofCategory| *2
                     (|PolynomialCategory| (|Fraction| (|Polynomial| *5)) *4
                                           *3))))
 ((*1 *2 *2 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $))
                              (SIGNATURE |variable|
                               ((|Union| $ #1="failed") (|Symbol|))))))
       (|isDomain| *1 (|PushVariables| *4 *5 *3 *2))
       (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *3))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| *6))
       (|ofCategory| *6
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $))
                              (SIGNATURE |variable|
                               ((|Union| $ #1#) (|Symbol|))))))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|PushVariables| *4 *5 *6 *2))
       (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *6))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $)))))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *3 *5 *2))
       (|ofCategory| *2
                     (|PolynomialCategory| (|Fraction| (|Polynomial| *5)) *4
                                           *3))))
 ((*1 *2 *2 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $))
                              (SIGNATURE |variable|
                               ((|Union| $ #1="failed") (|Symbol|))))))
       (|isDomain| *1 (|PushVariables| *4 *5 *3 *2))
       (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *3))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| *6))
       (|ofCategory| *6
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $))
                              (SIGNATURE |variable|
                               ((|Union| $ #1#) (|Symbol|))))))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|PushVariables| *4 *5 *6 *2))
       (|ofCategory| *2 (|PolynomialCategory| (|Polynomial| *4) *5 *6))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
   (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
   (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
   (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
   (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
   (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
   (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
   (|ofCategory| *2 (|TranscendentalFunctionCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *1 (|PartialTranscendentalFunctions| *2))
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       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|List| *5))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *3 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))
       (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))
       (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))
       (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3))
       (|ofCategory| *1 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|Permutation| *3)))
       (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3))
       (|isDomain| *2
        (|Record| (|:| |under| *1) (|:| |floor| *1) (|:| |upper| *1)))
       (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *3 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4)))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *6 *3))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |rnum| *4) (|:| |polnum| *3) (|:| |den| *4)))))) 
(((*1 *2 *2 *1)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *2 *2 *1)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|))
       (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|))
       (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|))
       (|isDomain| *2 (|Segment| (|DoubleFloat|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|))
       (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|))
       (|isDomain| *2 (|Segment| (|DoubleFloat|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|))
       (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|))
       (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|OrderedAbelianMonoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *3 *2)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *6
                     (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))
       (|ofType| *7
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *6))
                   (|Record| (|:| |index| *5) (|:| |exponent| *6))))
       (|isDomain| *2 (|ModuleMonomial| *5 *6 *7))
       (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *8))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *8
                     (|PolynomialCategory| *4 *6 (|OrderedVariableList| *3)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|Monoid|)) (|ofCategory| *2 (|OrderedSet|))
       (|isDomain| *1 (|MonoidRing| *3 *2)) (|ofCategory| *3 (|Ring|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *1 *2 *3)
  (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|OrderedAbelianMonoid|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|CliffordAlgebra| *4 *2 *5))
       (|ofType| *4 (|PositiveInteger|)) (|ofCategory| *2 (|Field|))
       (|ofType| *5 (|QuadraticForm| *4 *2))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|ModuleMonomial| *5 *6 *7))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6
                     (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|)))
       (|ofType| *7
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *6))
                   (|Record| (|:| |index| *5) (|:| |exponent| *6))))
       (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *6 *7 *8))
       (|ofCategory| *8
                     (|PolynomialCategory| *2 *6 (|OrderedVariableList| *4)))))
 ((*1 *1 *2 *3)
  (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3))
       (|ofCategory| *2 (|BasicType|)) (|ofCategory| *3 (|OrderedType|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|LaurentPolynomial| *2 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MonogenicLinearOperator| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|MonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|Monoid|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *5))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *2))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *6))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *2))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 (|List| *5))
       (|ofCategory| *1 (|PowerSeriesCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoid|))
       (|ofCategory| *6 (|OrderedSet|))))
 ((*1 *1 *1 *2 *3)
  (AND (|ofCategory| *1 (|PowerSeriesCategory| *4 *3 *2))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InnerTaylorSeries| *3))
       (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|ContinuedFraction| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2)))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))
       (|ofCategory| *4 (|OrderedSet|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|Partition|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|Partition|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Stream| (|Partition|))) (|isDomain| *1 (|Partition|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2 (|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))))
   (|isDomain| *1 (|Partition|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|Partition|))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |resultant| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |resultant| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *2 *2 *2 *3)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *2 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|EuclideanDomain|))))
 ((*1 *2 *1 *1)
  (|partial| AND (|ofCategory| *3 (|SetCategory|))
   (|isDomain| *2 (|Record| (|:| |lm| *1) (|:| |rm| *1)))
   (|ofCategory| *1 (|FreeMonoidCategory| *3))))
 ((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |quotient| #1=(|NonNegativeInteger|))
              (|:| |remainder| #1#)))
   (|isDomain| *1 (|NonNegativeInteger|))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |resultantReduit| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3)
                  (|:| |resultantReduit| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|GcdDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |discriminant| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |discriminant| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |gcd| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |gcd| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |gcd| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |subResultant| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |subResultant| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |subResultant| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3)))
       (|isDomain| *1 (|PseudoRemainderSequence| *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef1| *3) (|:| |resultant| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Record| (|:| |coef2| *3) (|:| |resultant| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *3) (|:| |coef2| *3) (|:| |resultant| *4)))
       (|isDomain| *1 (|PseudoRemainderSequence| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|FloatingPointSystem|))
       (|not| (|has| *1 (ATTRIBUTE |arbitraryPrecision|)))
       (|not| (|has| *1 (ATTRIBUTE |arbitraryExponent|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteSetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1) (|ofCategory| *1 (|OrderedFinite|)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|OrderedType|)))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2))
       (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2 *1 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3))
       (|ofCategory| *1 (|ExtensibleLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *1) (|ofCategory| *1 (|PropositionalLogic|)))) 
(((*1 *1) (|ofCategory| *1 (|PropositionalLogic|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|PropositionalLogic|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|PropositionalLogic|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|LinearBasis| *3)) (|ofType| *3 (|List| (|Symbol|)))
       (|isDomain| *1 (|DualBasis| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|DualBasis| *3)) (|ofType| *3 (|List| (|Symbol|)))
       (|isDomain| *1 (|LinearBasis| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|PropositionalFormulaFunctions1| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|PatternMatchResult| *3 *4))
       (|isDomain| *1 (|PatternMatchListResult| *3 *4 *5))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *5 (|ListAggregate| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|PropositionalFormula| *4))
       (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Set| *4))
       (|isDomain| *1 (|PropositionalFormulaFunctions1| *4))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| *3)) (|isDomain| *1 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| (|PropositionalFormula| *3)))
       (|isDomain| *1 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| (|Pair| #1=(|PropositionalFormula| *3) #1#)))
       (|isDomain| *1 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| (|Pair| #1=(|PropositionalFormula| *3) #1#)))
       (|isDomain| *1 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| (|Pair| #1=(|PropositionalFormula| *3) #1#)))
       (|isDomain| *1 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| (|Pair| #1=(|PropositionalFormula| *3) #1#)))
       (|isDomain| *1 (|PropositionalFormula| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|PropositionalFormula| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|PropositionalFormula| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| (|None|)))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *2 *1 *3)
  (|partial| AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|None|))
   (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|SExpression|))
       (|isDomain| *1 (|Property|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|Product| *2 *3)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|Product| *2 *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|SetCategory|)) (|isDomain| *1 (|Product| *3 *2))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|PrintPackage|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|IntegerPrimesPackage| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *1 (|IntegerPrimesPackage| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *1 (|IntegerPrimesPackage| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|)))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|FunctionSpace| *4))
       (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|Record| (|:| |primelt| *5)
                  (|:| |poly| (|List| (|SparseUnivariatePolynomial| *5)))
                  (|:| |prim| (|SparseUnivariatePolynomial| *5))))
       (|isDomain| *1 (|FunctionSpacePrimitiveElement| *4 *5))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|Record| (|:| |primelt| *3)
                  (|:| |pol1| (|SparseUnivariatePolynomial| *3))
                  (|:| |pol2| (|SparseUnivariatePolynomial| *3))
                  (|:| |prim| (|SparseUnivariatePolynomial| *3))))
       (|isDomain| *1 (|FunctionSpacePrimitiveElement| *4 *3))
       (|ofCategory| *3 (|AlgebraicallyClosedField|))
       (|ofCategory| *3 (|FunctionSpace| *4))))
 ((*1 *2 *3 *4 *3 *4)
  (AND (|isDomain| *3 (|Polynomial| *5)) (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|))
                  (|:| |prim| (|SparseUnivariatePolynomial| *5))))
       (|isDomain| *1 (|PrimitiveElement| *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|Record| (|:| |coef| (|List| (|Integer|)))
                  (|:| |poly| (|List| (|SparseUnivariatePolynomial| *5)))
                  (|:| |prim| (|SparseUnivariatePolynomial| *5))))
       (|isDomain| *1 (|PrimitiveElement| *5))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|List| (|Polynomial| *6)))
       (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *5 (|Symbol|))
       (|ofCategory| *6 (|Join| (|Field|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|Record| (|:| |coef| (|List| (|Integer|)))
                  (|:| |poly| (|List| (|SparseUnivariatePolynomial| *6)))
                  (|:| |prim| (|SparseUnivariatePolynomial| *6))))
       (|isDomain| *1 (|PrimitiveElement| *6))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *1 (|IntegrationResult| *2))
       (|ofCategory| *2 (|RetractableTo| *3)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *2 *2)
  (AND (|isDomain| *1 (|IntegrationResult| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *4 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|SegmentBinding| *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *4 *2))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PrimitiveFunctionCategory|))
       (|isDomain| *2 (|Symbol|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|SegmentBinding| *1))
       (|ofCategory| *1 (|PrimitiveFunctionCategory|))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|PositiveInteger|))
   (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Matrix| *5))
   (|isDomain| *1 (|PrecomputedAssociatedEquations| *5 *3))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|PortNumber|))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|))
       (|ofCategory| *3 (|PolynomialCategory| *7 *5 *6))
       (|isDomain| *2
        (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *3)
                  (|:| |radicand| (|List| *3))))
       (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *3 *8))
       (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *8
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *3))
                              (SIGNATURE |numer| (*3 $))
                              (SIGNATURE |denom| (*3 $)))))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *7 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|))
       (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6))
       (|isDomain| *2
        (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *3)
                  (|:| |radicand| *3)))
       (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *8 *3))
       (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *3
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *8))
                              (SIGNATURE |numer| (*8 $))
                              (SIGNATURE |denom| (*8 $)))))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Integer|)))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|IntegralDomain|))
       (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6))
       (|isDomain| *2
        (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *9)
                  (|:| |radicand| *9)))
       (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *8 *9))
       (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *9
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *8))
                              (SIGNATURE |numer| (*8 $))
                              (SIGNATURE |denom| (*8 $)))))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *7 (|PolynomialCategory| *3 *5 *6))
       (|isDomain| *2
        (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *8)
                  (|:| |radicand| *8)))
       (|isDomain| *1 (|PolynomialRoots| *5 *6 *3 *7 *8))
       (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *8
                     (|Join| (|Field|)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                              (SIGNATURE |numer| (*7 $))
                              (SIGNATURE |denom| (*7 $)))))))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|))
   (|isDomain| *2 (|Record| (|:| |val| *1) (|:| |exponent| (|Integer|))))
   (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (|partial| AND
   (|isDomain| *2
    (|Record| (|:| |val| #1=(|Pattern| *3)) (|:| |exponent| #1#)))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
   (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
   (|isDomain| *2 (|Record| (|:| |val| *3) (|:| |exponent| (|Integer|))))
   (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3))
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                          (SIGNATURE |numer| (*7 $))
                          (SIGNATURE |denom| (*7 $)))))))) 
(((*1 *2 *1 *3)
  (|partial| AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Ring|))
   (|ofCategory| *4 (|SetCategory|))
   (|isDomain| *2
    (|Record| (|:| |var| (|Kernel| *1)) (|:| |exponent| (|Integer|))))
   (|ofCategory| *1 (|FunctionSpace| *4))))
 ((*1 *2 *1 *3)
  (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Ring|))
   (|ofCategory| *4 (|SetCategory|))
   (|isDomain| *2
    (|Record| (|:| |var| (|Kernel| *1)) (|:| |exponent| (|Integer|))))
   (|ofCategory| *1 (|FunctionSpace| *4))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|SemiGroup|))
   (|ofCategory| *3 (|SetCategory|))
   (|isDomain| *2
    (|Record| (|:| |var| (|Kernel| *1)) (|:| |exponent| (|Integer|))))
   (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (|partial| AND
   (|isDomain| *2
    (|Record| (|:| |val| (|Pattern| *3))
              (|:| |exponent| (|NonNegativeInteger|))))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *2
    (|Record| (|:| |var| *5) (|:| |exponent| (|NonNegativeInteger|))))))
 ((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
   (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
   (|isDomain| *2 (|Record| (|:| |var| *5) (|:| |exponent| (|Integer|))))
   (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3))
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                          (SIGNATURE |numer| (*7 $))
                          (SIGNATURE |denom| (*7 $)))))))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|SemiGroup|))
   (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *1))
   (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3)))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|Ring|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
   (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
   (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
   (|isDomain| *2 (|List| *3))
   (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3))
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                          (SIGNATURE |numer| (*7 $))
                          (SIGNATURE |denom| (*7 $)))))))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|AbelianSemiGroup|))
   (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *1))
   (|ofCategory| *1 (|FunctionSpace| *3))))
 ((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3)))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|Ring|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
   (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
   (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
   (|isDomain| *2 (|List| *3))
   (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3))
   (|ofCategory| *3
                 (|Join| (|Field|)
                         (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                          (SIGNATURE |numer| (*7 $))
                          (SIGNATURE |denom| (*7 $)))))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|FreeModuleCat| *3 *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|MonoidRing| *3 *4)))
       (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|Monoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *6))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *6))
       (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3))
       (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *2 (|GcdDomain|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|)))
       (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|HeuGcd| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|GcdDomain|))))) 
(((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|Integer|))
       (|ofCategory| *5 (|OrderedRing|)) (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *5 *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|OrderedRing|))
       (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|OrderedRing|))
       (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *5)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *5))
       (|isDomain| *1 (|PolToPol| *4 *5)) (|ofType| *4 (|List| (|Symbol|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *4 *5))
       (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Polynomial| *5)) (|isDomain| *1 (|PolToPol| *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|HomogeneousDistributedMultivariatePolynomial| *4 *5))
       (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Polynomial| *5)) (|isDomain| *1 (|PolToPol| *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *5)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|HomogeneousDistributedMultivariatePolynomial| *4 *5))
       (|isDomain| *1 (|PolToPol| *4 *5)) (|ofType| *4 (|List| (|Symbol|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|HomogeneousDistributedMultivariatePolynomial| *4 *5))
       (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *5))
       (|isDomain| *1 (|PolToPol| *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *4 *5))
       (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|HomogeneousDistributedMultivariatePolynomial| *4 *5))
       (|isDomain| *1 (|PolToPol| *4 *5))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *1 (|CyclotomicPolynomialPackage|))
       (|isDomain| *3 (|Integer|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|PolynomialNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *4 *2 *5)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| (|Pattern| *6)))
       (|isDomain| *5
        (|Mapping| #1=(|PatternMatchResult| *6 *8) *8 (|Pattern| *6) #1#))
       (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *8
                     (|Join| (|Ring|) (|ConvertibleTo| (|Pattern| *6))
                             (|RetractableTo| *7)))
       (|isDomain| *2 (|PatternMatchResult| *6 *8)) (|ofCategory| *7 (|Ring|))
       (|isDomain| *1 (|PatternMatchTools| *6 *7 *8))))) 
(((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *5 *3))
       (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *3 (|ComplexCategory| *6))
       (|ofCategory| (|Polynomial| *6) (|PatternMatchable| *5))
       (|ofCategory| *6 (|Join| (|PatternMatchable| *5) (|CommutativeRing|)))
       (|isDomain| *1 (|ComplexPatternMatch| *5 *6 *3))))
 ((*1 *2 *1 *3 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *4 *1))
       (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *1 (|PatternMatchable| *4))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *5 *6))
       (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|Join| (|SetCategory|) (|RetractableTo| *3)))
       (|ofCategory| *3 (|PatternMatchable| *5))
       (|isDomain| *1 (|PatternMatchPushDown| *5 *3 *6))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *5 *3))
       (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| *6) (|ConvertibleTo| *4)
                             (|PatternMatchable| *5)
                             (|RetractableTo| (|Kernel| $))))
       (|isDomain| *4 (|Pattern| *5))
       (|ofCategory| *6 (|Join| (|IntegralDomain|) (|PatternMatchable| *5)))
       (|isDomain| *1 (|PatternMatchFunctionSpace| *5 *6 *3))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| (|Integer|) *3))
       (|isDomain| *4 (|Pattern| (|Integer|)))
       (|ofCategory| *3 (|IntegerNumberSystem|))
       (|isDomain| *1 (|PatternMatchIntegerNumberSystem| *3))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *5 *6))
       (|isDomain| *3 (|Kernel| *6)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6
                     (|Join| (|SetCategory|) (|RetractableTo| (|Kernel| $))
                             (|ConvertibleTo| *4) (|PatternMatchable| *5)))
       (|isDomain| *4 (|Pattern| *5))
       (|isDomain| *1 (|PatternMatchKernel| *5 *6))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchListResult| *5 *6 *3))
       (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|PatternMatchable| *5))
       (|ofCategory| *3 (|ListAggregate| *6))
       (|isDomain| *1 (|PatternMatchListAggregate| *5 *6 *3))))
 ((*1 *2 *3 *4 *2 *5)
  (AND
   (|isDomain| *5
    (|Mapping| #1=(|PatternMatchResult| *6 *3) *8 (|Pattern| *6) #1#))
   (|ofCategory| *8 (|OrderedSet|))
   (|isDomain| *2 (|PatternMatchResult| *6 *3)) (|isDomain| *4 (|Pattern| *6))
   (|ofCategory| *6 (|SetCategory|))
   (|ofCategory| *3
                 (|Join| (|PolynomialCategory| *9 *7 *8) (|ConvertibleTo| *4)))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *9 (|Join| (|Ring|) (|PatternMatchable| *6)))
   (|isDomain| *1 (|PatternMatchPolynomialCategory| *6 *7 *8 *9 *3))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *5 *3))
       (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *3
                     (|Join| (|PolynomialCategory| *8 *6 *7)
                             (|ConvertibleTo| *4)))
       (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *7 (|PatternMatchable| *5))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|Join| (|Ring|) (|PatternMatchable| *5)))
       (|isDomain| *1 (|PatternMatchPolynomialCategory| *5 *6 *7 *8 *3))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *5 *3))
       (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *3 (|QuotientFieldCategory| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|) (|PatternMatchable| *5)
                             (|ConvertibleTo| *4)))
       (|isDomain| *4 (|Pattern| *5))
       (|isDomain| *1 (|PatternMatchQuotientFieldCategory| *5 *6 *3))))
 ((*1 *2 *3 *4 *2)
  (AND (|isDomain| *2 (|PatternMatchResult| *5 (|Symbol|)))
       (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Pattern| *5))
       (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *1 (|PatternMatchSymbol| *5))))
 ((*1 *2 *3 *4 *5 *2 *6)
  (AND (|isDomain| *4 (|List| (|Pattern| *7)))
       (|isDomain| *5 (|Mapping| *9 (|List| *9)))
       (|isDomain| *6
        (|Mapping| #2=(|PatternMatchResult| *7 *9) *9 (|Pattern| *7) #2#))
       (|ofCategory| *7 (|SetCategory|))
       (|ofCategory| *9
                     (|Join| (|Ring|) (|ConvertibleTo| (|Pattern| *7))
                             (|RetractableTo| *8)))
       (|isDomain| *2 (|PatternMatchResult| *7 *9)) (|isDomain| *3 (|List| *9))
       (|ofCategory| *8 (|Ring|))
       (|isDomain| *1 (|PatternMatchTools| *7 *8 *9))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *6))
       (|ofCategory| *6 (|Join| (|SetCategory|) (|RetractableTo| *5)))
       (|ofCategory| *5 (|PatternMatchable| *4))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Mapping| (|Boolean|) *5))
       (|isDomain| *1 (|PatternMatchPushDown| *4 *5 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|PatternMatchAssertions|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|FunctionSpaceAssertions| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|PatternMatchAssertions|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|FunctionSpaceAssertions| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|BasicOperator|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Identifier|))
       (|isDomain| *2 (|Expression| (|Integer|)))
       (|isDomain| *1 (|PatternMatchAssertions|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Identifier|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|FunctionSpaceAssertions| *4 *2))
       (|ofCategory| *2 (|FunctionSpace| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *2 (|List| (|Segment| (|DoubleFloat|))))
       (|isDomain| *1 (|PlotTools|))))) 
(((*1 *1 *2 *3 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *3 *3 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *2 *3 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *3 *3)
  (AND (|isDomain| *2 (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Segment| (|DoubleFloat|)))
       (|isDomain| *2 (|Plot|)) (|isDomain| *1 (|PlotFunctions1| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *2 *3 *3 *4 *5)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Segment| (|DoubleFloat|)))
       (|isDomain| *2 (|Plot|)) (|isDomain| *1 (|PlotFunctions1| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))
 ((*1 *1 *2 *2 *2 *2 *3 *3 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))
 ((*1 *1 *2 *2 *2 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|List| (|DoubleFloat|))))
       (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Plot3D|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *1 (|Plot|))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *3 (|Segment| (|DoubleFloat|))) (|isDomain| *1 (|Plot|))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|Segment| (|DoubleFloat|)))
       (|isDomain| *2 (|Plot|)) (|isDomain| *1 (|PlotFunctions1| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Plot|))
       (|isDomain| *1 (|PlotFunctions1| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Plot|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *4 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|ParametricLinearEquations| *3 *4 *5 *2))
       (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4))))) 
(((*1 *2 *3 *4 *5 *6 *7 *7 *8)
  (AND
   (|isDomain| *3
    (|Record| (|:| |det| *12) (|:| |rows| (|List| #1=(|Integer|)))
              (|:| |cols| (|List| #1#))))
   (|isDomain| *4 (|Matrix| *12))
   (|isDomain| *5 (|List| (|Fraction| (|Polynomial| *9))))
   (|isDomain| *6 (|List| (|List| *12))) (|isDomain| *7 (|NonNegativeInteger|))
   (|isDomain| *8 (|Integer|))
   (|ofCategory| *9 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *12 (|PolynomialCategory| *9 *11 *10))
   (|ofCategory| *10 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
   (|ofCategory| *11 (|OrderedAbelianMonoidSup|))
   (|isDomain| *2
    (|Record| (|:| |eqzro| (|List| *12)) (|:| |neqzro| (|List| *12))
              (|:| |wcond| (|List| (|Polynomial| *9)))
              (|:| |bsoln|
                   (|Record|
                    (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| *9))))
                    (|:| |basis|
                         (|List|
                          (|Vector| (|Fraction| (|Polynomial| *9)))))))))
   (|isDomain| *1 (|ParametricLinearEquations| *9 *10 *11 *12))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *7)) (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *8)) (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |det| *8) (|:| |rows| (|List| (|Integer|)))
                   (|:| |cols| (|List| (|Integer|))))))
       (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|List| *8))) (|isDomain| *3 (|List| *8))
       (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| (|List| (|Integer|))))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))
       (|isDomain| *3 (|Integer|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|List| *6)))
       (|ofCategory| *6 (|PolynomialCategory| *3 *5 *4))
       (|ofCategory| *3 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *4 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|ParametricLinearEquations| *3 *4 *5 *6))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |rank| (|NonNegativeInteger|))
               (|:| |eqns|
                    (|List|
                     (|Record| (|:| |det| *7) (|:| |rows| (|List| (|Integer|)))
                               (|:| |cols| (|List| (|Integer|))))))
               (|:| |fgb| (|List| *7)))))
   (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
   (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|isDomain| *2 (|NonNegativeInteger|))
   (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |rank| (|NonNegativeInteger|))
               (|:| |eqns|
                    (|List|
                     (|Record| (|:| |det| *7) (|:| |rows| (|List| (|Integer|)))
                               (|:| |cols| (|List| (|Integer|))))))
               (|:| |fgb| (|List| *7)))))
   (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
   (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|isDomain| *2 (|NonNegativeInteger|))
   (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *6 *5))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| *4))))
              (|:| |vec| (|List| (|Fraction| (|Polynomial| *4))))
              (|:| |rank| (|NonNegativeInteger|))
              (|:| |rows| (|List| (|Integer|)))
              (|:| |cols| (|List| (|Integer|)))))
   (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|isDomain| *2
    (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| *4))))
              (|:| |basis|
                   (|List| (|Vector| (|Fraction| (|Polynomial| *4)))))))
   (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))
   (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))))) 
(((*1 *2 *2 *3)
  (AND
   (|isDomain| *2
    (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| *4))))
              (|:| |basis|
                   (|List| (|Vector| (|Fraction| (|Polynomial| *4)))))))
   (|isDomain| *3 (|List| *7))
   (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
   (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *8))
       (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |rank| (|NonNegativeInteger|))
                   (|:| |eqns|
                        (|List|
                         (|Record| (|:| |det| *8)
                                   (|:| |rows| (|List| (|Integer|)))
                                   (|:| |cols| (|List| (|Integer|))))))
                   (|:| |fgb| (|List| *8)))))
       (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))
       (|isDomain| *4 (|NonNegativeInteger|))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
       (|isDomain| *2
        (|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| #1=(|List| *7))
                  (|:| |n0| #1#)))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))
       (|isDomain| *3 (|List| *7))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *4))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *2 (|PolynomialCategory| *4 *6 *5))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *2))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Symbol|)))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| (|Fraction| (|Polynomial| *4))))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Fraction| (|Polynomial| *4)))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *6 *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Matrix| (|Fraction| (|Polynomial| *4))))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| (|Fraction| (|Polynomial| *4))))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))) 
(((*1 *2 *3 *4 *5 *6 *7)
  (AND (|isDomain| *3 (|Matrix| *11))
       (|isDomain| *4 (|List| (|Fraction| (|Polynomial| *8))))
       (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|String|))
       (|ofCategory| *8 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *11 (|PolynomialCategory| *8 *10 *9))
       (|ofCategory| *9 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *10 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|Record|
         (|:| |rgl|
              (|List|
               (|Record| (|:| |eqzro| (|List| *11)) (|:| |neqzro| (|List| *11))
                         (|:| |wcond| (|List| (|Polynomial| *8)))
                         (|:| |bsoln|
                              (|Record|
                               (|:| |partsol|
                                    (|Vector| (|Fraction| (|Polynomial| *8))))
                               (|:| |basis|
                                    (|List|
                                     (|Vector|
                                      (|Fraction| (|Polynomial| *8))))))))))
         (|:| |rgsz| (|Integer|))))
       (|isDomain| *1 (|ParametricLinearEquations| *8 *9 *10 *11))
       (|isDomain| *7 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eqzro| (|List| *7)) (|:| |neqzro| (|List| *7))
                   (|:| |wcond| (|List| (|Polynomial| *4)))
                   (|:| |bsoln|
                        (|Record|
                         (|:| |partsol|
                              (|Vector| (|Fraction| (|Polynomial| *4))))
                         (|:| |basis|
                              (|List|
                               (|Vector| (|Fraction| (|Polynomial| *4))))))))))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))))) 
(((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |eqzro| (|List| *8)) (|:| |neqzro| (|List| *8))
               (|:| |wcond| (|List| (|Polynomial| *5)))
               (|:| |bsoln|
                    (|Record|
                     (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| *5))))
                     (|:| |basis|
                          (|List|
                           (|Vector| (|Fraction| (|Polynomial| *5))))))))))
   (|isDomain| *4 (|String|))
   (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
   (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
   (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *8))
       (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eqzro| #1=(|List| *8)) (|:| |neqzro| #1#)
                   (|:| |wcond| (|List| (|Polynomial| *5)))
                   (|:| |bsoln|
                        (|Record|
                         (|:| |partsol|
                              (|Vector| (|Fraction| (|Polynomial| *5))))
                         (|:| |basis|
                              (|List|
                               (|Vector| (|Fraction| (|Polynomial| *5))))))))))
       (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))
       (|isDomain| *4 (|List| *8))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *8)) (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eqzro| (|List| *8)) (|:| |neqzro| (|List| *8))
                   (|:| |wcond| (|List| (|Polynomial| *5)))
                   (|:| |bsoln|
                        (|Record|
                         (|:| |partsol|
                              (|Vector| (|Fraction| (|Polynomial| *5))))
                         (|:| |basis|
                              (|List|
                               (|Vector| (|Fraction| (|Polynomial| *5))))))))))
       (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5))
       (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eqzro| (|List| *7)) (|:| |neqzro| (|List| *7))
                   (|:| |wcond| (|List| (|Polynomial| *4)))
                   (|:| |bsoln|
                        (|Record|
                         (|:| |partsol|
                              (|Vector| (|Fraction| (|Polynomial| *4))))
                         (|:| |basis|
                              (|List|
                               (|Vector| (|Fraction| (|Polynomial| *4))))))))))
       (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Matrix| *9)) (|isDomain| *5 (|PositiveInteger|))
       (|ofCategory| *9 (|PolynomialCategory| *6 *8 *7))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *7 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eqzro| #2=(|List| *9)) (|:| |neqzro| #2#)
                   (|:| |wcond| (|List| (|Polynomial| *6)))
                   (|:| |bsoln|
                        (|Record|
                         (|:| |partsol|
                              (|Vector| (|Fraction| (|Polynomial| *6))))
                         (|:| |basis|
                              (|List|
                               (|Vector| (|Fraction| (|Polynomial| *6))))))))))
       (|isDomain| *1 (|ParametricLinearEquations| *6 *7 *8 *9))
       (|isDomain| *4 (|List| *9))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Matrix| *9)) (|isDomain| *4 (|List| (|Symbol|)))
       (|isDomain| *5 (|PositiveInteger|))
       (|ofCategory| *9 (|PolynomialCategory| *6 *8 *7))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *7 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eqzro| (|List| *9)) (|:| |neqzro| (|List| *9))
                   (|:| |wcond| (|List| (|Polynomial| *6)))
                   (|:| |bsoln|
                        (|Record|
                         (|:| |partsol|
                              (|Vector| (|Fraction| (|Polynomial| *6))))
                         (|:| |basis|
                              (|List|
                               (|Vector| (|Fraction| (|Polynomial| *6))))))))))
       (|isDomain| *1 (|ParametricLinearEquations| *6 *7 *8 *9))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *8)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |eqzro| (|List| *8)) (|:| |neqzro| (|List| *8))
                   (|:| |wcond| (|List| (|Polynomial| *5)))
                   (|:| |bsoln|
                        (|Record|
                         (|:| |partsol|
                              (|Vector| (|Fraction| (|Polynomial| *5))))
                         (|:| |basis|
                              (|List|
                               (|Vector| (|Fraction| (|Polynomial| *5))))))))))
       (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Matrix| *9)) (|isDomain| *4 (|List| *9))
       (|isDomain| *5 (|String|))
       (|ofCategory| *9 (|PolynomialCategory| *6 *8 *7))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *7 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ParametricLinearEquations| *6 *7 *8 *9))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Matrix| *9)) (|isDomain| *4 (|List| (|Symbol|)))
       (|isDomain| *5 (|String|))
       (|ofCategory| *9 (|PolynomialCategory| *6 *8 *7))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *7 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ParametricLinearEquations| *6 *7 *8 *9))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *8)) (|isDomain| *4 (|String|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *7 *6))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *3 (|Matrix| *10)) (|isDomain| *4 (|List| *10))
       (|isDomain| *5 (|PositiveInteger|)) (|isDomain| *6 (|String|))
       (|ofCategory| *10 (|PolynomialCategory| *7 *9 *8))
       (|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *8 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *9 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ParametricLinearEquations| *7 *8 *9 *10))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *3 (|Matrix| *10)) (|isDomain| *4 (|List| (|Symbol|)))
       (|isDomain| *5 (|PositiveInteger|)) (|isDomain| *6 (|String|))
       (|ofCategory| *10 (|PolynomialCategory| *7 *9 *8))
       (|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *8 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *9 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ParametricLinearEquations| *7 *8 *9 *10))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Matrix| *9)) (|isDomain| *4 (|PositiveInteger|))
       (|isDomain| *5 (|String|))
       (|ofCategory| *9 (|PolynomialCategory| *6 *8 *7))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *7 (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|))))
       (|ofCategory| *8 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|ParametricLinearEquations| *6 *7 *8 *9))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Field|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|PolynomialInterpolationAlgorithms| *4 *2))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *1 (|PrincipalIdealDomain|))
       (|isDomain| *2 (|Record| (|:| |coef| (|List| *1)) (|:| |generator| *1)))
       (|isDomain| *3 (|List| *1))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|PrincipalIdealDomain|))
       (|isDomain| *2 (|Maybe| (|List| *1))) (|isDomain| *3 (|List| *1))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| (|Polynomial| *4)))
       (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|GcdDomain|))
       (|isDomain| *1 (|PolyGroebner| *4))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| (|Polynomial| *4)))
       (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|GcdDomain|))
       (|isDomain| *1 (|PolyGroebner| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Partition|))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|PermutationGroup| (|Integer|)))
       (|isDomain| *1 (|PermutationGroupExamples|))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|))
       (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *2))
       (|ofCategory| *2 (|PolynomialCategory| *5 *3 *4))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6))
       (|ofCategory| *6 (|PolynomialCategory| *5 *3 *4))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|EuclideanDomain|))
       (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *6))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2 (|PolynomialCategory| *6 *4 *5))
       (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *2))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Factored| *2)) (|ofCategory| *2 (|EuclideanDomain|))
       (|isDomain| *1 (|PartialFraction| *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|Any|)) (|isDomain| *1 (|PartialFractionPackage| *5))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Factored| (|Polynomial| *6)))
       (|isDomain| *5 (|Symbol|)) (|isDomain| *3 (|Polynomial| *6))
       (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|Any|)) (|isDomain| *1 (|PartialFractionPackage| *6))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|PartialFraction| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|PartialFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *1 (|PartialFraction| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PartialFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|PartialFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
       (|isDomain| *1 (|PartialFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|PartialFraction| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))) 
(((*1 *2 *2)
  (AND
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))
   (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Fraction| *3)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2)))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|Record| (|:| |den| #1=(|Integer|)) (|:| |gcdnum| #1#))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2)))
   (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *5))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))
   (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *4))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2)))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8))
   (|ofCategory| *5 (|FunctionSpace| *4))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
   (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7))
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| *8)))
   (|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8))))
 ((*1 *2 *3)
  (|partial| AND
   (|isDomain| *3 (|FiniteDivisor| (|Fraction| (|Integer|)) *4 *5 *6))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
   (|ofCategory| *6 (|FunctionFieldCategory| (|Fraction| (|Integer|)) *4 *5))
   (|isDomain| *2
    (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| *6)))
   (|isDomain| *1 (|PointsOfFiniteOrderRational| *4 *5 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8))
       (|ofCategory| *5 (|FunctionSpace| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
       (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|FiniteDivisor| (|Fraction| (|Integer|)) *4 *5 *6))
       (|ofCategory| *4
                     (|UnivariatePolynomialCategory| (|Fraction| (|Integer|))))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *6
                     (|FunctionFieldCategory| (|Fraction| (|Integer|)) *4 *5))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PointsOfFiniteOrderRational| *4 *5 *6))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|GcdDomain|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6))
       (|ofCategory| *6 (|PolynomialCategory| *5 *3 *4))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|PolynomialFactorizationExplicit|))
       (|isDomain| *1 (|GeneralPolynomialGcdPackage| *3 *4 *5 *6))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|PolynomialFactorizationExplicit|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1)))
       (|isDomain| *1 (|Expression| *4))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1)))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *1))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1)))
       (|isDomain| *1 (|Expression| *4))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1)))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *1))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1)))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *1))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *5)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *5))
   (|ofCategory| *5 (|ComplexCategory| *4))
   (|ofCategory| *4 (|IntegerNumberSystem|))
   (|isDomain| *1 (|ComplexIntegerSolveLinearPolynomialEquation| *4 *5))))
 ((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|List| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|ofCategory| *4 (|FiniteFieldCategory|))
   (|isDomain| *1 (|FiniteFieldSolveLinearPolynomialEquation| *4 *5 *3))))
 ((*1 *2 *2 *3)
  (|partial| AND
   (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| (|Integer|))))
   (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|)))
   (|isDomain| *1 (|IntegerSolveLinearPolynomialEquation|))))
 ((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *1)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
   (|ofCategory| *1 (|PolynomialFactorizationExplicit|))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Matrix| *1))
   (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Vector| *1))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Matrix| *1))
   (|ofCategory| *1 (|CharacteristicNonZero|))
   (|ofCategory| *1 (|PolynomialFactorizationExplicit|))
   (|isDomain| *2 (|Vector| *1))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| *1))
       (|ofCategory| *1 (|CharacteristicNonZero|))))
 ((*1 *1 *1) (|ofCategory| *1 (|FiniteFieldCategory|)))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CharacteristicNonZero|))
       (|ofCategory| *1 (|PolynomialFactorizationExplicit|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *5 (|PolynomialFactorizationExplicit|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *8)))
       (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *7 *8))
       (|isDomain| *4 (|SparseUnivariatePolynomial| *8))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *5)))
       (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *5))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *2 (|PolynomialFactorizationExplicit|))
       (|isDomain| *1 (|GeneralPolynomialGcdPackage| *3 *4 *2 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *2 (|PolynomialFactorizationExplicit|))
       (|isDomain| *1 (|PolynomialFactorizationByRecursion| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4))))
 ((*1 *2)
  (AND (|ofCategory| *2 (|PolynomialFactorizationExplicit|))
       (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7)))
       (|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *7))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *5)))
       (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *7)))
       (|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *7))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *5)))
       (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *5))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *7)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *7))
   (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
   (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *6 (|OrderedSet|))
   (|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7))))
 ((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *5)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *5))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
   (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5))))) 
(((*1 *2 *2 *3 *4)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *7)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *7))
   (|ofCategory| *7 (|PolynomialCategory| *5 *6 *4))
   (|ofCategory| *5 (|PolynomialFactorizationExplicit|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *4 (|OrderedSet|))
   (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *4 *7))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Permutation| *3)))
       (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|AddAst|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FloatingPointSystem|))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Permutation| *3)))
       (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|List| (|NonNegativeInteger|))))
       (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Permutation| *3)))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|PermutationGroup| *3))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|PermutationCategory| *3))
       (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Set| (|List| *4)))
       (|isDomain| *1 (|PermutationGroup| *4)) (|isDomain| *3 (|List| *4))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Set| (|Set| *4)))
       (|isDomain| *1 (|PermutationGroup| *4)) (|isDomain| *3 (|Set| *4))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Set| (|Set| *3)))
       (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Permutation| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|PermutationGroup| *4))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Permutation| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|PermutationGroup| *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PermutationCategory| *3))
       (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|PermutationCategory| *3))
       (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|PermutationGroup| *4))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PermutationGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|PermutationCategory| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|PermutationCategory| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SquareMatrix| *4 *2)) (|ofType| *4 (|PositiveInteger|))
       (|ofCategory| *2
                     (|Join| (|Ring|)
                             (CATEGORY |package|
                              (ATTRIBUTE (|commutative| "*")))))
       (|isDomain| *1 (|Permanent| *4 *2))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |preimage| (|List| *3)) (|:| |image| (|List| *3))))
   (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Permutation| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Permutation| *3))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Partition|)) (|isDomain| *1 (|Permutation| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RetractableTo| (|Integer|)))
       (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Permutation| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|RetractableTo| (|Integer|)))
       (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Permutation| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|Permutation| *3))
       (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Permutation| *3))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|PendantTree| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|PendantTree| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialDomain| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|DifferentialSpace|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|DifferentialSpaceExtension| *4))
       (|ofCategory| *4 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|ofCategory| *1 (|DifferentialSpaceExtension| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|PartialDifferentialDomain| *2 *3))
       (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| *4))
       (|isDomain| *3 (|List| (|NonNegativeInteger|)))
       (|ofCategory| *1 (|PartialDifferentialSpace| *4))
       (|ofCategory| *4 (|BasicType|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|PartialDifferentialSpace| *2))
       (|ofCategory| *2 (|BasicType|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| *3))
       (|ofCategory| *1 (|PartialDifferentialSpace| *3))
       (|ofCategory| *3 (|BasicType|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|))
       (|isDomain| *1 (|PolynomialDecomposition| *2 *4))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *2)
  (|partial| AND (|ofCategory| *3 (|Field|))
   (|isDomain| *1 (|PolynomialDecomposition| *2 *3))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|GradedAlgebra| *2 *3))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|))))
 ((*1 *1) (|isDomain| *1 (|InputForm|)))
 ((*1 *1) (|ofCategory| *1 (|MonadWithUnit|)))
 ((*1 *1) (|ofCategory| *1 (|Monoid|)))
 ((*1 *1)
  (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|List| (|Record| (|:| |k| *4) (|:| |c| *3))))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| *3)) (|:| |c| *4))))
   (|isDomain| *1 (|LieExponentials| *3 *4 *5))
   (|ofCategory| *3 (|OrderedSet|))
   (|ofCategory| *4
                 (|Join| (|CommutativeRing|)
                         (|Module| (|Fraction| (|Integer|)))))
   (|ofType| *5 (|PositiveInteger|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|LyndonWord| *3)))
       (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3))
       (|ofCategory| *3 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AntiSymm| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Any|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|AnyFunctions1| *4)) (|ofCategory| *4 (|Type|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DeRhamComplex| *3 *4))
       (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FreeMagma| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3))
       (|ofCategory| *3 (|OrderedSet|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|PatternFunctions1| *4 *5))
       (|ofCategory| *5 (|Type|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Any|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|PatternFunctions1| *4 *3)) (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *1 *3)
  (|partial| AND (|isDomain| *3 (|Pattern| *4))
   (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|PatternMatchResult| *4 *5))
   (|ofCategory| *5 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternFunctions1| *5 *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Pattern| *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|Type|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PatternFunctions1| *5 *6))))) 
(((*1 *1) (|ofCategory| *1 (|AbelianMonoid|)))
 ((*1 *1)
  (AND (|ofCategory| *1 (|GradedModule| *2 *3))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|))))
 ((*1 *1) (|isDomain| *1 (|InputForm|)))
 ((*1 *1)
  (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (|partial| AND
   (|isDomain| *2
    (|Record| (|:| |op| (|BasicOperator|))
              (|:| |arg| (|List| (|Pattern| *3)))))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (|partial| AND (|isDomain| *3 (|BasicOperator|))
   (|isDomain| *2 (|List| (|Pattern| *4))) (|isDomain| *1 (|Pattern| *4))
   (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2 *1)
  (|partial| AND
   (|isDomain| *2 (|Record| (|:| |num| #1=(|Pattern| *3)) (|:| |den| #1#)))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3)))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2 *3 *3 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Boolean|))
       (|isDomain| *1 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|Any|))
       (|isDomain| *1 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Any|))) (|isDomain| *1 (|Pattern| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|List| (|Pattern| *3)))
   (|isDomain| *1 (|Pattern| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PatternMatchListResult| *3 *4 *5))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *5 (|ListAggregate| *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|PatternMatchResult| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|PatternMatchListResult| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *4 (|ListAggregate| *3))))
 ((*1 *1)
  (AND (|isDomain| *1 (|PatternMatchResult| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3 *1)
  (|partial| AND (|isDomain| *3 (|Pattern| *4))
   (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))
   (|isDomain| *1 (|PatternMatchResult| *4 *2))))) 
(((*1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|PatternMatchResult| *4 *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|PatternMatchResult| *4 *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2 *3 *1 *3)
  (AND (|isDomain| *2 (|Pattern| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|PatternMatchResult| *4 *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|PatternMatchable| *5))
       (|isDomain| *2 (|PatternMatchListResult| *5 *6 (|List| *6)))
       (|isDomain| *1 (|PatternMatch| *5 *6 *4)) (|isDomain| *3 (|List| *6))
       (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5)))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *2 (|List| (|Equation| *3)))
       (|isDomain| *1 (|PatternMatch| *5 *3 *4))
       (|ofCategory| *3 (|RetractableTo| (|Symbol|)))
       (|ofCategory| *3 (|PatternMatchable| *5))
       (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5)))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *2 (|List| (|Equation| (|Polynomial| *3))))
       (|isDomain| *1 (|PatternMatch| *5 *3 *4)) (|ofCategory| *3 (|Ring|))
       (|not| (|ofCategory| *3 (|RetractableTo| (|Symbol|))))
       (|ofCategory| *3 (|PatternMatchable| *5))
       (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5)))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *2 (|PatternMatchResult| *5 *3))
       (|isDomain| *1 (|PatternMatch| *5 *3 *4))
       (|not| (|ofCategory| *3 (|RetractableTo| (|Symbol|))))
       (|not| (|ofCategory| *3 (|Ring|)))
       (|ofCategory| *3 (|PatternMatchable| *5))
       (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5)))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|Symbol|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|BasicOperator|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Kernel| *4)) (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|Kernel| *4)) (|ofCategory| *4 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|OperatorCategory| *3))
       (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PatternMatch| *5 *3 *4))
       (|ofCategory| *3 (|PatternMatchable| *5))
       (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|PatternMatchable| *5))
       (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PatternMatch| *5 *6 *4))
       (|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5)))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|PatternMatchResult| *4 *5))
       (|isDomain| *3 (|PatternMatchResult| *4 *6))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|ListAggregate| *5))
       (|isDomain| *1 (|PatternMatchListResult| *4 *5 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|PatternMatchResult| *3 *5))
       (|isDomain| *1 (|PatternMatchListResult| *3 *4 *5))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *5 (|ListAggregate| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Stream| (|List| (|Integer|))))
       (|isDomain| *1 (|PartitionsAndPermutations|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|Stream| (|List| (|Integer|))))
       (|isDomain| *1 (|PartitionsAndPermutations|))
       (|isDomain| *3 (|List| (|Integer|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|Stream| (|List| (|Integer|))))
       (|isDomain| *1 (|PartitionsAndPermutations|))
       (|isDomain| *3 (|List| (|Integer|)))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Stream| (|List| (|Integer|))))
       (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *1 (|PartitionsAndPermutations|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|Stream| (|List| (|Integer|))))
       (|isDomain| *1 (|PartitionsAndPermutations|))
       (|isDomain| *3 (|List| (|Integer|)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Stream| (|List| (|PositiveInteger|))))
       (|isDomain| *1 (|PartitionsAndPermutations|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|ParametricPlaneCurve| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|ParametricSpaceCurve| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|ParametricSurface| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *2 *2 *2)
  (AND (|isDomain| *1 (|ParametricSurface| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|List| (|Syntax|)))
       (|isDomain| *1 (|Parser|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|DisplayPackage|))
       (|isDomain| *3 (|String|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|String|))) (|isDomain| *1 (|DisplayPackage|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|Pair| *2 *3)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|ContinuedFraction| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|BalancedPAdicRational| *3)) (|ofType| *3 (|Integer|))))
 ((*1 *1 *2 *3 *3)
  (AND (|isDomain| *3 (|Stream| *2)) (|ofCategory| *2 (|EuclideanDomain|))
       (|isDomain| *1 (|ContinuedFraction| *2))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| *3)) (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|ContinuedFraction| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *2 (|ContinuedFraction| (|Integer|)))
       (|isDomain| *1 (|NumericContinuedFraction| *3))
       (|ofCategory| *3 (|FloatingPointSystem|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|ContinuedFraction| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|PAdicRational| *3)) (|ofType| *3 (|Integer|))))
 ((*1 *2 *1)
  (AND (|ofType| *3 (|Integer|))
       (|isDomain| *2 (|ContinuedFraction| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|PAdicRationalConstructor| *3 *4))
       (|ofCategory| *4 (|PAdicIntegerCategory| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|FloatingPointSystem&| *3))
       (|ofCategory| *3 (|FloatingPointSystem|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|FloatingPointSystem&| *3))
       (|ofCategory| *3 (|FloatingPointSystem|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|has| *1 (ATTRIBUTE |arbitraryPrecision|))
       (|ofCategory| *1 (|FloatingPointSystem|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FloatingPointSystem|))
       (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3))
       (|isDomain| *2 (|Stream| (|Integer|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *2 (|AbelianMonoid|))
       (|isDomain| *1 (|EuclideanModularRing| *3 *4 *2 *5 *6 *7))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofType| *5 (|Mapping| *4 *4 *2))
       (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2))
       (|ofType| *7 (|Mapping| (|Union| *4 "failed") *4 *4 *2))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|AbelianMonoid|))
       (|isDomain| *1 (|ModularField| *3 *2 *4 *5 *6))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2))
       (|ofType| *5 (|Mapping| (|Union| *2 "failed") *2 *2))
       (|ofType| *6 (|Mapping| (|Union| *3 "failed") *3 *3 *2))))
 ((*1 *2)
  (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|ModMonic| *3 *2)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|AbelianMonoid|))
       (|isDomain| *1 (|ModularRing| *3 *2 *4 *5 *6))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2))
       (|ofType| *5 (|Mapping| (|Union| *2 "failed") *2 *2))
       (|ofType| *6 (|Mapping| (|Union| *3 "failed") *3 *3 *2))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3))
       (|isDomain| *2 (|Integer|))))) 
(((*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|)))
       (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|PAdicIntegerCategory| *4))))) 
(((*1 *2 *3 *3 *4 *4)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Fraction| *6))
   (|isDomain| *1 (|PadeApproximants| *5 *4 *6))
   (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))))
 ((*1 *2 *3 *3 *4 *4)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|isDomain| *4 (|UnivariateTaylorSeries| *5 *6 *7))
   (|ofCategory| *5 (|Field|)) (|ofType| *6 (|Symbol|)) (|ofType| *7 *5)
   (|isDomain| *2 (|Fraction| (|UnivariatePolynomial| *6 *5)))
   (|isDomain| *1 (|PadeApproximantPackage| *5 *6 *7))))
 ((*1 *2 *3 *3 *4)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|isDomain| *4 (|UnivariateTaylorSeries| *5 *6 *7))
   (|ofCategory| *5 (|Field|)) (|ofType| *6 (|Symbol|)) (|ofType| *7 *5)
   (|isDomain| *2 (|Fraction| (|UnivariatePolynomial| *6 *5)))
   (|isDomain| *1 (|PadeApproximantPackage| *5 *6 *7))))) 
(((*1 *2 *3 *3 *4 *4)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|ContinuedFraction| *6))
   (|isDomain| *1 (|PadeApproximants| *5 *4 *6))
   (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|List| *3))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|FunctionDescriptor|)))
       (|isDomain| *1 (|OverloadSet|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|OutputForm|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntervalCategory| *2))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Kernel| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|)))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1) (|isDomain| *1 (|Character|)))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|OutputForm|))) (|isDomain| *1 (|OutputForm|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *2 *1 *1)
  (|partial| AND
   (|isDomain| *2
    (|Record| (|:| |lm| #1=(|OrderedFreeMonoid| *3)) (|:| |rm| #1#)))
   (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|EuclideanDomain|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|EuclideanDomain|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|NonNegativeInteger|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|)))
 ((*1 *1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *1) (|ofCategory| *1 (|BooleanLogic|)))
 ((*1 *1 *1) (|isDomain| *1 (|OutputForm|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|OutputBinaryFile|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|FileName|)) (|isDomain| *1 (|OutputBinaryFile|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InputBinaryFile|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InputOutputBinaryFile|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OutputBinaryFile|))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|OutputByteConduit|))
       (|isDomain| *2 (|Maybe| (|Byte|))) (|isDomain| *3 (|Byte|))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|OutputByteConduit|))
       (|isDomain| *2 (|Maybe| (|Int8|))) (|isDomain| *3 (|Int8|))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|OutputByteConduit|))
       (|isDomain| *2 (|Maybe| (|UInt8|))) (|isDomain| *3 (|UInt8|))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *3 (|ByteBuffer|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Any|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|OutputPackage|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *3 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|OrthogonalPolynomialFunctions| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|Field|))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3))
       (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Field|))
       (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|NonCommutativeOperatorDivision| *3 *4))
       (|ofCategory| *3 (|MonogenicLinearOperator| *4))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|Field|))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3))
       (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3))
       (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1)))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|Automorphism| *5)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3))
       (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5))))) 
(((*1 *2 *3 *4 *2)
  (AND (|isDomain| *4 (|Mapping| *2 *2)) (|ofCategory| *2 (|LeftModule| *5))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *1 (|ApplyUnivariateSkewPolynomial| *5 *2 *3))
       (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *5))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Matrix| *3))
       (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))))
 ((*1 *2 *1 *2 *2)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *3 *2 *2 *4 *5)
  (AND (|isDomain| *4 (|Automorphism| *2)) (|isDomain| *5 (|Mapping| *2 *2))
       (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *2 *3))
       (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *2))))) 
(((*1 *2 *2 *2 *3 *4)
  (AND (|isDomain| *3 (|Automorphism| *5)) (|isDomain| *4 (|Mapping| *5 *5))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *2))
       (|ofCategory| *2 (|UnivariateSkewPolynomialCategory| *5))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3))
       (|ofCategory| *2 (|MonogenicLinearOperator| *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3))
       (|ofCategory| *2 (|MonogenicLinearOperator| *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *2 *2)
  (|partial| AND (|ofCategory| *3 (|Field|))
   (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3))
   (|ofCategory| *2 (|MonogenicLinearOperator| *3))))
 ((*1 *1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3))
       (|ofCategory| *2 (|MonogenicLinearOperator| *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1)))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
   (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1)))
       (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3))
       (|ofCategory| *2 (|MonogenicLinearOperator| *3))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|FloatingPointSystem|))
       (|not| (|has| *1 (ATTRIBUTE |arbitraryPrecision|)))
       (|not| (|has| *1 (ATTRIBUTE |arbitraryExponent|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteSetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|OrderedMultisetAggregate| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1) (|ofCategory| *1 (|OrderedFinite|)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|OrderedType|)))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5))
       (|ofType| *4 (|NonNegativeInteger|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5))
       (|ofType| *4 (|NonNegativeInteger|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5))
       (|ofType| *4 (|NonNegativeInteger|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|OrderedCompletion| (|Integer|)))
       (|isDomain| *1 (|Infinity|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|OrderedCompletion| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|OrderedCompletion| (|Integer|)))
       (|isDomain| *1 (|Infinity|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|OrderedCompletion| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OnePointCompletion| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedCompletion| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OnePointCompletion| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedCompletion| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|SingleInteger|))
       (|isDomain| *1 (|OrderedCompletion| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Database| (|IndexCard|)))
       (|isDomain| *1 (|OperationsQuery|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OperatorCategory| *3))
       (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Arity|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *2 (|Record| (|:| |adjMat| *3) (|:| |detMat| *4)))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3))
       (|ofCategory| *3 (|MatrixCategory| *4 *5 *6))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|ModuleOperator| *2 *3))
       (|ofCategory| *3 (|LeftModule| *2))))
 ((*1 *1 *1)
  (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|ModuleOperator| *2 *3))
       (|ofCategory| *3 (|LeftModule| *2))))
 ((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *2 (|Ring|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|ModuleOperator| *2 *3))
       (|ofCategory| *3 (|LeftModule| *2))))
 ((*1 *2 *2)
  (AND (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|List| *2))
   (|isDomain| *1 (|BasicOperatorFunctions1| *2))
   (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|))
       (|isDomain| *3 (|Mapping| *4 (|List| *4)))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|BasicOperatorFunctions1| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *4 *4))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|BasicOperatorFunctions1| *4))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|BasicOperator|))
   (|isDomain| *2 (|Mapping| *4 (|List| *4)))
   (|isDomain| *1 (|BasicOperatorFunctions1| *4))
   (|ofCategory| *4 (|SetCategory|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *4 (|LeftModule| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *3 *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|Operator| *3))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *4 (|LeftModule| *3))
       (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *3 *4))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|Operator| *3))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|ModuleOperator| *4 *2))
       (|ofCategory| *2 (|LeftModule| *4))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *1 (|Operator| *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|FreeGroup| (|BasicOperator|)))
       (|ofCategory| *2 (|Ring|)) (|isDomain| *1 (|ModuleOperator| *2 *4))
       (|ofCategory| *4 (|LeftModule| *2))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|FreeGroup| (|BasicOperator|)))
       (|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|Ring|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|OnePointCompletion| (|Integer|)))
       (|isDomain| *1 (|Infinity|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|OnePointCompletion| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3))
       (|ofCategory| *2 (|MonogenicLinearOperator| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|MonogenicLinearOperator| *3))
       (|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FreeMagma| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3))
       (|ofCategory| *3 (|OrderedSet|))))
 ((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedFreeMonoid| *3))
       (|ofCategory| *3 (|OrderedSet|))))) 
(((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *5 (|List| *4)) (|ofCategory| *4 (|Field|))
   (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|ODETools| *4 *3))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|Field|))
       (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|ODETools| *4 *5))
       (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Matrix| *5))
       (|isDomain| *1 (|ODETools| *5 *6))
       (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Polynomial| *5)))
       (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *5))))))
       (|isDomain| *1 (|NonLinearSolvePackage| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2
        (|List| (|List| (|Equation| (|Fraction| (|Polynomial| *4))))))
       (|isDomain| *1 (|NonLinearSolvePackage| *4))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Matrix| *7))
       (|isDomain| *5
        (|Mapping|
         (|Record| (|:| |particular| (|Union| *6 "failed"))
                   (|:| |basis| (|List| *6)))
         *7 *6))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| *6))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| #1=(|Vector| *6) "failed"))
                  (|:| |basis| (|List| #1#))))
       (|isDomain| *1 (|SystemODESolver| *6 *7))
       (|isDomain| *4 (|Vector| *6))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|Record| (|:| A #1=(|Matrix| *5))
                  (|:| |eqs|
                       (|List|
                        (|Record| (|:| C #1#) (|:| |g| (|Vector| *5))
                                  (|:| |eq| *6) (|:| |rh| *5))))))
       (|isDomain| *1 (|SystemODESolver| *5 *6)) (|isDomain| *3 (|Matrix| *5))
       (|isDomain| *4 (|Vector| *5))
       (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5))
       (|isDomain| *2
        (|Record| (|:| |mat| (|Matrix| *6)) (|:| |vec| (|Vector| *5))))
       (|isDomain| *1 (|SystemODESolver| *5 *6)) (|isDomain| *3 (|Matrix| *6))
       (|isDomain| *4 (|Vector| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))
       (|isDomain| *4 (|Mapping| (|List| *5) *6))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2 (|List| (|Fraction| *6)))
       (|isDomain| *1 (|RationalRicDE| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *7)))
       (|isDomain| *4 (|Mapping| (|List| *6) *7))
       (|isDomain| *5 (|Mapping| (|Factored| *7) *7))
       (|ofCategory| *6
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|isDomain| *2 (|List| (|Fraction| *7)))
       (|isDomain| *1 (|RationalRicDE| *6 *7))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))
   (|isDomain| *4 (|Mapping| (|List| *5) *6))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *2 (|List| (|Fraction| *6)))
   (|isDomain| *1 (|RationalRicDE| *5 *6))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *7 (|Fraction| *7)))
   (|isDomain| *4 (|Mapping| (|List| *6) *7))
   (|isDomain| *5 (|Mapping| (|Factored| *7) *7))
   (|ofCategory| *6
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
   (|isDomain| *2 (|List| (|Fraction| *7)))
   (|isDomain| *1 (|RationalRicDE| *6 *7))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5)))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|AlgebraicallyClosedField|))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|isDomain| *2 (|List| (|Fraction| *5)))
       (|isDomain| *1 (|RationalRicDE| *4 *5))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))
       (|isDomain| *4 (|Mapping| (|Factored| *6) *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|AlgebraicallyClosedField|))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|isDomain| *2 (|List| (|Fraction| *6)))
       (|isDomain| *1 (|RationalRicDE| *5 *6))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *5 (|Fraction| *5)))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|ofCategory| *4 (|AlgebraicallyClosedField|))
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|isDomain| *2 (|List| (|Fraction| *5)))
   (|isDomain| *1 (|RationalRicDE| *4 *5))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))
   (|isDomain| *4 (|Mapping| (|Factored| *6) *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5 (|AlgebraicallyClosedField|))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|isDomain| *2 (|List| (|Fraction| *6)))
   (|isDomain| *1 (|RationalRicDE| *5 *6))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|List| *5) *6))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2 (|List| (|Record| (|:| |poly| *6) (|:| |eq| *3))))
       (|isDomain| *1 (|PrimitiveRatRicDE| *5 *6 *3 *7))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *6))
       (|ofCategory| *7
                     (|LinearOrdinaryDifferentialOperatorCategory|
                      (|Fraction| *6)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|List| *5) *6))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |poly| *6)
                   (|:| |eq|
                        (|LinearOrdinaryDifferentialOperator2| *6
                                                               (|Fraction|
                                                                *6))))))
       (|isDomain| *1 (|RationalRicDE| *5 *6))
       (|isDomain| *3
        (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))))) 
(((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *4 (|Mapping| (|List| *7) *7 (|SparseUnivariatePolynomial| *7)))
   (|isDomain| *5 (|Mapping| (|Factored| *7) *7))
   (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
   (|ofCategory| *6
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|isDomain| *2
    (|List| (|Record| (|:| |frac| (|Fraction| *7)) (|:| |eq| *3))))
   (|isDomain| *1 (|PrimitiveRatRicDE| *6 *7 *3 *8))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *7))
   (|ofCategory| *8
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *7)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |frac| (|Fraction| *6))
                   (|:| |eq|
                        (|LinearOrdinaryDifferentialOperator2| *6
                                                               (|Fraction|
                                                                *6))))))
       (|isDomain| *1 (|RationalRicDE| *5 *6))
       (|isDomain| *3
        (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *4 (|MonogenicAlgebra| *5 *7))
       (|isDomain| *2
        (|Record| (|:| |mat| (|Matrix| *6)) (|:| |vec| (|Vector| *5))))
       (|isDomain| *1 (|ReduceLODE| *5 *6 *7 *4 *3))
       (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *2)))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|RationalLODE| *4 *2))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *2 (|Fraction| *2)))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *1 (|RationalLODE| *4 *2))
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))
       (|isDomain| *4 (|Fraction| *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| *4 #1="failed"))
                  (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|RationalLODE| *5 *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|isDomain| *2
        (|Record| (|:| |basis| (|List| (|Fraction| *6)))
                  (|:| |mat| (|Matrix| *5))))
       (|isDomain| *1 (|RationalLODE| *5 *6))
       (|isDomain| *4 (|List| (|Fraction| *6)))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))
   (|isDomain| *4 (|Fraction| *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|isDomain| *2
    (|Record| (|:| |particular| (|Union| *4 #1#)) (|:| |basis| (|List| *4))))
   (|isDomain| *1 (|RationalLODE| *5 *6))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 (|Fraction| *6)))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|isDomain| *2
    (|Record| (|:| |basis| (|List| (|Fraction| *6)))
              (|:| |mat| (|Matrix| *5))))
   (|isDomain| *1 (|RationalLODE| *5 *6))
   (|isDomain| *4 (|List| (|Fraction| *6)))))) 
(((*1 *2 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *1 (|PrimitiveRatRicDE| *4 *3 *2 *5))
   (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *3))
   (|ofCategory| *5
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *3)))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Fraction| *5))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *2 *6))
       (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *5))
       (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| (|List| *5) *6))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2 (|List| (|Record| (|:| |constant| *5) (|:| |eq| *3))))
       (|isDomain| *1 (|PrimitiveRatRicDE| *5 *6 *3 *7))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *6))
       (|ofCategory| *7
                     (|LinearOrdinaryDifferentialOperatorCategory|
                      (|Fraction| *6)))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2
    (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| *5))))
   (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *3 *6))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))
   (|ofCategory| *6
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *5)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|PrimitiveRatRicDE| *4 *2 *3 *5))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *5
                     (|LinearOrdinaryDifferentialOperatorCategory|
                      (|Fraction| *2)))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *3 *5))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *5
                     (|LinearOrdinaryDifferentialOperatorCategory|
                      (|Fraction| *2)))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *5 *3))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *3
                     (|LinearOrdinaryDifferentialOperatorCategory|
                      (|Fraction| *2)))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2 (|List| (|Record| (|:| |center| *5) (|:| |equation| *5))))
   (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *3 *6))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))
   (|ofCategory| *6
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *5)))))
 ((*1 *2 *3 *4)
  (AND
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *2 (|List| (|Record| (|:| |center| *4) (|:| |equation| *4))))
   (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *3 *6))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))
   (|ofCategory| *6
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *4)))))
 ((*1 *2 *3)
  (AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2 (|List| (|Record| (|:| |center| *5) (|:| |equation| *5))))
   (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *6 *3))
   (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5))
   (|ofCategory| *3
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *5)))))
 ((*1 *2 *3 *4)
  (AND
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *2 (|List| (|Record| (|:| |center| *4) (|:| |equation| *4))))
   (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *6 *3))
   (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *4))
   (|ofCategory| *3
                 (|LinearOrdinaryDifferentialOperatorCategory|
                  (|Fraction| *4)))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|Fraction| *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *1 (|PrimitiveRatDE| *5 *2 *3 *6))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2))
   (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|Fraction| *2)))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *1 (|PrimitiveRatDE| *5 *2 *3 *6))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *6
                     (|LinearOrdinaryDifferentialOperatorCategory|
                      (|Fraction| *2)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| *4))
       (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7))
       (|ofCategory| *5
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| *4 "failed"))
                  (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|PureAlgebraicLODE| *5 *6 *7 *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *2 (|Mapping| *5 *5))
       (|isDomain| *1 (|ODEIntegration| *4 *5))
       (|ofCategory| *5
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *4)
                             (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *1 (|ODEIntegration| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *4)
                             (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Symbol|))
       (|ofCategory| *6
                     (|Join| (|EuclideanDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))
                             (|CharacteristicZero|)))
       (|ofCategory| *4
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *6)
                             (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)))
       (|isDomain| *2
        (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|ConstantLODE| *6 *4 *3))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|Quaternion| *3)) (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *1 (|Octonion| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *1 *1) (|ofCategory| *1 (|DivisionRing|)))
 ((*1 *1 *1)
  (AND (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *3 *3 *4))
       (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4))
       (|ofType| *7 (|Mapping| (|Union| *3 "failed") *3 *3 *4))))
 ((*1 *1 *1)
  (OR
   (AND #1=(|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Field|))
        . #2=((|ofCategory| *2 (|Type|))))
   (AND #1# (|ofCategory| *2 (|Group|)) . #2#)))
 ((*1 *1 *1) (|ofCategory| *1 (|Group|)))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3))
       (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3))
       (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|OctonionCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntervalCategory| *2))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|OrderedAbelianMonoidSup|)))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
  (AND (|isDomain| *3 (|Mapping| #1=(|Float|) #1#)) (|isDomain| *4 (|Float|))
       (|isDomain| *2
        (|Record| (|:| |value| *4) (|:| |error| *4)
                  (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))))
       (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 (|Integer|))))) 
(((*1 *2 *3 *4 *5 *5 *4 *6)
  (AND (|isDomain| *4 (|Integer|))
       (|isDomain| *6 (|Mapping| (|Void|) #1=(|Vector| *5) #1# #2=(|Float|)))
       (|isDomain| *3 (|Vector| #2#)) (|isDomain| *5 (|Float|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|))))) 
(((*1 *2 *3 *4 *5 *6 *5 *3 *7)
  (AND (|isDomain| *4 (|Integer|))
       (|isDomain| *6
        (|Record| (|:| |tryValue| #1=(|Float|)) (|:| |did| #1#)
                  (|:| |next| #1#)))
       (|isDomain| *7 (|Mapping| (|Void|) #2=(|Vector| *5) #2# #1#))
       (|isDomain| *3 (|Vector| #1#)) (|isDomain| *5 (|Float|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|))))
 ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3)
  (AND (|isDomain| *4 (|Integer|))
       (|isDomain| *6
        (|Record| (|:| |tryValue| #3=(|Float|)) (|:| |did| #3#)
                  (|:| |next| #3#)))
       (|isDomain| *7 (|Mapping| (|Void|) #4=(|Vector| *5) #4# #3#))
       (|isDomain| *3 (|Vector| #3#)) (|isDomain| *5 (|Float|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|))))) 
(((*1 *2 *3 *4 *5 *5 *5 *5 *4 *6)
  (AND (|isDomain| *4 (|Integer|))
       (|isDomain| *6 (|Mapping| (|Void|) #1=(|Vector| *5) #1# #2=(|Float|)))
       (|isDomain| *3 (|Vector| #2#)) (|isDomain| *5 (|Float|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|))))) 
(((*1 *2 *3 *4 *5 *5 *6)
  (AND (|isDomain| *4 (|Integer|))
       (|isDomain| *6 (|Mapping| (|Void|) #1=(|Vector| *5) #1# #2=(|Float|)))
       (|isDomain| *3 (|Vector| #2#)) (|isDomain| *5 (|Float|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|))))
 ((*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3)
  (AND (|isDomain| *4 (|Integer|))
       (|isDomain| *6 (|Mapping| (|Void|) #3=(|Vector| *5) #3# #4=(|Float|)))
       (|isDomain| *3 (|Vector| #4#)) (|isDomain| *5 (|Float|))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|))
   (|isDomain| *1 (|NumberFormats|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Float|))
       (|isDomain| *1 (|NumberFormats|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|NumberFormats|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|NumberFormats|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|NumberFormats|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|NumberFormats|))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Polynomial| (|Complex| *4)))
   (|ofCategory| *4 (|CommutativeRing|))
   (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Polynomial| (|Complex| *5)))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|CommutativeRing|))
   (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Polynomial| *4)) (|ofCategory| *4 (|Ring|))
   (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Polynomial| *5))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Ring|))
   (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
   (|ofCategory| *4 (|IntegralDomain|))
   (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Complex| *4))))
   (|ofCategory| *4 (|IntegralDomain|))
   (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Complex| *5))))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Expression| *4))
   (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedSet|))
   (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Expression| *5))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Expression| (|Complex| *4)))
   (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedSet|))
   (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Expression| (|Complex| *5)))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *5 (|OrderedSet|))
   (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
   (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Polynomial| *4)) (|ofCategory| *4 (|Ring|))
   (|ofCategory| *4 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
   (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Polynomial| *5))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Ring|))
   (|ofCategory| *5 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
   (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
   (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|ConvertibleTo| *2))
   (|isDomain| *2 (|Float|)) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *5 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
   (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Expression| *4))
   (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedSet|))
   (|ofCategory| *4 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
   (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Expression| *5))
   (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
   (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *5 (|ConvertibleTo| *2))
   (|isDomain| *2 (|Float|)) (|isDomain| *1 (|Numeric| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|Float|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|Float|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Complex| *4)) (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Complex| *5)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|CommutativeRing|))
       (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| (|Complex| *4)))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Polynomial| (|Complex| *5)))
       (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|CommutativeRing|))
       (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *4)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Polynomial| *5)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Complex| *4))))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Complex| *5))))
       (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Expression| *4)) (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Expression| *5)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Expression| (|Complex| *4)))
       (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *4 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Expression| (|Complex| *5)))
       (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *5 (|ConvertibleTo| (|Float|)))
       (|isDomain| *2 (|Complex| (|Float|))) (|isDomain| *1 (|Numeric| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|Numeric| *3))
       (|ofCategory| *3 (|ConvertibleTo| *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Float|))
       (|isDomain| *1 (|Numeric| *3)) (|ofCategory| *3 (|ConvertibleTo| *2))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *4)) (|ofCategory| *4 (|Ring|))
       (|ofCategory| *4 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
       (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Polynomial| *5)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *5 (|ConvertibleTo| *2))
       (|isDomain| *2 (|Float|)) (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *4)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
       (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *5 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
       (|isDomain| *1 (|Numeric| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Expression| *4)) (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *4 (|ConvertibleTo| *2))
       (|isDomain| *2 (|Float|)) (|isDomain| *1 (|Numeric| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Expression| *5)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *5 (|ConvertibleTo| *2)) (|isDomain| *2 (|Float|))
       (|isDomain| *1 (|Numeric| *5))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|NewSparseUnivariatePolynomial| *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|List| (|NewSparseUnivariatePolynomial| *3)))
       (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |resultant| *3)
              (|:| |coef1| #1=(|NewSparseUnivariatePolynomial| *3))
              (|:| |coef2| #1#)))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |resultant| *3)
              (|:| |coef1| (|NewSparseUnivariatePolynomial| *3))))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |resultant| *3)
              (|:| |coef2| (|NewSparseUnivariatePolynomial| *3))))
   (|isDomain| *1 (|NewSparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|))))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |outval| *4) (|:| |outmult| (|Integer|))
                   (|:| |outvect| (|List| (|Matrix| *4))))))
       (|isDomain| *1 (|NumericRealEigenPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|NumericRealEigenPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|Matrix| *2)) (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|CharacteristicPolynomialPackage| *2))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1
        (|CharacteristicPolynomialInMonogenicalAlgebra| *4 *2 *3))
       (|ofCategory| *3 (|MonogenicAlgebra| *4 *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Polynomial| *5))
       (|isDomain| *1 (|EigenPackage| *5)) (|ofCategory| *5 (|GcdDomain|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4))))
       (|isDomain| *2 (|Polynomial| *4)) (|isDomain| *1 (|EigenPackage| *4))
       (|ofCategory| *4 (|GcdDomain|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *2))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|)))))
       (|isDomain| *2 (|Polynomial| (|Complex| (|Fraction| (|Integer|)))))
       (|isDomain| *1 (|NumericComplexEigenPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|)))))
       (|isDomain| *4 (|Symbol|))
       (|isDomain| *2 (|Polynomial| (|Complex| (|Fraction| (|Integer|)))))
       (|isDomain| *1 (|NumericComplexEigenPackage| *5))
       (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|NumericRealEigenPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Integer|))))
       (|isDomain| *4 (|Symbol|))
       (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|NumericRealEigenPackage| *5))
       (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|NPCoef| *3 *4 *5 *6 *7))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *6))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))))) 
(((*1 *2 *3 *4 *5)
  (AND (|ofCategory| *6 (|UnivariatePolynomialCategory| *9))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *9 (|EuclideanDomain|))
       (|ofCategory| *10 (|PolynomialCategory| *9 *7 *8))
       (|isDomain| *2
        (|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| *10)))
                  (|:| |dterm|
                       (|List|
                        (|List|
                         (|Record| (|:| |expt| (|NonNegativeInteger|))
                                   (|:| |pcoef| *10)))))
                  (|:| |nfacts| (|List| *6)) (|:| |nlead| (|List| *10))))
       (|isDomain| *1 (|NPCoef| *6 *7 *8 *9 *10))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *10))
       (|isDomain| *4 (|List| *6)) (|isDomain| *5 (|List| *10))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|ofCategory| *5 (|FiniteAlgebraicExtensionField| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|NormRetractPackage| *4 *5 *6 *3 *7))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *6))
       (|ofType| *7 (|PositiveInteger|))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2
        (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *4))))
       (|isDomain| *1 (|NormalizationPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *3 *3 *4 *5)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *6 (|GcdDomain|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|OrderedSet|))
       (|ofCategory| *4 (|RecursivePolynomialCategory| *6 *7 *8))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|NormalizationPackage| *6 *7 *8 *4 *5))
       (|ofCategory| *5 (|RegularTriangularSetCategory| *6 *7 *8 *4))))) 
(((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|ElementaryFunctionStructurePackage| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))
 ((*1 *1 *1) (|isDomain| *1 (|Float|)))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4))))
       (|isDomain| *1 (|NormalizationPackage| *5 *6 *7 *3 *4))
       (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *6))
       (|isDomain| *1 (|NormalizationPackage| *4 *5 *6 *2 *3))
       (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *2))))) 
(((*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Float|))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|NonNegativeInteger|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Hostname|)) (|isDomain| *4 (|PortNumber|))
       (|isDomain| *2 (|Maybe| (|InetClientStreamSocket|)))
       (|isDomain| *1 (|InetClientStreamSocket|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PortNumber|)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|Maybe| *1))
       (|ofCategory| *1 (|NetworkClientSocket| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|NetworkClientSocket| *3))
       (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|)))))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |outval| (|Complex| *4)) (|:| |outmult| (|Integer|))
                   (|:| |outvect| (|List| (|Matrix| (|Complex| *4)))))))
       (|isDomain| *1 (|NumericComplexEigenPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| (|Complex| (|Fraction| (|Integer|)))))
       (|isDomain| *2 (|List| (|Complex| *4)))
       (|isDomain| *1 (|NumericComplexEigenPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|Group|)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|)))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|ofCategory| *1 (|NonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6))
       (|isDomain| *3 (|Integer|)) (|ofCategory| *6 (|EuclideanDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *9))
       (|isDomain| *4 (|List| *7)) (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *8 (|EuclideanDomain|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))
       (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9))
       (|isDomain| *5 (|NonNegativeInteger|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *4 (|Factored| *2))
       (|ofCategory| *2 (|PolynomialCategory| *7 *5 *6))
       (|isDomain| *1 (|MultivariateSquareFree| *5 *6 *7 *2))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|EuclideanDomain|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *9))
       (|isDomain| *4 (|List| *7)) (|isDomain| *5 (|List| (|List| *8)))
       (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|))
       (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|Record| (|:| |upol| (|SparseUnivariatePolynomial| *8))
                  (|:| |Lval| (|List| *8))
                  (|:| |Lfact|
                       (|List|
                        (|Record|
                         (|:| |factor| (|SparseUnivariatePolynomial| *8))
                         (|:| |exponent| (|Integer|)))))
                  (|:| |ctpol| *8)))
       (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|List| *7)) (|isDomain| *5 (|List| (|List| *8)))
       (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |unitPart| *9)
                  (|:| |suPart|
                       (|List|
                        (|Record|
                         (|:| |factor| (|SparseUnivariatePolynomial| *9))
                         (|:| |exponent| (|Integer|)))))))
       (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *9))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Integer|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|))
       (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7))
       (|isDomain| *2
        (|Record| (|:| |pol| (|SparseUnivariatePolynomial| *9))
                  (|:| |polval| (|SparseUnivariatePolynomial| *8))))
       (|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *9))
       (|isDomain| *4 (|SparseUnivariatePolynomial| *8))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MultivariateSquareFree| *5 *4 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |factor| (|SparseUnivariatePolynomial| *6))
               (|:| |exponent| (|Integer|)))))
   (|ofCategory| *6 (|EuclideanDomain|))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7))
   (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|EuclideanDomain|))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *6 *4 *5))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|MergeThing| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|MoreSystemCommands|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Multiset| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|Multiset| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1)
  (AND (|isDomain| *1 (|Multiset| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Multiset| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|MonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|Monoid|))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *6 (|IntegralDomain|))
       (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4))
       (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2))
       (|isDomain| *3 (|Fraction| (|Polynomial| *6)))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $)))))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Polynomial| *6)))
       (|ofCategory| *6 (|IntegralDomain|))
       (|ofCategory| *2
                     (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *5
                                           *4))
       (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $)))))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2))
       (|ofCategory| *2
                     (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *5
                                           *4))
       (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $)))))
       (|ofCategory| *6 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |convert| ((|Symbol|) $)))))
       (|ofCategory| *6 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |sup| (|Polynomial| *6)) (|:| |inf| (|Polynomial| *6))))
       (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3))
       (|ofCategory| *3
                     (|PolynomialCategory| (|Fraction| (|Polynomial| *6)) *4
                                           *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|CartesianTensor| *5 *6 *7))
       (|ofType| *5 (|Integer|)) (|ofType| *6 (|NonNegativeInteger|))
       (|ofCategory| *7 (|CommutativeRing|))
       (|ofCategory| *8 (|CommutativeRing|))
       (|isDomain| *2 (|CartesianTensor| *5 *6 *8))
       (|isDomain| *1 (|CartesianTensorFunctions2| *5 *6 *7 *8))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *9)) (|ofCategory| *9 (|Ring|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|Ring|))
       (|ofCategory| *2 (|PolynomialCategory| *9 *7 *5))
       (|isDomain| *1 (|MPolyCatFunctions2| *5 *6 *7 *8 *9 *4 *2))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|PolynomialCategory| *8 *6 *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| *2)) (|isDomain| *4 (|Mapping| *2 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *1 (|MonomialExtensionTools| *5 *2))
       (|ofCategory| *5 (|Field|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *3 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|Record| (|:| |normal| (|Factored| *3))
                  (|:| |special| (|Factored| *3))))
       (|isDomain| *1 (|MonomialExtensionTools| *5 *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MonoidOperatorCategory| *2))
       (|ofCategory| *2 (|BasicType|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|))
       (|isDomain| *1 (|MonoidOperation| *3))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Arity|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|AntiSymm| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|DeRhamComplex| *3 *4))
       (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2))
       (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2))
   (|ofCategory| *3 (|Field|))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
   (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 *2)
       (|ofType| *4 *2) (|ofCategory| *5 (|CommutativeRing|))))
 ((*1 *1)
  (AND (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *1 (|MonogenicAlgebra| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Vector| *1)) (|isDomain| *4 (|Mapping| *5 *5))
       (|ofCategory| *5 (|Field|)) (|ofCategory| *1 (|MonogenicAlgebra| *5 *6))
       (|ofCategory| *5 (|CommutativeRing|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2 (|Matrix| *5))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|MonadWithUnit|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|MonadWithUnit|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
   (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|)))) 
(((*1 *1 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
   (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|)))) 
(((*1 *1 *2 *2 *2 *2)
  (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1 *1 *1)
  (|partial| AND (|ofCategory| *2 (|CommutativeRing|))
   (|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
   (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *3 *3 *4))
   (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4))
   (|ofType| *7 (|Mapping| (|Union| *3 "failed") *3 *3 *4))))
 ((*1 *1 *1 *1)
  (|partial| AND (|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6))
   (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|))
   (|ofType| *4 (|Mapping| *2 *2 *3))
   (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3))
   (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))
 ((*1 *1 *1 *1)
  (|partial| AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6))
   (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|))
   (|ofType| *4 (|Mapping| *2 *2 *3))
   (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3))
   (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5))
       (|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5))
       (|ofCategory| *3 (|Field|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Factored| *3))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|ModuleMonomial| *3 *2 *4))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofType| *4
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *3) (|:| |exponent| *2))
                   (|Record| (|:| |index| *3) (|:| |exponent| *2))))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|Finite|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|OrderedType|))
       (|isDomain| *1 (|IndexedProductTerm| *3 *2))
       (|ofCategory| *3 (|BasicType|))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *4))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *2 (|OrderedSet|))
       (|isDomain| *1 (|ModuleMonomial| *2 *3 *4))
       (|ofCategory| *3 (|SetCategory|))
       (|ofType| *4
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *3))
                   (|Record| (|:| |index| *2) (|:| |exponent| *3))))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|ModMonic| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Vector| *3))
       (|isDomain| *1 (|ModMonic| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|ModMonic| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Vector| *3))
       (|isDomain| *1 (|ModMonic| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|PrimitiveArray| (|ModMonic| *3 *4)))
       (|isDomain| *1 (|ModMonic| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *2 (|PrimitiveArray| (|ModMonic| *3 *4)))
       (|isDomain| *1 (|ModMonic| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *2 (|FiniteFieldCategory|)) (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|ModMonic| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|MathMLFormat|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|MathMLFormat|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|))
       (|isDomain| *1 (|MathMLFormat|))))) 
(((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *13)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *13))
   (|isDomain| *4 (|List| *12)) (|isDomain| *5 (|List| *10))
   (|isDomain| *6 (|List| *13))
   (|isDomain| *7
    (|List|
     (|List|
      (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| *13)))))
   (|isDomain| *8 (|List| (|NonNegativeInteger|)))
   (|isDomain| *9 (|Vector| (|List| (|SparseUnivariatePolynomial| *10))))
   (|ofCategory| *12 (|OrderedSet|)) (|ofCategory| *10 (|EuclideanDomain|))
   (|ofCategory| *13 (|PolynomialCategory| *10 *11 *12))
   (|ofCategory| *11 (|OrderedAbelianMonoidSup|))
   (|isDomain| *1 (|MultivariateLifting| *11 *12 *10 *13))))) 
(((*1 *2 *3 *4 *5 *6 *7 *8 *9)
  (|partial| AND (|isDomain| *4 (|List| *11))
   (|isDomain| *5 (|List| (|SparseUnivariatePolynomial| *9)))
   (|isDomain| *6 (|List| *9)) (|isDomain| *7 (|List| *12))
   (|isDomain| *8 (|List| (|NonNegativeInteger|)))
   (|ofCategory| *11 (|OrderedSet|)) (|ofCategory| *9 (|EuclideanDomain|))
   (|ofCategory| *12 (|PolynomialCategory| *9 *10 *11))
   (|ofCategory| *10 (|OrderedAbelianMonoidSup|))
   (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *12)))
   (|isDomain| *1 (|MultivariateLifting| *10 *11 *9 *12))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *12))))) 
(((*1 *2 *3 *4 *5 *6 *2 *7 *8)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *11)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *11))
   (|isDomain| *4 (|List| *10)) (|isDomain| *5 (|List| *8))
   (|isDomain| *6 (|List| (|NonNegativeInteger|)))
   (|isDomain| *7 (|Vector| (|List| (|SparseUnivariatePolynomial| *8))))
   (|ofCategory| *10 (|OrderedSet|)) (|ofCategory| *8 (|EuclideanDomain|))
   (|ofCategory| *11 (|PolynomialCategory| *8 *9 *10))
   (|ofCategory| *9 (|OrderedAbelianMonoidSup|))
   (|isDomain| *1 (|MultivariateLifting| *9 *10 *8 *11))))) 
(((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Mapping| *7 *5 *6))
       (|isDomain| *1 (|MakeBinaryCompiledFunction| *3 *5 *6 *7))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *7 (|Type|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Mapping| *6 *5))
       (|isDomain| *1 (|MakeUnaryCompiledFunction| *3 *5 *6))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| *6 *5))
       (|isDomain| *1 (|MakeUnaryCompiledFunction| *4 *5 *6))
       (|ofCategory| *4 (|ConvertibleTo| (|InputForm|)))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *2 (|Record| (|:| |part1| *3) (|:| |part2| *4)))
       (|isDomain| *1 (|MakeRecord| *3 *4)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *4 (|Type|))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|Symbol|))
       (|isDomain| *1 (|InputForm|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|MakeFunction| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *2 *3 *2 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|MakeFunction| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *2 *3 *2 *2 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|MakeFunction| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *2 *3 *2 *4)
  (AND (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|Symbol|))
       (|isDomain| *1 (|MakeFunction| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *1 (|MakeFloatCompiledFunction| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|isDomain| *2
        (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *1 (|MakeFloatCompiledFunction| *3))
       (|ofCategory| *3 (|ConvertibleTo| (|InputForm|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Mapping| *7 *5 *6))
       (|isDomain| *1 (|MakeBinaryCompiledFunction| *4 *5 *6 *7))
       (|ofCategory| *4 (|ConvertibleTo| (|InputForm|)))
       (|ofCategory| *5 (|Type|)) (|ofCategory| *6 (|Type|))
       (|ofCategory| *7 (|Type|))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *6))
       (|ofCategory| *6 (|MatrixCategory| *3 *4 *5))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3)))
       (|isDomain| *1 (|ModularHermitianRowReduction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|ModularHermitianRowReduction| *3))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|ModularHermitianRowReduction| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|ModularHermitianRowReduction| *3))))) 
(((*1 *2 *3 *3 *3 *4)
  (AND
   (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4
    (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)
               (|DoubleFloat|)))
   (|isDomain| *2
    (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|))))) 
(((*1 *2 *3 *3 *3 *4 *5 *6)
  (AND (|isDomain| *3 (|Expression| (|Integer|)))
       (|isDomain| *4 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *5 (|Segment| (|DoubleFloat|)))
       (|isDomain| *6 (|List| (|DrawOption|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|))))) 
(((*1 *2 *3 *4 *5 *5 *6)
  (AND
   (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4
    (|Union|
     (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)
                (|DoubleFloat|))
     "undefined"))
   (|isDomain| *5 (|Segment| (|DoubleFloat|)))
   (|isDomain| *6 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|))))) 
(((*1 *2 *3 *3 *3 *4 *5 *5 *6)
  (AND
   (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4
    (|Union|
     (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)
                (|DoubleFloat|))
     "undefined"))
   (|isDomain| *5 (|Segment| (|DoubleFloat|)))
   (|isDomain| *6 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3
    (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|DoubleFloat|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|))))
 ((*1 *2 *2 *3 *4 *4 *5)
  (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *3
        (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *4 (|Segment| (|DoubleFloat|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|))))) 
(((*1 *2 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *2 *3 *2 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| *5))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| *5))
   (|isDomain| *1 (|DistinctDegreeFactorize| *4 *5))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|Record| (|:| |factor| *5) (|:| |degree| (|Integer|)))))
   (|isDomain| *4 (|Integer|))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2 (|List| *5))
   (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Integer|))
       (|isDomain| *2 (|List| (|Record| (|:| |factor| *3) (|:| |degree| *4))))
       (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2))
       (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|MultiDictionary| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|MultiDictionary| *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |entry| *3) (|:| |count| (|NonNegativeInteger|)))))))) 
(((*1 *1 *2) (AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *1) (AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *2 *2 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *4))))) 
(((*1 *2 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))) 
(((*1 *2 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))) 
(((*1 *2 *2 *3 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))
 ((*1 *2 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))) 
(((*1 *2 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|StorageEfficientMatrixOperations| *3))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *3 (|CommutativeRing|))
   (|ofCategory| *4 (|FiniteLinearAggregate| *3))
   (|ofCategory| *5 (|FiniteLinearAggregate| *3))
   (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2))
   (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(((*1 *2 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|ofCategory| *6 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *5 *6 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *5 *6))))) 
(((*1 *2 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|ofCategory| *6 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *5 *6 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *5 *6))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))
       (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *2))
       (|ofCategory| *2 (|MatrixCategory| *4 *5 *6))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))) 
(((*1 *1 *1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))) 
(((*1 *1 *1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))) 
(((*1 *1 *1 *2 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))) 
(((*1 *1 *1 *2 *2 *1)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *6 *4 *5)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|Mapping| *6 *5 *4))
       (|isDomain| *1 (|MappingPackage3| *4 *5 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6 *4 *5))
       (|isDomain| *1 (|MappingPackage3| *4 *5 *6))
       (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *6 *4)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *6 (|SetCategory|)) (|isDomain| *2 (|Mapping| *6 *4 *5))
       (|isDomain| *1 (|MappingPackage3| *4 *5 *6))
       (|ofCategory| *5 (|SetCategory|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *4 *5)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|Mapping| *6 *5))
       (|isDomain| *1 (|MappingPackage3| *4 *5 *6))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *6 *5 *4)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|isDomain| *2 (|Mapping| *6 *5))
       (|isDomain| *1 (|MappingPackage3| *5 *4 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *5 *4 *4)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Mapping| *5 *4))
       (|isDomain| *1 (|MappingPackage2| *4 *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *5 *4)) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Mapping| *5))
       (|isDomain| *1 (|MappingPackage2| *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *3 *4))
       (|isDomain| *1 (|MappingPackage2| *4 *3))
       (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 (|NonNegativeInteger|) *2))
       (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|MappingPackageInternalHacks1| *2))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Mapping| *3 (|NonNegativeInteger|) *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|MappingPackage1| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *1 (|MappingPackage1| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *2 *2)) (|isDomain| *1 (|MappingPackage1| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| #1=(|List| *5) #1#))
       (|isDomain| *4 (|Integer|)) (|isDomain| *2 (|List| *5))
       (|isDomain| *1 (|MappingPackage1| *5))
       (|ofCategory| *5 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *3)) (|isDomain| *1 (|MappingPackage1| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *3 (|TypeAst|))
       (|isDomain| *1 (|MappingAst|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| *2 *6)) (|isDomain| *4 (|Mapping| *6 *5))
       (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))
       (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|MappingPackageInternalHacks3| *5 *6 *2))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *1 (|MappingPackageInternalHacks2| *3 *2))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *1 (|MappingPackageInternalHacks2| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3 *4 *2)
  (AND (|isDomain| *3 (|Mapping| *2 *2)) (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|MappingPackageInternalHacks1| *2))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|OrderedFreeMonoid| *4))
       (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|LyndonWord| *4))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|OrderedFreeMonoid| *3))
       (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|LyndonWord| *3))))) 
(((*1 *1 *2)
  (|partial| AND (|isDomain| *2 (|OrderedFreeMonoid| *3))
   (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|LyndonWord| *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|OneDimensionalArray| (|List| (|LyndonWord| *5))))
       (|isDomain| *1 (|LyndonWord| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|List| (|LyndonWord| *5)))
       (|isDomain| *1 (|LyndonWord| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *7))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|IntegralDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|Record|
         (|:| |particular| (|Union| (|Vector| (|Fraction| *8)) "failed"))
         (|:| |basis| (|List| (|Vector| (|Fraction| *8))))))
       (|isDomain| *1 (|LinearSystemPolynomialPackage| *5 *6 *7 *8))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|))
       (|ofCategory| *6
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|ofCategory| *4
                     (|Join| (|FiniteLinearAggregate| *5)
                             (|ShallowlyMutableAggregate| *5)))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *4 *3))
       (|ofCategory| *3 (|MatrixCategory| *5 *6 *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *5)) (|isDomain| *4 (|Vector| *5))
       (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|LinearSystemMatrixPackage1| *5))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *4)))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
   (|ofCategory| *4 (|PolynomialFactorizationExplicit|))
   (|isDomain| *1 (|LinearPolynomialEquationByFractions| *4))))) 
(((*1 *1 *1) (|ofCategory| *1 (|Logic|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|Logic|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|Logic|)))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 (|Field|))
       (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *4 *2))
       (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *3))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|Field|))))
 ((*1 *2 *2 *3 *4)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Mapping| *5 *5))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *5 *2))
       (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *2 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 (|Field|))
       (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *4 *2))
       (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|AlgebraicallyClosedField|))
       (|ofCategory| *4
                     (|Join| (|Field|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|RetractableTo| (|Fraction| (|Integer|)))))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2
        (|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5))))
       (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *4 *5))
       (|isDomain| *3
        (|LinearOrdinaryDifferentialOperator1| (|Fraction| *5)))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|UniversalSegment| (|Integer|)))
       (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4))))
       (|isDomain| *1 (|ListMonoidOps| *3 *4 *5))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|))
       (|ofType| *5 *4)))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4))))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|))
       (|ofType| *5 *4) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|FreeGroup| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeMonoidCategory| *4))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|AbelianMonoid|))
       (|isDomain| *1 (|ListMonoidOps| *4 *2 *5))
       (|ofCategory| *4 (|SetCategory|)) (|ofType| *5 *2)))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *4))
       (|ofCategory| *4 (|CancellationAbelianMonoid|))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|FreeGroup| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeMonoidCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2))
       (|ofCategory| *2 (|IntegralDomain|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|ListMonoidOps| *2 *4 *5))
       (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4)))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))) 
(((*1 *1)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))
 ((*1 *1 *2 *3 *1)
  (AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|AbelianMonoid|))
       (|ofType| *4 *3)))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|AbelianMonoid|))
       (|ofType| *5 *4)))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Integer|) (|Integer|)))
       (|isDomain| *1 (|FreeGroup| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND
   (|isDomain| *2 (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)))
   (|ofCategory| *1 (|FreeMonoidCategory| *3))
   (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *4 (|AbelianMonoid|))
       (|ofType| *5 *4) (|isDomain| *1 (|ListMonoidOps| *3 *4 *5))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4 (|CancellationAbelianMonoid|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|FreeGroup| *3))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|ofCategory| *1 (|FreeMonoidCategory| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|ListMonoidOps| *3 *4 *5))
       (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 *4)))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ListMultiDictionary| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2 *2 *1)
  (AND (|isDomain| *1 (|ListMultiDictionary| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|List| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *1 *1 *1) (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|List| *2)) (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|LinearForm| *3 *4)) (|ofType| *4 (|List| (|Symbol|)))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|LinearlyExplicitRingOver| *4))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |mat| (|Matrix| *4)) (|:| |vec| (|Vector| *4))))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|LinearlyExplicitRingOver| *4))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Matrix| *1)) (|isDomain| *4 (|Vector| *1))
       (|ofCategory| *1 (|LinearlyExplicitRingOver| *5))
       (|ofCategory| *5 (|Ring|))
       (|isDomain| *2
        (|Record| (|:| |mat| (|Matrix| *5)) (|:| |vec| (|Vector| *5))))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *1))
       (|ofCategory| *1 (|LinearlyExplicitRingOver| *4))
       (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|LinearElement| *3 *4))
       (|ofType| *4 (|List| (|Symbol|)))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Vector| *4))
   (|ofCategory| *4 (|Join| (|Ring|) (|LinearlyExplicitRingOver| *5)))
   (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|IntegralDomain|))
   (|isDomain| *2 (|Vector| *5)) (|isDomain| *1 (|LinearDependence| *5 *4))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Vector| *4))
   (|ofCategory| *4 (|Join| (|Ring|) (|LinearlyExplicitRingOver| *5)))
   (|not| (|ofCategory| *5 (|Field|))) (|ofCategory| *5 (|IntegralDomain|))
   (|isDomain| *2 (|Vector| (|Fraction| *5)))
   (|isDomain| *1 (|LinearDependence| *5 *4))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Vector| *5))
   (|ofCategory| *5 (|Join| (|Ring|) (|LinearlyExplicitRingOver| *4)))
   (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Vector| *4))
   (|isDomain| *1 (|LinearDependence| *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *5))
       (|ofCategory| *5 (|Join| (|Ring|) (|LinearlyExplicitRingOver| *4)))
       (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|LinearDependence| *4 *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| (|OrderedCompletion| *3)))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Union| (|OrderedCompletion| *3)
                 (|Record|
                  (|:| |leftHandLimit|
                       (|Union| (|OrderedCompletion| *3) #1="failed"))
                  (|:| |rightHandLimit|
                       (|Union| (|OrderedCompletion| *3) #1#)))
                 "failed"))
       (|isDomain| *1 (|PowerSeriesLimitPackage| *5 *3))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Equation| *3)) (|isDomain| *5 (|String|))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *6)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|OrderedCompletion| *3))
   (|isDomain| *1 (|PowerSeriesLimitPackage| *6 *3))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| (|OrderedCompletion| (|Polynomial| *5))))
       (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *2
        (|Union| (|OrderedCompletion| #2=(|Fraction| (|Polynomial| *5)))
                 (|Record|
                  (|:| |leftHandLimit|
                       (|Union| (|OrderedCompletion| #2#) #3="failed"))
                  (|:| |rightHandLimit|
                       (|Union| (|OrderedCompletion| #2#) #3#)))
                 #4="failed"))
       (|isDomain| *1 (|RationalFunctionLimitPackage| *5))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *2
        (|Union| (|OrderedCompletion| *3)
                 (|Record|
                  (|:| |leftHandLimit| (|Union| (|OrderedCompletion| *3) #3#))
                  (|:| |rightHandLimit|
                       (|Union| (|OrderedCompletion| *3) #3#)))
                 #4#))
       (|isDomain| *1 (|RationalFunctionLimitPackage| *5))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Equation| (|Fraction| (|Polynomial| *6))))
   (|isDomain| *5 (|String|)) (|isDomain| *3 (|Fraction| (|Polynomial| *6)))
   (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|OrderedCompletion| *3))
   (|isDomain| *1 (|RationalFunctionLimitPackage| *6))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|Equation| (|OnePointCompletion| *3)))
   (|ofCategory| *5
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|OnePointCompletion| *3))
   (|isDomain| *1 (|PowerSeriesLimitPackage| *5 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| (|OnePointCompletion| (|Polynomial| *5))))
       (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *2 (|OnePointCompletion| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *1 (|RationalFunctionLimitPackage| *5))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Equation| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *2 (|OnePointCompletion| *3))
       (|isDomain| *1 (|RationalFunctionLimitPackage| *5))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) (|isDomain| *1 (|Library|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|KeyedAccessFile| *2))
       (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *1) (|isDomain| *1 (|Library|)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|DistributedMultivariatePolynomial| *4 *5))
       (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *2 (|HomogeneousDistributedMultivariatePolynomial| *4 *5))
       (|isDomain| *1 (|LinGroebnerPackage| *4 *5))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| (|DistributedMultivariatePolynomial| *4 *5)))
       (|isDomain| *2 (|DistributedMultivariatePolynomial| *4 *5))
       (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *1 (|LinGroebnerPackage| *4 *5))))) 
(((*1 *2 *3 *2 *2)
  (AND
   (|isDomain| *2
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5)))
   (|isDomain| *3 (|OrderedVariableList| *4)) (|ofType| *4 (|List| (|Symbol|)))
   (|ofCategory| *5 (|GcdDomain|))
   (|isDomain| *1 (|LinGroebnerPackage| *4 *5))))) 
(((*1 *2 *3 *2 *4)
  (AND (|isDomain| *3 (|List| *6))
       (|isDomain| *4 (|List| (|DistributedMultivariatePolynomial| *5 *6)))
       (|ofCategory| *6 (|GcdDomain|))
       (|isDomain| *2 (|DistributedMultivariatePolynomial| *5 *6))
       (|ofType| *5 (|List| (|Symbol|)))
       (|isDomain| *1 (|LinGroebnerPackage| *5 *6))))) 
(((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))))
   (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND
   (|isDomain| *2
    (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))))
   (|isDomain| *3 (|List| (|DrawOption|)))
   (|isDomain| *1 (|DrawOptionFunctions0|))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *4
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *5 *6)))
   (|isDomain| *3 (|HomogeneousDistributedMultivariatePolynomial| *5 *6))
   (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|GcdDomain|))
   (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|LinGroebnerPackage| *5 *6))))) 
(((*1 *2 *2)
  (AND
   (|isDomain| *2
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *3 *4)))
   (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|GcdDomain|))
   (|isDomain| *1 (|LinGroebnerPackage| *3 *4))))) 
(((*1 *2 *3 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *5 *6)))
   (|isDomain| *4 (|OrderedVariableList| *5)) (|ofType| *5 (|List| (|Symbol|)))
   (|isDomain| *2 (|HomogeneousDistributedMultivariatePolynomial| *5 *6))
   (|isDomain| *1 (|LinGroebnerPackage| *5 *6))
   (|ofCategory| *6 (|GcdDomain|))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *5 *6)))
   (|isDomain| *4 (|OrderedVariableList| *5)) (|ofType| *5 (|List| (|Symbol|)))
   (|isDomain| *2 (|HomogeneousDistributedMultivariatePolynomial| *5 *6))
   (|isDomain| *1 (|LinGroebnerPackage| *5 *6))
   (|ofCategory| *6 (|GcdDomain|))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5)))
   (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|GcdDomain|))
   (|isDomain| *2 (|List| (|DistributedMultivariatePolynomial| *4 *5)))
   (|isDomain| *1 (|LinGroebnerPackage| *4 *5))))) 
(((*1 *2 *3)
  (AND (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *2
        (|Record|
         (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| *4 *5)))
         (|:| |glval| (|List| (|Integer|)))))
       (|isDomain| *1 (|LinGroebnerPackage| *4 *5))
       (|isDomain| *3 (|List| (|DistributedMultivariatePolynomial| *4 *5)))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5)))
   (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|GcdDomain|))
   (|isDomain| *2
    (|Record|
     (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| *4 *5)))
     (|:| |gvlist| (|List| (|Integer|)))))
   (|isDomain| *1 (|LinGroebnerPackage| *4 *5))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|LiouvillianFunction| *3 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *3) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AlgebraicFunction| *4 *5))
       (|ofCategory| *5 (|FunctionSpace| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|CombinatorialFunction| *4 *5))
       (|ofCategory| *5 (|FunctionSpace| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ElementaryFunction| *4 *5))
       (|ofCategory| *5 (|Join| (|FunctionSpace| *4) (|RadicalCategory|)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|ExpressionSpace&| *4))
       (|ofCategory| *4 (|ExpressionSpace|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|BasicOperator|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FunctionSpace&| *4 *5))
       (|ofCategory| *4 (|FunctionSpace| *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *4 *5))
       (|ofCategory| *5 (|FunctionSpace| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|LiouvillianFunction| *4 *5))
       (|ofCategory| *5
                     (|Join| (|FunctionSpace| *4) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6))))
   (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
   (|ofType| *6 (|List| (|Symbol|)))
   (|isDomain| *2
    (|List|
     (|SquareFreeRegularTriangularSet| *5
                                       (|IndexedExponents|
                                        (|OrderedVariableList| *6))
                                       (|OrderedVariableList| *6)
                                       (|NewSparseMultivariatePolynomial| *5
                                                                          (|OrderedVariableList|
                                                                           *6)))))
   (|isDomain| *1 (|LexTriangularPackage| *5 *6))))) 
(((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6))))
   (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|))
   (|ofType| *6 (|List| (|Symbol|)))
   (|isDomain| *2 (|List| (|RegularChain| *5 *6)))
   (|isDomain| *1 (|LexTriangularPackage| *5 *6))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| (|Polynomial| *3)))
       (|ofCategory| *3 (|GcdDomain|))
       (|isDomain| *1 (|FGLMIfCanPackage| *3 *4))
       (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerPackage| *3 *4 *5 *6))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *7))))
 ((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *7))))
 ((*1 *1 *1)
  (AND (|ofCategory| *2 (|Field|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4))))
 ((*1 *2 *2)
  (AND
   (|isDomain| *2
    (|List| (|NewSparseMultivariatePolynomial| *3 (|OrderedVariableList| *4))))
   (|ofCategory| *3 (|GcdDomain|)) (|ofType| *4 (|List| (|Symbol|)))
   (|isDomain| *1 (|LexTriangularPackage| *3 *4))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|List| (|Polynomial| *3)))
   (|ofCategory| *3 (|GcdDomain|)) (|isDomain| *1 (|FGLMIfCanPackage| *3 *4))
   (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *2)
  (|partial| AND
   (|isDomain| *2
    (|List| (|NewSparseMultivariatePolynomial| *3 (|OrderedVariableList| *4))))
   (|ofCategory| *3 (|GcdDomain|)) (|ofType| *4 (|List| (|Symbol|)))
   (|isDomain| *1 (|LexTriangularPackage| *3 *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Polynomial| *4)))
       (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FGLMIfCanPackage| *4 *5))
       (|ofType| *5 (|List| (|Symbol|)))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *5))))
   (|ofCategory| *4 (|GcdDomain|)) (|ofType| *5 (|List| (|Symbol|)))
   (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LexTriangularPackage| *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *2 (|List| (|LiePolynomial| *4 *5)))
       (|isDomain| *1 (|LieExponentials| *4 *5 *6))
       (|ofCategory| *5
                     (|Join| (|CommutativeRing|)
                             (|Module| (|Fraction| (|Integer|)))))
       (|ofType| *6 (|PositiveInteger|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2 (|List| (|Record| (|:| |k| (|LyndonWord| *3)) (|:| |c| *4))))
   (|isDomain| *1 (|LieExponentials| *3 *4 *5))
   (|ofCategory| *3 (|OrderedSet|))
   (|ofCategory| *4
                 (|Join| (|CommutativeRing|)
                         (|Module| (|Fraction| (|Integer|)))))
   (|ofType| *5 (|PositiveInteger|))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|List| (|Equation| *4)))
       (|isDomain| *1 (|LieExponentials| *3 *4 *5))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4
                     (|Join| (|CommutativeRing|)
                             (|Module| (|Fraction| (|Integer|)))))
       (|ofType| *5 (|PositiveInteger|))))) 
(((*1 *2 *3 *4 *5 *6 *7 *6)
  (|partial| AND
   (|isDomain| *5
    (|Record| (|:| |contp| *3)
              (|:| |factors|
                   (|List|
                    (|Record| (|:| |irr| *10) (|:| |pow| (|Integer|)))))))
   (|isDomain| *6 (|List| *3)) (|isDomain| *7 (|List| *8))
   (|ofCategory| *8 (|OrderedSet|)) (|ofCategory| *3 (|EuclideanDomain|))
   (|ofCategory| *10 (|PolynomialCategory| *3 *9 *8))
   (|ofCategory| *9 (|OrderedAbelianMonoidSup|))
   (|isDomain| *2
    (|Record| (|:| |polfac| (|List| *10)) (|:| |correct| *3)
              (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| *3)))))
   (|isDomain| *1 (|LeadingCoefDetermination| *8 *9 *3 *10))
   (|isDomain| *4 (|List| (|SparseUnivariatePolynomial| *3)))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *5 (|List| *3))
       (|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|LeadingCoefDetermination| *6 *7 *3 *8))
       (|ofCategory| *8 (|PolynomialCategory| *3 *7 *6))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5))
       (|isDomain| *1 (|LazardSetSolvingPackage| *3 *4 *5 *6 *7 *2))
       (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6))
       (|ofCategory| *2
                     (|SquareFreeRegularTriangularSetCategory| *3 *4 *5 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|IntegralDomain|))
       (|isDomain| *1 (|LaurentPolynomial| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|LaplaceTransform| *4 *2))
       (|ofCategory| *2
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *4)))))) 
(((*1 *1) (|isDomain| *1 (|KleeneTrivalentLogic|)))) 
(((*1 *2 *3 *3 *3)
  (|partial| AND
   (|ofCategory| *4
                 (|Join| (|CharacteristicZero|) (|AlgebraicallyClosedField|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| *5)))
   (|isDomain| *1 (|Kovacic| *4 *5)) (|isDomain| *3 (|Fraction| *5))))
 ((*1 *2 *3 *3 *3 *4)
  (|partial| AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5
                 (|Join| (|CharacteristicZero|) (|AlgebraicallyClosedField|)
                         (|RetractableTo| (|Integer|))
                         (|RetractableTo| (|Fraction| (|Integer|)))))
   (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| *6)))
   (|isDomain| *1 (|Kovacic| *5 *6)) (|isDomain| *3 (|Fraction| *6))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|Kernel| *4))
   (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))
   (|isDomain| *1 (|KernelFunctions2| *2 *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Kernel| *4)) (|isDomain| *1 (|KernelFunctions2| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *2 (|TranscendentalFunctionCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *1 (|FourierComponent| *2))
       (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Kernel| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *2 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|BasicOperator|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Kernel| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| *5))
       (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *1 (|Kernel| *5))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Kernel| *3))
   (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|KeyedDictionary| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|KeyedDictionary| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|List| *3))))) 
(((*1 *2 *3 *1)
  (|partial| AND (|ofCategory| *1 (|KeyedDictionary| *3 *2))
   (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1) (|isDomain| *1 (|JVMClassFileAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMFieldAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMFieldAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMFieldAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMFieldAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMClassFileAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMFieldAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMClassFileAccess|)))
 ((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMMethodAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMFieldAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMFieldAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMConstantTag|)))) 
(((*1 *1) (|isDomain| *1 (|JVMClassFileAccess|)))) 
(((*1 *1) (|isDomain| *1 (|JVMClassFileAccess|)))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))))
   (|isDomain| *1 (|FunctorData|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|JoinAst|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|List| *4))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|List| *3))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|BasicType|))
       (|ofCategory| *1 (|IndexedAggregate| *4 *3))
       (|ofCategory| *4 (|BasicType|)) (|ofCategory| *3 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *2 (|BasicType|)) (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *2 (|BasicType|)) (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *3 *4))
       (|ofCategory| *2 (|Type|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *2))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|IndexedAggregate| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *4))
       (|ofCategory| *1 (|IndexedAggregate| *3 *4))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Void|))))) 
(((*1 *2 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Kernel| *2)))
       (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| (|Complex| *5))
                             (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *1 (|InnerTrigonometricManipulations| *5 *6 *2))
       (|ofCategory| *6
                     (|Join| (|FunctionSpace| *5) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Complex| *5))
       (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *5 *3))
       (|ofCategory| *5
                     (|Join| (|FunctionSpace| *4) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| (|Complex| *4))
                             (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| (|Complex| *4))
                             (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))
       (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *3 *2))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| *4) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *4) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))
       (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *2 *3))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| (|Complex| *4))
                             (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Complex| *5))
       (|ofCategory| *5
                     (|Join| (|FunctionSpace| *4) (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| (|Complex| *4))
                             (|RadicalCategory|)
                             (|TranscendentalFunctionCategory|)))
       (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *5 *2))))) 
(((*1 *1) (|isDomain| *1 (|InternalTypeForm|)))) 
(((*1 *1) (|isDomain| *1 (|InternalTypeForm|)))) 
(((*1 *1) (|isDomain| *1 (|InternalTypeForm|)))) 
(((*1 *1) (|isDomain| *1 (|InternalTypeForm|)))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|InternalTypeForm|)))
       (|isDomain| *1 (|InternalTypeForm|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Reference| (|OrderedCompletion| (|Integer|))))
       (|isDomain| *3 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *4))))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *4))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Reference| (|OrderedCompletion| (|Integer|))))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3))))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1 *1 *2)
  (|partial| AND (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3))
   (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *3 *4 *5 *6 *7)
  (AND (|isDomain| *3 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *6))))
       (|isDomain| *4 (|Reference| (|OrderedCompletion| (|Integer|))))
       (|isDomain| *5 (|Symbol|)) (|isDomain| *7 (|Fraction| (|Integer|)))
       (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|OutputForm|))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *6))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3))
       (|ofCategory| *3 (|Algebra| *2)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2))
       (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))
       (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *3))
       (|ofCategory| *3 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1
        (|InternalRationalUnivariateRepresentationPackage| *5 *6 *7 *8 *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *4 (|Permutation| (|Integer|)))
       (|isDomain| *2 (|Matrix| (|Integer|)))
       (|isDomain| *1 (|IrrRepSymNatPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *2 (|List| (|Matrix| (|Integer|))))
       (|isDomain| *1 (|IrrRepSymNatPackage|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *4 (|List| (|Permutation| (|Integer|))))
       (|isDomain| *2 (|List| (|Matrix| (|Integer|))))
       (|isDomain| *1 (|IrrRepSymNatPackage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|IrrRepSymNatPackage|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|FunctionSpaceComplexIntegration| *4 *2))
       (|ofCategory| *2
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *4)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5)))
       (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|CharacteristicZero|))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Expression| *5))
       (|isDomain| *1 (|IntegrationResultRFToFunction| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|IntegrationResult| *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedFunctionSpace| *4)
                             (|TranscendentalFunctionCategory|)))
       (|isDomain| *1 (|IntegrationResultToFunction| *4 *2))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|IntegrationResult| (|Fraction| (|Polynomial| *4))))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Expression| *4))
       (|isDomain| *1 (|IntegrationResultRFToFunction| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|IrredPolyOverFiniteField| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *1 (|IntegerRoots| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *1 (|IntegerRoots| *2))
   (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegerRoots| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|IntegerRoots| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|isDomain| *1 (|IntegerRoots| *2))
   (|ofCategory| *2 (|IntegerNumberSystem|))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *2
    (|Record| (|:| |base| *3) (|:| |exponent| (|NonNegativeInteger|))))
   (|isDomain| *1 (|IntegerRoots| *3))
   (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|IntegerRoots| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|InternalTypeForm|))
       (|isDomain| *1 (|InternalRepresentationForm|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|InternalTypeForm|))
       (|isDomain| *1 (|InternalRepresentationForm|))))) 
(((*1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|InternalTypeForm|))
       (|isDomain| *1 (|InternalRepresentationForm|))))) 
(((*1 *1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |scalar| (|Fraction| (|Integer|)))
               (|:| |coeff| (|SparseUnivariatePolynomial| *2))
               (|:| |logand| (|SparseUnivariatePolynomial| *2)))))
   (|isDomain| *4 (|List| (|Record| (|:| |integrand| *2) (|:| |intvar| *2))))
   (|ofCategory| *2 (|Field|)) (|isDomain| *1 (|IntegrationResult| *2))))) 
(((*1 *2 *1)
  (AND (|isDomain| *1 (|IntegrationResult| *2)) (|ofCategory| *2 (|Field|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |scalar| (|Fraction| (|Integer|)))
               (|:| |coeff| (|SparseUnivariatePolynomial| *3))
               (|:| |logand| (|SparseUnivariatePolynomial| *3)))))
   (|isDomain| *1 (|IntegrationResult| *3)) (|ofCategory| *3 (|Field|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2 (|List| (|Record| (|:| |integrand| *3) (|:| |intvar| *3))))
   (|isDomain| *1 (|IntegrationResult| *3)) (|ofCategory| *3 (|Field|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|IntegrationResult| *3))
       (|ofCategory| *3 (|Field|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|InternalPrintPackage|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|IP4Address|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|DataArray| 4 (|Byte|)))
       (|isDomain| *1 (|IP4Address|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Hostname|)) (|isDomain| *2 (|Maybe| (|IP4Address|)))
       (|isDomain| *1 (|IP4Address|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2 (|Maybe| (|Mapping| (|InputForm|) (|List| (|InputForm|)))))
   (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|InputForm|) (|List| (|InputForm|))))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1) (|isDomain| *1 (|IOMode|)))) 
(((*1 *1) (|isDomain| *1 (|IOMode|)))) 
(((*1 *1) (|isDomain| *1 (|IOMode|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|InputOutputBinaryFile|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|FileName|)) (|isDomain| *1 (|InputOutputBinaryFile|))))) 
(((*1 *2 *2 *3 *3)
  (|partial| AND (|isDomain| *3 (|Symbol|))
   (|ofCategory| *4
                 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|InverseLaplaceTransform| *4 *2))
   (|ofCategory| *2
                 (|Join| (|TranscendentalFunctionCategory|)
                         (|PrimitiveFunctionCategory|)
                         (|SpecialFunctionCategory|)
                         (|AlgebraicallyClosedFunctionSpace| *4)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *3 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *2 (|Record| (|:| |answer| *3) (|:| |polypart| *3)))
       (|isDomain| *1 (|TranscendentalIntegration| *5 *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *6 *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|Record| (|:| |ir| (|IntegrationResult| #1=(|Fraction| *6)))
                  (|:| |specpart| #1#) (|:| |polypart| *6)))
       (|isDomain| *1 (|TranscendentalIntegration| *5 *6))
       (|isDomain| *3 (|Fraction| *6))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|LaurentPolynomial| *4 *5))
   (|isDomain| *3
    (|Mapping|
     (|Record| (|:| |ans| *4) (|:| |right| *4) (|:| |sol?| (|Boolean|)))
     (|Integer|) *4))
   (|ofCategory| *4 (|Field|))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *1 (|TranscendentalIntegration| *4 *5))))) 
(((*1 *2 *2 *3 *4)
  (|partial| AND
   (|isDomain| *3
    (|Mapping|
     (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) "failed") *4))
   (|ofCategory| *4 (|Field|))
   (|isDomain| *1 (|TranscendentalIntegration| *4 *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Mapping| *7 *7))
   (|isDomain| *5 (|List| (|Fraction| *7)))
   (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
   (|isDomain| *3 (|Fraction| *7)) (|ofCategory| *6 (|Field|))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *3)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
   (|isDomain| *1 (|TranscendentalIntegration| *6 *7))))) 
(((*1 *2 *3 *4 *3)
  (|partial| AND (|isDomain| *4 (|Mapping| *6 *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5 (|Field|))
   (|isDomain| *2
    (|Record| (|:| |ratpart| #1=(|Fraction| *6)) (|:| |coeff| #1#)))
   (|isDomain| *1 (|TranscendentalIntegration| *5 *6))
   (|isDomain| *3 (|Fraction| *6))))) 
(((*1 *2 *3 *4 *5 *6)
  (|partial| AND (|isDomain| *4 (|Mapping| *8 *8))
   (|isDomain| *5
    (|Mapping|
     (|Record| (|:| |ans| *7) (|:| |right| *7) (|:| |sol?| (|Boolean|)))
     (|Integer|) *7))
   (|isDomain| *6 (|List| (|Fraction| *8))) (|ofCategory| *7 (|Field|))
   (|ofCategory| *8 (|UnivariatePolynomialCategory| *7))
   (|isDomain| *3 (|Fraction| *8))
   (|isDomain| *2
    (|Record|
     (|:| |answer|
          (|Record| (|:| |mainpart| *3)
                    (|:| |limitedlogs|
                         (|List|
                          (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
     (|:| |a0| *7)))
   (|isDomain| *1 (|TranscendentalIntegration| *7 *8))))) 
(((*1 *2 *3 *4 *5 *6)
  (|partial| AND (|isDomain| *4 (|Mapping| *8 *8))
   (|isDomain| *5
    (|Mapping|
     (|Union| (|Record| (|:| |ratpart| *7) (|:| |coeff| *7)) "failed") *7))
   (|isDomain| *6 (|List| (|Fraction| *8))) (|ofCategory| *7 (|Field|))
   (|ofCategory| *8 (|UnivariatePolynomialCategory| *7))
   (|isDomain| *3 (|Fraction| *8))
   (|isDomain| *2
    (|Record|
     (|:| |answer|
          (|Record| (|:| |mainpart| *3)
                    (|:| |limitedlogs|
                         (|List|
                          (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
     (|:| |a0| *7)))
   (|isDomain| *1 (|TranscendentalIntegration| *7 *8))))) 
(((*1 *2 *3 *4 *5 *3)
  (AND (|isDomain| *4 (|Mapping| *7 *7))
       (|isDomain| *5
        (|Mapping|
         (|Record| (|:| |ans| *6) (|:| |right| *6) (|:| |sol?| (|Boolean|)))
         (|Integer|) *6))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|isDomain| *2
        (|Union| (|Record| (|:| |answer| #1=(|Fraction| *7)) (|:| |a0| *6))
                 (|Record| (|:| |ratpart| #1#) (|:| |coeff| #1#)) "failed"))
       (|isDomain| *1 (|TranscendentalIntegration| *6 *7))
       (|isDomain| *3 (|Fraction| *7))))) 
(((*1 *2 *3 *4 *5 *3)
  (AND (|isDomain| *4 (|Mapping| *7 *7))
       (|isDomain| *5
        (|Mapping|
         (|Union| (|Record| (|:| |ratpart| *6) (|:| |coeff| *6)) "failed") *6))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|isDomain| *2
        (|Union| (|Record| (|:| |answer| #1=(|Fraction| *7)) (|:| |a0| *6))
                 (|Record| (|:| |ratpart| #1#) (|:| |coeff| #1#)) "failed"))
       (|isDomain| *1 (|TranscendentalIntegration| *6 *7))
       (|isDomain| *3 (|Fraction| *7))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Mapping| *7 *7))
       (|isDomain| *5
        (|Mapping| (|Union| (|List| *6) "failed") (|Integer|) *6 *6))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|isDomain| *2
        (|Record| (|:| |answer| (|IntegrationResult| (|Fraction| *7)))
                  (|:| |a0| *6)))
       (|isDomain| *1 (|TranscendentalIntegration| *6 *7))
       (|isDomain| *3 (|Fraction| *7))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Mapping| *7 *7))
       (|isDomain| *5
        (|Mapping|
         (|Record| (|:| |ans| *6) (|:| |right| *6) (|:| |sol?| (|Boolean|)))
         (|Integer|) *6))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|isDomain| *2
        (|Record| (|:| |answer| (|IntegrationResult| (|Fraction| *7)))
                  (|:| |a0| *6)))
       (|isDomain| *1 (|TranscendentalIntegration| *6 *7))
       (|isDomain| *3 (|Fraction| *7))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Mapping| *7 *7))
       (|isDomain| *5
        (|Mapping|
         (|Union| (|Record| (|:| |ratpart| *6) (|:| |coeff| *6)) "failed") *6))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|isDomain| *2
        (|Record| (|:| |answer| (|IntegrationResult| (|Fraction| *7)))
                  (|:| |a0| *6)))
       (|isDomain| *1 (|TranscendentalIntegration| *6 *7))
       (|isDomain| *3 (|Fraction| *7))))) 
(((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *5 (|Mapping| (|IntegrationResult| *3) *3 #1=(|Symbol|)))
       (|isDomain| *6
        (|Mapping|
         (|Union| (|Record| (|:| |special| *3) (|:| |integrand| *3)) "failed")
         *3 #1#))
       (|ofCategory| *3 (|ElementaryFunctionCategory|))
       (|ofCategory| *3 (|LiouvillianFunctionCategory|))
       (|ofCategory| *3 (|RetractableTo| *4))
       (|ofCategory| *3 (|FunctionSpace| *7)) (|isDomain| *4 (|Symbol|))
       (|ofCategory| *7 (|ConvertibleTo| (|Pattern| (|Integer|))))
       (|ofCategory| *7 (|GcdDomain|))
       (|ofCategory| *7 (|PatternMatchable| (|Integer|)))
       (|ofCategory| *7 (|SetCategory|))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|IntegrationTools| *7 *3))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|IntegrationTools| *4 *2))
       (|ofCategory| *2 (|ElementaryFunctionCategory|))
       (|ofCategory| *2 (|FunctionSpace| *4))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|IntegrationTools| *4 *2))
       (|ofCategory| *2 (|FunctionSpace| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|Symbol|))
       (|ofCategory| *6 (|FunctionSpace| *5)) (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *2 (|List| (|Kernel| *6)))
       (|isDomain| *1 (|IntegrationTools| *5 *6))))) 
(((*1 *2 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Kernel| *6))) (|isDomain| *4 (|Symbol|))
       (|isDomain| *2 (|Kernel| *6)) (|ofCategory| *6 (|FunctionSpace| *5))
       (|ofCategory| *5 (|SetCategory|))
       (|isDomain| *1 (|IntegrationTools| *5 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Kernel| *5))) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Kernel| *5)) (|isDomain| *1 (|IntegrationTools| *4 *5))
       (|ofCategory| *5 (|FunctionSpace| *4))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| (|Kernel| *5))) (|isDomain| *3 (|Symbol|))
       (|ofCategory| *5 (|FunctionSpace| *4)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|IntegrationTools| *4 *5))))) 
(((*1 *2 *3 *4 *3)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|ofCategory| *5
                 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2
    (|Record| (|:| |ratpart| #1=(|Fraction| (|Polynomial| *5)))
              (|:| |coeff| #1#)))
   (|isDomain| *1 (|RationalFunctionIntegration| *5))
   (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))) 
(((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|isDomain| *5 (|List| (|Fraction| (|Polynomial| *6))))
   (|isDomain| *3 (|Fraction| (|Polynomial| *6)))
   (|ofCategory| *6
                 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *3)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
   (|isDomain| *1 (|RationalFunctionIntegration| *6))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *2 (|Fraction| (|Polynomial| *4)))
   (|isDomain| *3 (|Symbol|))
   (|ofCategory| *4
                 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)))
   (|isDomain| *1 (|RationalFunctionIntegration| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|FunctionSpaceComplexIntegration| *5 *3))
       (|ofCategory| *3
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *5)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)))
       (|isDomain| *2 (|IntegrationResult| (|Fraction| (|Polynomial| *5))))
       (|isDomain| *1 (|RationalFunctionIntegration| *5))
       (|isDomain| *3 (|Fraction| (|Polynomial| *5)))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|IntegerRetractions| *3))
   (|ofCategory| *3 (|RetractableTo| *2))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|List| (|Fraction| *6)))
   (|isDomain| *3 (|Fraction| *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *3)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
   (|isDomain| *1 (|RationalIntegration| *5 *6))))) 
(((*1 *2 *3 *3)
  (|partial| AND
   (|ofCategory| *4
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2
    (|Record| (|:| |ratpart| #1=(|Fraction| *5)) (|:| |coeff| #1#)))
   (|isDomain| *1 (|RationalIntegration| *4 *5))
   (|isDomain| *3 (|Fraction| *5))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|Fraction| *4))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|ofCategory| *3
                 (|Join| (|Field|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))))
   (|isDomain| *1 (|RationalIntegration| *3 *4))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|ofCategory| *5 (|ConvertibleTo| (|Pattern| (|Integer|))))
   (|ofCategory| *5 (|PatternMatchable| (|Integer|)))
   (|ofCategory| *5
                 (|Join| (|RetractableTo| (|Integer|)) (|GcdDomain|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Record| (|:| |special| *3) (|:| |integrand| *3)))
   (|isDomain| *1 (|PatternMatchIntegration| *5 *3))
   (|ofCategory| *3 (|LiouvillianFunctionCategory|))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *5)))))
 ((*1 *2 *2 *3 *4 *4)
  (|partial| AND (|isDomain| *3 (|Symbol|))
   (|isDomain| *4 (|OrderedCompletion| *2))
   (|ofCategory| *2 (|SpecialFunctionCategory|))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *5)))
   (|ofCategory| *5 (|ConvertibleTo| (|Pattern| (|Integer|))))
   (|ofCategory| *5 (|PatternMatchable| (|Integer|)))
   (|ofCategory| *5
                 (|Join| (|RetractableTo| (|Integer|)) (|GcdDomain|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|PatternMatchIntegration| *5 *2))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|ofCategory| *5 (|ConvertibleTo| (|Pattern| (|Integer|))))
   (|ofCategory| *5 (|PatternMatchable| (|Integer|)))
   (|ofCategory| *5
                 (|Join| (|RetractableTo| (|Integer|)) (|GcdDomain|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Record| (|:| |special| *3) (|:| |integrand| *3)))
   (|isDomain| *1 (|PatternMatchIntegration| *5 *3))
   (|ofCategory| *3 (|LiouvillianFunctionCategory|))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *5)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|RetractableTo| (|Integer|)) (|GcdDomain|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Record| (|:| |const| *3) (|:| |nconst| *3)))
       (|isDomain| *1 (|PatternMatchIntegration| *5 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))))) 
(((*1 *2 *3 *4 *5 *5 *6)
  (AND (|isDomain| *5 (|Kernel| *4)) (|isDomain| *6 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *7
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| *4 "failed"))
                  (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|PureAlgebraicIntegration| *7 *4 *3))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *2 *2 *2 *3 *3 *4)
  (|partial| AND (|isDomain| *3 (|Kernel| *2))
   (|isDomain| *4 (|Mapping| (|Union| *2 "failed") *2 *2 (|Symbol|)))
   (|ofCategory| *2
                 (|Join| (|FunctionSpace| *5) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *5
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|PureAlgebraicIntegration| *5 *2 *6))
   (|ofCategory| *6 (|SetCategory|))))) 
(((*1 *2 *3 *4 *4 *5)
  (|partial| AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|List| *3))
   (|ofCategory| *3
                 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *3)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
   (|isDomain| *1 (|PureAlgebraicIntegration| *6 *3 *7))
   (|ofCategory| *7 (|SetCategory|))))) 
(((*1 *2 *3 *4 *4 *3)
  (|partial| AND (|isDomain| *4 (|Kernel| *3))
   (|ofCategory| *3
                 (|Join| (|FunctionSpace| *5) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *5
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Record| (|:| |ratpart| *3) (|:| |coeff| *3)))
   (|isDomain| *1 (|PureAlgebraicIntegration| *5 *3 *6))
   (|ofCategory| *6 (|SetCategory|))))) 
(((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|Kernel| *3))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| *5) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|PureAlgebraicIntegration| *5 *3 *6))
       (|ofCategory| *6 (|SetCategory|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *6 *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
       (|isDomain| *2 (|Record| (|:| |answer| *3) (|:| |logpart| *3)))
       (|isDomain| *1 (|AlgebraicHermiteIntegration| *5 *6 *7 *3))
       (|ofCategory| *3 (|FunctionFieldCategory| *5 *6 *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *6 *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Field|))
       (|isDomain| *2
        (|Record| (|:| |answer| #1=(|Fraction| *6)) (|:| |logpart| #1#)
                  (|:| |specpart| #1#) (|:| |polypart| *6)))
       (|isDomain| *1 (|TranscendentalHermiteIntegration| *5 *6))
       (|isDomain| *3 (|Fraction| *6))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|CRApackage| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|List| (|List| *4))) (|isDomain| *2 (|List| *4))
       (|ofCategory| *4 (|EuclideanDomain|))
       (|isDomain| *1 (|CRApackage| *4))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|List| *8))
       (|isDomain| *4
        (|List|
         (|Record| (|:| |basis| (|Matrix| *7)) (|:| |basisDen| *7)
                   (|:| |basisInv| (|Matrix| *7)))))
       (|isDomain| *5 (|NonNegativeInteger|))
       (|ofCategory| *8 (|UnivariatePolynomialCategory| *7))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|ofCategory| *6 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|Record| (|:| |basis| (|Matrix| *7)) (|:| |basisDen| *7)
                  (|:| |basisInv| (|Matrix| *7))))
       (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *6 *7 *8))))
 ((*1 *2 *2 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) 
(((*1 *2 *3 *4 *5 *5 *4 *6)
  (AND (|isDomain| *5 (|Kernel| *4))
       (|isDomain| *6 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4
                     (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *7
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| *4 #1="failed"))
                  (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|GenusZeroIntegration| *7 *4 *3))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *3 *4 *5 *5 *5 *4 *6)
  (AND (|isDomain| *5 (|Kernel| *4))
       (|isDomain| *6 (|Fraction| (|SparseUnivariatePolynomial| *4)))
       (|ofCategory| *4
                     (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *7
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Record| (|:| |particular| (|Union| *4 #1#))
                  (|:| |basis| (|List| *4))))
       (|isDomain| *1 (|GenusZeroIntegration| *7 *4 *3))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *2 *2 *3 *3 *4 *2 *5)
  (|partial| AND (|isDomain| *3 (|Kernel| *2))
   (|isDomain| *4 (|Mapping| (|Union| *2 #1="failed") *2 *2 (|Symbol|)))
   (|isDomain| *5 (|SparseUnivariatePolynomial| *2))
   (|ofCategory| *2
                 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|GenusZeroIntegration| *6 *2 *7))
   (|ofCategory| *7 (|SetCategory|))))
 ((*1 *2 *2 *2 *3 *3 *4 *3 *2 *5)
  (|partial| AND (|isDomain| *3 (|Kernel| *2))
   (|isDomain| *4 (|Mapping| (|Union| *2 #1#) *2 *2 (|Symbol|)))
   (|isDomain| *5 (|Fraction| (|SparseUnivariatePolynomial| *2)))
   (|ofCategory| *2
                 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|GenusZeroIntegration| *6 *2 *7))
   (|ofCategory| *7 (|SetCategory|))))) 
(((*1 *2 *3 *4 *4 *5 *3 *6)
  (|partial| AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|List| *3))
   (|isDomain| *6 (|SparseUnivariatePolynomial| *3))
   (|ofCategory| *3
                 (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *7
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *3)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
   (|isDomain| *1 (|GenusZeroIntegration| *7 *3 *8))
   (|ofCategory| *8 (|SetCategory|))))
 ((*1 *2 *3 *4 *4 *5 *4 *3 *6)
  (|partial| AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|List| *3))
   (|isDomain| *6 (|Fraction| (|SparseUnivariatePolynomial| *3)))
   (|ofCategory| *3
                 (|Join| (|FunctionSpace| *7) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *7
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *3)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
   (|isDomain| *1 (|GenusZeroIntegration| *7 *3 *8))
   (|ofCategory| *8 (|SetCategory|))))) 
(((*1 *2 *3 *4 *4 *3 *3 *5)
  (|partial| AND (|isDomain| *4 (|Kernel| *3))
   (|isDomain| *5 (|SparseUnivariatePolynomial| *3))
   (|ofCategory| *3
                 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Record| (|:| |ratpart| *3) (|:| |coeff| *3)))
   (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7))
   (|ofCategory| *7 (|SetCategory|))))
 ((*1 *2 *3 *4 *4 *3 *4 *3 *5)
  (|partial| AND (|isDomain| *4 (|Kernel| *3))
   (|isDomain| *5 (|Fraction| (|SparseUnivariatePolynomial| *3)))
   (|ofCategory| *3
                 (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|CharacteristicZero|)
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Record| (|:| |ratpart| *3) (|:| |coeff| *3)))
   (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7))
   (|ofCategory| *7 (|SetCategory|))))) 
(((*1 *2 *3 *4 *4 *3 *5)
  (AND (|isDomain| *4 (|Kernel| *3))
       (|isDomain| *5 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7))
       (|ofCategory| *7 (|SetCategory|))))
 ((*1 *2 *3 *4 *4 *4 *3 *5)
  (AND (|isDomain| *4 (|Kernel| *3))
       (|isDomain| *5 (|Fraction| (|SparseUnivariatePolynomial| *3)))
       (|ofCategory| *3
                     (|Join| (|FunctionSpace| *6) (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|CharacteristicZero|)
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7))
       (|ofCategory| *7 (|SetCategory|))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *1 (|IntegerFactorizationPackage| *2))
   (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|IntegerFactorizationPackage| *3))
       (|ofCategory| *3 (|IntegerNumberSystem|))))) 
(((*1 *2 *3 *4 *5 *6)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|isDomain| *6 (|List| (|Kernel| *3))) (|isDomain| *5 (|Kernel| *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *7)))
   (|ofCategory| *7
                 (|Join| (|GcdDomain|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Record| (|:| |ratpart| *3) (|:| |coeff| *3)))
   (|isDomain| *1 (|ElementaryIntegration| *7 *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|ElementaryIntegration| *5 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *3 (|Symbol|))
   (|ofCategory| *4
                 (|Join| (|GcdDomain|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|ElementaryIntegration| *4 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *4)))))) 
(((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|List| *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *6)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2
    (|Record| (|:| |mainpart| *3)
              (|:| |limitedlogs|
                   (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3))))))
   (|isDomain| *1 (|ElementaryIntegration| *6 *3))))) 
(((*1 *2 *3 *4 *3)
  (|partial| AND (|isDomain| *4 (|Symbol|))
   (|ofCategory| *5
                 (|Join| (|GcdDomain|) (|CharacteristicZero|)
                         (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *2 (|Record| (|:| |ratpart| *3) (|:| |coeff| *3)))
   (|isDomain| *1 (|ElementaryIntegration| *5 *3))
   (|ofCategory| *3
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *5)))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |unit| *1) (|:| |canonical| *1) (|:| |associate| *1)))
   (|ofCategory| *1 (|IntegralDomain|))))) 
(((*1 *1 *1) (|ofCategory| *1 (|IntegralDomain|)))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|ofCategory| *1 (|IntervalCategory| *3))
       (|ofCategory| *3
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *2)
  (AND (|ofCategory| *1 (|IntervalCategory| *2))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))))
 ((*1 *1 *2 *2)
  (AND (|ofCategory| *1 (|IntervalCategory| *2))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *1 *2 *2)
  (AND (|ofCategory| *1 (|IntervalCategory| *2))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IntervalCategory| *2))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|IntervalCategory| *3))
       (|ofCategory| *3
                     (|Join| (|FloatingPointSystem|)
                             (|TranscendentalFunctionCategory|)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|IntegerBits|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerBits|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerBits|))))) 
(((*1 *2 *2 *3)
  (|partial| AND (|isDomain| *3 (|Mapping| *6 *6))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|ofCategory| *5 (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| *4)))
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
   (|isDomain| *1 (|AlgebraicIntegrate| *4 *5 *6 *7 *2))
   (|ofCategory| *2 (|FunctionFieldCategory| *5 *6 *7))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *7 *7))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|ofCategory| *6
                     (|Join| (|AlgebraicallyClosedField|)
                             (|FunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|ofCategory| *8 (|UnivariatePolynomialCategory| (|Fraction| *7)))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|AlgebraicIntegrate| *5 *6 *7 *8 *3))
       (|ofCategory| *3 (|FunctionFieldCategory| *6 *7 *8))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *7 *7))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))
       (|ofCategory| *6
                     (|Join| (|AlgebraicallyClosedField|)
                             (|FunctionSpace| *5)))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|ofCategory| *8 (|UnivariatePolynomialCategory| (|Fraction| *7)))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|AlgebraicIntegrate| *5 *6 *7 *8 *3))
       (|ofCategory| *3 (|FunctionFieldCategory| *6 *7 *8))))) 
(((*1 *2 *3 *4 *4 *5)
  (AND (|isDomain| *4 (|Kernel| *3))
       (|isDomain| *5
        (|Mapping| (|SparseUnivariatePolynomial| *3)
                   (|SparseUnivariatePolynomial| *3)))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|FunctionSpace| *6)))
       (|ofCategory| *6 (|IntegralDomain|))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|AlgebraicIntegration| *6 *3))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|IntegerNumberSystem|)))) 
(((*1 *2 *3 *2 *4)
  (|partial| AND
   (|isDomain| *4 (|Mapping| (|Union| (|Integer|) #1="failed") *5))
   (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|InnerPolySign| *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))
 ((*1 *2 *3 *4 *2 *5)
  (|partial| AND (|isDomain| *5 (|Mapping| (|Union| (|Integer|) #1#) *4))
   (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|InnerPolySign| *4 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *5 (|Mapping| (|Union| (|Integer|) #1#) *4))
   (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|))
   (|isDomain| *1 (|InnerPolySign| *4 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|GenExEuclid| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|GeneralHenselPackage| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|EuclideanDomain|)) (|ofType| *4 *3)
       (|ofType| *5 (|Mapping| *3 *3 (|NonNegativeInteger|)))
       (|isDomain| *1 (|InnerModularGcd| *3 *2 *4 *5))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|InnerModularGcd| *4 *2 *5 *6))
       (|ofCategory| *4 (|EuclideanDomain|)) (|ofType| *5 *4)
       (|ofType| *6 (|Mapping| *4 *4 (|NonNegativeInteger|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *1 (|InnerModularGcd| *4 *2 *5 *6))
       (|ofCategory| *4 (|EuclideanDomain|)) (|ofType| *5 *4)
       (|ofType| *6 (|Mapping| *4 *4 (|NonNegativeInteger|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| (|Symbol|)))
       (|ofCategory| *6 (|Field|))
       (|isDomain| *2 (|List| (|Equation| (|Polynomial| *6))))
       (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *7 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3 *3 *4 *5)
  (AND (|isDomain| *3 (|List| (|Polynomial| *6)))
       (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|GcdDomain|))
       (|isDomain| *2 (|List| (|List| *7)))
       (|isDomain| *1 (|InnerNumericFloatSolvePackage| *6 *7 *5))
       (|ofCategory| *7 (|Field|))
       (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *5))
       (|ofCategory| *5 (|GcdDomain|)) (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *4))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Polynomial| *5)) (|ofCategory| *5 (|GcdDomain|))
       (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *4))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Any|)) (|isDomain| *1 (|InputForm|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|InputForm|)) (|isDomain| *1 (|InputFormFunctions1| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|InputForm|))
       (|isDomain| *1 (|InputFormFunctions1| *4)) (|ofCategory| *4 (|Type|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|BinaryExpansion|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|InputForm|))) (|isDomain| *1 (|InputForm|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *1 (|InputForm|))))) 
(((*1 *1 *1) (|isDomain| *1 (|InputForm|)))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|InputForm|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|InputForm|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|InputForm|))) (|isDomain| *2 (|Symbol|))
       (|isDomain| *1 (|InputForm|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|List| (|InputForm|)))
       (|isDomain| *1 (|InputForm|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Matrix| *6))
       (|isDomain| *5
        (|Mapping| (|Factored| (|SparseUnivariatePolynomial| *6))
                   (|SparseUnivariatePolynomial| *6)))
       (|ofCategory| *6 (|Field|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |outval| *7) (|:| |outmult| (|Integer|))
                   (|:| |outvect| (|List| (|Matrix| *7))))))
       (|isDomain| *1 (|InnerNumericEigenPackage| *6 *7 *4))
       (|ofCategory| *7 (|Field|))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *5))
       (|ofCategory| *5 (|Field|)) (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|InnerNumericEigenPackage| *5 *6 *4))
       (|ofCategory| *6 (|Field|))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| *4)) (|ofCategory| *4 (|Field|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|InnerNumericEigenPackage| *4 *5 *6))
       (|ofCategory| *5 (|Field|))
       (|ofCategory| *6 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|isDomain| *1 (|IncrementingMaps| *3))
       (|ofCategory| *3 (|Join| (|Monoid|) (|AbelianSemiGroup|)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3))
       (|isDomain| *1 (|IncrementingMaps| *3))
       (|ofCategory| *3 (|Join| (|Monoid|) (|AbelianSemiGroup|)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|InputBinaryFile|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|FileName|)) (|isDomain| *1 (|InputBinaryFile|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InputBinaryFile|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|InputBinaryFile|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|))
       (|ofCategory| *4 (|Field|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *2))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2))
       (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *4))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Vector| *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|))
       (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))))
 ((*1 *2)
  (AND (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FramedAlgebra| *3 *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Vector| *6))
       (|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6))
       (|ofCategory| *6
                     (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Vector| *6))
       (|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7))
       (|ofCategory| *6 (|FramedAlgebra| *4 *5)) (|ofType| *7 *2)))
 ((*1 *2)
  (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|Vector| (|Vector| *4)))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|PositiveInteger|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|SingleInteger|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *2 *2 *3 *4)
  (AND (|isDomain| *2 (|Vector| *5)) (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *4 (|SingleInteger|))
       (|ofCategory| *5 (|FiniteFieldCategory|))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|Vector|
     (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|))))))
   (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Void|))
   (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|InputByteConduit|))
       (|isDomain| *2 (|Maybe| (|Byte|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|InputByteConduit|))
       (|isDomain| *2 (|Maybe| (|Int8|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|InputByteConduit|))
       (|isDomain| *2 (|Maybe| (|UInt8|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|InputByteConduit|))
       (|isDomain| *2 (|Maybe| (|Int16|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|InputByteConduit|))
       (|isDomain| *2 (|Maybe| (|UInt16|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|InputByteConduit|))
       (|isDomain| *2 (|Maybe| (|Int32|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|InputByteConduit|))
       (|isDomain| *2 (|Maybe| (|UInt32|)))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *3 (|ByteBuffer|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|InAst|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|ImportAst|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *3))
       (|ofCategory| *5 (|FiniteLinearAggregate| *3))
       (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *3 *4 *5 *2))
       (|ofCategory| *2 (|MatrixCategory| *3 *4 *5))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IfAst|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IfAst|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|FlexibleArray| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|IndexedFlexibleArray| *3 *4))
       (|ofType| *4 (|Integer|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FlexibleArray| *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|IndexedFlexibleArray| *3 *4))
       (|ofCategory| *3 (|Type|)) (|ofType| *4 (|Integer|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|FlexibleArray| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|IndexedFlexibleArray| *3 *4))
       (|ofCategory| *3 (|Type|)) (|ofType| *4 *2)))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FlexibleArray| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|IndexedFlexibleArray| *3 *4))
       (|ofCategory| *3 (|Type|)) (|ofType| *4 (|Integer|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|IndexedProductTerm| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|OrderedType|))))) 
(((*1 *1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| *4 *4 *4))
       (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4))
       (|ofCategory| *4 (|BasicType|))
       (|isDomain| *1 (|IndexedDirectProductObject| *4 *5))
       (|ofCategory| *5 (|OrderedType|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|OrderedType|))))) 
(((*1 *1) (|isDomain| *1 (|Identifier|)))) 
(((*1 *1 *1 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5))
       (|ofType| *3 *2) (|ofType| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|CommutativeRing|))))
 ((*1 *1 *1 *2 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5))
       (|ofType| *3 *2) (|ofType| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|CommutativeRing|))))
 ((*1 *2 *2 *3)
  (AND
   (|isDomain| *2
    (|PolynomialIdeals| (|Fraction| (|Integer|))
                        (|DirectProduct| *5 (|NonNegativeInteger|))
                        (|OrderedVariableList| *4)
                        (|DistributedMultivariatePolynomial| *4
                                                             (|Fraction|
                                                              (|Integer|)))))
   (|isDomain| *3 (|List| (|OrderedVariableList| *4)))
   (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|))
   (|isDomain| *1 (|IdealDecompositionPackage| *4 *5))))) 
(((*1 *2 *3)
  (AND (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|))
       (|isDomain| *2
        (|List|
         (|PolynomialIdeals| (|Fraction| (|Integer|))
                             (|DirectProduct| *5 (|NonNegativeInteger|))
                             (|OrderedVariableList| *4)
                             (|DistributedMultivariatePolynomial| *4
                                                                  (|Fraction|
                                                                   (|Integer|))))))
       (|isDomain| *1 (|IdealDecompositionPackage| *4 *5))
       (|isDomain| *3
        (|PolynomialIdeals| (|Fraction| (|Integer|))
                            (|DirectProduct| *5 (|NonNegativeInteger|))
                            (|OrderedVariableList| *4)
                            (|DistributedMultivariatePolynomial| *4
                                                                 (|Fraction|
                                                                  (|Integer|)))))))) 
(((*1 *2 *2)
  (AND
   (|isDomain| *2
    (|PolynomialIdeals| (|Fraction| (|Integer|))
                        (|DirectProduct| *4 (|NonNegativeInteger|))
                        (|OrderedVariableList| *3)
                        (|DistributedMultivariatePolynomial| *3
                                                             (|Fraction|
                                                              (|Integer|)))))
   (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 (|NonNegativeInteger|))
   (|isDomain| *1 (|IdealDecompositionPackage| *3 *4))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|PolynomialIdeals| (|Fraction| (|Integer|))
                        (|DirectProduct| *5 (|NonNegativeInteger|))
                        (|OrderedVariableList| *4)
                        (|DistributedMultivariatePolynomial| *4
                                                             (|Fraction|
                                                              (|Integer|)))))
   (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|IdealDecompositionPackage| *4 *5))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|PolynomialIdeals| (|Fraction| (|Integer|))
                        (|DirectProduct| *5 (|NonNegativeInteger|))
                        (|OrderedVariableList| *4)
                        (|DistributedMultivariatePolynomial| *4
                                                             (|Fraction|
                                                              (|Integer|)))))
   (|ofType| *4 (|List| (|Symbol|))) (|ofType| *5 (|NonNegativeInteger|))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|IdealDecompositionPackage| *4 *5))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *2))
       (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5))))
 ((*1 *1 *1 *1)
  (AND (|ofCategory| *2 (|Field|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2
        (|Record| (|:| |mval| (|Matrix| *4)) (|:| |invmval| (|Matrix| *4))
                  (|:| |genIdeal| (|PolynomialIdeals| *4 *5 *6 *7))))
       (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|Record| (|:| |mval| (|Matrix| *3)) (|:| |invmval| (|Matrix| *3))
              (|:| |genIdeal| (|PolynomialIdeals| *3 *4 *5 *6))))
   (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
   (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *2 (|Field|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5))
       (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5))
       (|isDomain| *2 (|FractionalIdeal| *4 (|Fraction| *4) *5 *6))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *6))
       (|ofCategory| *6 (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4)))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *2))
       (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *2))
       (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *6 (|ConvertibleTo| (|Symbol|)))
       (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *2
        (|SuchThat| (|List| (|Polynomial| *4))
                    (|List| (|Equation| (|Polynomial| *4)))))
       (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *7))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|Database| *4))
       (|ofCategory| *4
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |elt| ((|String|) $ (|Symbol|)))
                              (SIGNATURE |display| (*2 $))
                              (SIGNATURE |fullDisplay| (*2 $)))))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Database| *3))
       (|ofCategory| *3
                     (|Join| (|OrderedSet|)
                             (CATEGORY |domain|
                              (SIGNATURE |elt| ((|String|) $ (|Symbol|)))
                              (SIGNATURE |display| (*2 $))
                              (SIGNATURE |fullDisplay| (*2 $)))))))
 ((*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|IndexCard|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *7 (|Ring|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2
        (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *7)))
       (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *6 *4 *7))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *6))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *5 "failed") *8))
   (|isDomain| *4 (|Matrix| (|SparseUnivariatePolynomial| *8)))
   (|ofCategory| *5 (|Ring|)) (|ofCategory| *8 (|Ring|))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *2 (|Matrix| *6))
   (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *6 *7 *8))
   (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *5 "failed") *7))
   (|isDomain| *4 (|SparseUnivariatePolynomial| *7)) (|ofCategory| *5 (|Ring|))
   (|ofCategory| *7 (|Ring|))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
   (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *2 *6 *7))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *5 *7))
       (|isDomain| *4 (|SparseUnivariatePolynomial| *7))
       (|ofCategory| *5 (|Ring|)) (|ofCategory| *7 (|Ring|))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *2 *6 *7))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *2))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *7 (|Ring|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *7))
       (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *4 *6 *7))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *2)
  (AND
   (|isDomain| *2
    (|Record| (|:| |basis| (|Matrix| *3)) (|:| |basisDen| *3)
              (|:| |basisInv| (|Matrix| *3))))
   (|ofCategory| *3
                 (|Join| (|EuclideanDomain|)
                         (CATEGORY |domain|
                          (SIGNATURE |squareFree| ((|Factored| $) $)))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
   (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5))
   (|ofCategory| *5 (|FramedAlgebra| *3 *4))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3))
       (|ofCategory| *3
                     (|Join| (|EuclideanDomain|)
                             (CATEGORY |domain|
                              (SIGNATURE |squareFree| ((|Factored| $) $)))))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5))
       (|ofCategory| *5 (|FramedAlgebra| *3 *4))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Matrix| *3))
       (|ofCategory| *3
                     (|Join| (|EuclideanDomain|)
                             (CATEGORY |domain|
                              (SIGNATURE |squareFree| ((|Factored| $) $)))))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5))
       (|ofCategory| *5 (|FramedAlgebra| *3 *4))))
 ((*1 *2 *2 *2 *3)
  (AND (|isDomain| *2 (|Matrix| *3))
       (|ofCategory| *3
                     (|Join| (|EuclideanDomain|)
                             (CATEGORY |domain|
                              (SIGNATURE |squareFree| ((|Factored| $) $)))))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5))
       (|ofCategory| *5 (|FramedAlgebra| *3 *4))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *3
                     (|Join| (|EuclideanDomain|)
                             (CATEGORY |domain|
                              (SIGNATURE |squareFree| ((|Factored| $) $)))))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|IntegralBasisTools| *3 *4 *5))
       (|ofCategory| *5 (|FramedAlgebra| *3 *4))))) 
(((*1 *2 *3 *3 *2 *4)
  (AND (|isDomain| *3 (|Matrix| *2)) (|isDomain| *4 (|Integer|))
       (|ofCategory| *2
                     (|Join| (|EuclideanDomain|)
                             (CATEGORY |domain|
                              (SIGNATURE |squareFree| ((|Factored| $) $)))))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *2))
       (|isDomain| *1 (|IntegralBasisTools| *2 *5 *6))
       (|ofCategory| *6 (|FramedAlgebra| *2 *5))))) 
(((*1 *2 *3 *2 *4)
  (AND (|isDomain| *3 (|Matrix| *2)) (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *2
                     (|Join| (|EuclideanDomain|)
                             (CATEGORY |domain|
                              (SIGNATURE |squareFree| ((|Factored| $) $)))))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *2))
       (|isDomain| *1 (|IntegralBasisTools| *2 *5 *6))
       (|ofCategory| *6 (|FramedAlgebra| *2 *5))))) 
(((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|FiniteFieldCategory|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |basis| (|Matrix| *6)) (|:| |basisDen| *6)
                   (|:| |basisInv| (|Matrix| *6)))))
       (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *5 *6 *7))
       (|isDomain| *3
        (|Record| (|:| |basis| (|Matrix| *6)) (|:| |basisDen| *6)
                  (|:| |basisInv| (|Matrix| *6))))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime"))
               (|:| |fctr| *3) (|:| |xpnt| (|Integer|)))))
   (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *2 *3 *4 *4 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *3)))
       (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *3 *5 *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|InnerAlgebraicNumber|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Hostname|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|HexadecimalExpansion|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Integer|))) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|HeuGcd| *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))
       (|isDomain| *1 (|HeuGcd| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))
       (|isDomain| *1 (|HeuGcd| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|HeuGcd| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|Heap| *3))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|List| (|ParameterAst|)))
       (|isDomain| *1 (|HeadAst|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Identifier|)))
       (|isDomain| *1 (|AnonymousFunction|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|ParameterAst|))) (|isDomain| *1 (|HeadAst|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|DistributedMultivariatePolynomial| *3 *4))
       (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Ring|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Integer|))) (|ofType| *3 (|List| (|Symbol|)))
       (|isDomain| *1 (|GeneralDistributedMultivariatePolynomial| *3 *4 *5))
       (|ofCategory| *4 (|Ring|))
       (|ofCategory| *5
                     (|DirectProductCategory| (|#| *3)
                                              (|NonNegativeInteger|)))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|HomogeneousDistributedMultivariatePolynomial| *3 *4))
       (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Ring|))))) 
(((*1 *2 *3 *3 *3 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|HallBasis|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|HallBasis|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|OrderedVariableList| *5)))
       (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|GcdDomain|))
       (|isDomain| *2
        (|Record|
         (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| *5 *6)))
         (|:| |coords| (|List| (|Integer|)))))
       (|isDomain| *1 (|GroebnerSolve| *5 *6 *7))
       (|isDomain| *3 (|List| (|DistributedMultivariatePolynomial| *5 *6)))
       (|ofCategory| *7 (|GcdDomain|))))) 
(((*1 *2 *2 *3)
  (|partial| AND
   (|isDomain| *2
    (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5)))
   (|isDomain| *3 (|List| (|OrderedVariableList| *4)))
   (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *5 (|GcdDomain|))
   (|isDomain| *1 (|GroebnerSolve| *4 *5 *6)) (|ofCategory| *6 (|GcdDomain|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|OrderedVariableList| *5)))
       (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *6 (|GcdDomain|))
       (|isDomain| *2
        (|List| (|List| (|DistributedMultivariatePolynomial| *5 *6))))
       (|isDomain| *1 (|GroebnerSolve| *5 *6 *7))
       (|isDomain| *3 (|List| (|DistributedMultivariatePolynomial| *5 *6)))
       (|ofCategory| *7 (|GcdDomain|))))) 
(((*1 *1) (|isDomain| *1 (|GraphImage|)))) 
(((*1 *1 *2 *3 *3 *4 *5)
  (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *3 (|List| (|Palette|)))
       (|isDomain| *4 (|List| (|PositiveInteger|)))
       (|isDomain| *5 (|List| (|DrawOption|))) (|isDomain| *1 (|GraphImage|))))
 ((*1 *1 *2 *3 *3 *4)
  (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *3 (|List| (|Palette|)))
       (|isDomain| *4 (|List| (|PositiveInteger|)))
       (|isDomain| *1 (|GraphImage|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *1 (|GraphImage|))))
 ((*1 *1 *1) (|isDomain| *1 (|GraphImage|)))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *1 (|GraphImage|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Segment| (|Float|))))
       (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| (|Segment| (|Float|))))
       (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))
 ((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|List| (|Segment| (|Float|))))
       (|isDomain| *1 (|GraphImage|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Segment| (|Float|))))
       (|isDomain| *1 (|GraphImage|))))) 
(((*1 *2 *1 *3 *4 *4 *5)
  (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *4 (|Palette|))
       (|isDomain| *5 (|PositiveInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|GraphImage|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|GraphImage|))))
 ((*1 *2 *1 *3 *4 *4 *5)
  (AND (|isDomain| *3 (|List| (|Point| (|DoubleFloat|))))
       (|isDomain| *4 (|Palette|)) (|isDomain| *5 (|PositiveInteger|))
       (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GraphImage|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Point| (|DoubleFloat|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|GraphImage|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *3 (|List| (|Palette|))) (|isDomain| *1 (|GraphImage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))
       (|isDomain| *2 (|List| (|DoubleFloat|)))
       (|isDomain| *1 (|GraphImage|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GraphicsDefaults|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|Vector| (|Vector| (|Integer|))))
       (|isDomain| *1 (|GrayCode|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|Vector| (|Vector| (|Integer|))))
       (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|GrayCode|))))) 
(((*1 *2 *2 *3 *4)
  (|partial| AND (|isDomain| *4 (|Mapping| *3))
   (|ofCategory| *3 (|OrderedSet|))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *6 (|IntegralDomain|))
   (|ofCategory| *7 (|PolynomialCategory| *6 *5 *3))
   (|isDomain| *1 (|GosperSummationMethod| *5 *3 *6 *7 *2))
   (|ofCategory| *2
                 (|Join| (|RetractableTo| (|Fraction| (|Integer|))) (|Field|)
                         (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))
                          (SIGNATURE |numer| (*7 $))
                          (SIGNATURE |denom| (*7 $)))))))) 
(((*1 *2 *1)
  (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|))
       (|ofType| *6
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *2))
                   (|Record| (|:| |index| *5) (|:| |exponent| *2))))
       (|ofCategory| *2
                     (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))
       (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *2 *6 *7))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *7
                     (|PolynomialCategory| *4 *2 (|OrderedVariableList| *3)))))) 
(((*1 *2 *1)
  (AND (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5
                     (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))
       (|ofType| *6
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *2) (|:| |exponent| *5))
                   (|Record| (|:| |index| *2) (|:| |exponent| *5))))
       (|ofCategory| *2 (|OrderedSet|))
       (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *2 *5 *6 *7))
       (|ofCategory| *7
                     (|PolynomialCategory| *4 *5 (|OrderedVariableList| *3)))))) 
(((*1 *1 *2 *3 *4)
  (AND (|ofType| *5 (|List| (|Symbol|))) (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *4
                     (|DirectProductCategory| (|#| *5) (|NonNegativeInteger|)))
       (|ofType| *6
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *3) (|:| |exponent| *4))
                   (|Record| (|:| |index| *3) (|:| |exponent| *4))))
       (|isDomain| *1 (|GeneralModulePolynomial| *5 *2 *3 *4 *6 *7))
       (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *7
                     (|PolynomialCategory| *2 *4 (|OrderedVariableList| *5)))))) 
(((*1 *1 *2 *3 *1)
  (AND (|ofType| *4 (|List| (|Symbol|))) (|ofCategory| *2 (|CommutativeRing|))
       (|ofCategory| *3
                     (|DirectProductCategory| (|#| *4) (|NonNegativeInteger|)))
       (|ofType| *6
        (|Mapping| (|Boolean|) (|Record| (|:| |index| *5) (|:| |exponent| *3))
                   (|Record| (|:| |index| *5) (|:| |exponent| *3))))
       (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *3 *6 *7))
       (|ofCategory| *5 (|OrderedSet|))
       (|ofCategory| *7
                     (|PolynomialCategory| *2 *3 (|OrderedVariableList| *4)))))) 
(((*1 *2 *3 *2 *4 *5)
  (AND (|isDomain| *2 (|List| *3)) (|isDomain| *5 (|PositiveInteger|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|EuclideanDomain|))
       (|isDomain| *1 (|GeneralHenselPackage| *4 *3))))) 
(((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *6 (|PositiveInteger|))
       (|ofCategory| *5 (|EuclideanDomain|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2 (|Record| (|:| |plist| (|List| *3)) (|:| |modulo| *5)))
       (|isDomain| *1 (|GeneralHenselPackage| *5 *3))
       (|isDomain| *4 (|List| *3))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|GenExEuclid| *3 *5))))) 
(((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *5 (|Vector| (|List| *3)))
   (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|List| *3))
   (|isDomain| *1 (|GenExEuclid| *4 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *4 *5)
  (|partial| AND (|isDomain| *3 (|NonNegativeInteger|))
   (|ofCategory| *4 (|EuclideanDomain|))
   (|ofCategory| *6 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2 (|Vector| (|List| *6))) (|isDomain| *1 (|GenExEuclid| *4 *6))
   (|isDomain| *5 (|List| *6))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|EuclideanDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|GenExEuclid| *5 *3))))) 
(((*1 *2)
  (|partial| AND (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *3 (|CommutativeRing|))
   (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1))))
   (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))))
 ((*1 *2)
  (|partial| AND
   (|isDomain| *2
    (|Record|
     (|:| |particular| #1=(|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
     (|:| |basis| (|List| #1#))))
   (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
   (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
   (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2)
  (|partial| AND (|ofCategory| *3 (|IntegralDomain|))
   (|ofCategory| *3 (|CommutativeRing|))
   (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1))))
   (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))))
 ((*1 *2)
  (|partial| AND
   (|isDomain| *2
    (|Record|
     (|:| |particular| #1=(|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
     (|:| |basis| (|List| #1#))))
   (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
   (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
   (|ofType| *5 (|List| (|Symbol|))) (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Vector| (|Symbol|)))
       (|isDomain| *3 (|Vector| (|GenericNonAssociativeAlgebra| *4 *5 *6 *7)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *4 *5 *6 *7))
       (|ofCategory| *4 (|CommutativeRing|)) (|ofType| *5 (|PositiveInteger|))
       (|ofType| *6 (|List| (|Symbol|)))
       (|ofType| *7 (|Vector| (|Matrix| *4)))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|))
       (|isDomain| *3 (|Vector| (|GenericNonAssociativeAlgebra| *4 *5 *6 *7)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *4 *5 *6 *7))
       (|ofCategory| *4 (|CommutativeRing|)) (|ofType| *5 (|PositiveInteger|))
       (|ofType| *6 (|List| *2)) (|ofType| *7 (|Vector| (|Matrix| *4)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| (|GenericNonAssociativeAlgebra| *3 *4 *5 *6)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| (|Symbol|)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| *2)) (|ofType| *6 (|Vector| (|Matrix| *3)))))
 ((*1 *1)
  (AND (|isDomain| *1 (|GenericNonAssociativeAlgebra| *2 *3 *4 *5))
       (|ofCategory| *2 (|CommutativeRing|)) (|ofType| *3 (|PositiveInteger|))
       (|ofType| *4 (|List| (|Symbol|)))
       (|ofType| *5 (|Vector| (|Matrix| *2)))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *4)))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *3)))))
 ((*1 *2)
  (AND
   (|isDomain| *2
    (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *3))))
   (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|))
   (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))
   (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *3))))
   (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|))
   (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))
   (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *4)))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *3)))))
 ((*1 *2)
  (AND
   (|isDomain| *2
    (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *3))))
   (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|))
   (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))
   (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| *3))))
   (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
   (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|))
   (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))
   (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|List| (|Polynomial| *4)))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|List| (|Polynomial| *4)))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *2 (|List| (|Polynomial| *3)))))
 ((*1 *2)
  (AND (|isDomain| *2 (|List| (|Polynomial| *3)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *3 *4 *5 *6))
       (|ofCategory| *3 (|IntegralDomain|))
       (|ofCategory| *3 (|CommutativeRing|)) (|ofType| *4 (|PositiveInteger|))
       (|ofType| *5 (|List| (|Symbol|)))
       (|ofType| *6 (|Vector| (|Matrix| *3)))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| (|GenericNonAssociativeAlgebra| *4 *5 *6 *7)))
       (|isDomain| *2 (|List| (|Polynomial| *4)))
       (|isDomain| *1 (|GenericNonAssociativeAlgebra| *4 *5 *6 *7))
       (|ofCategory| *4 (|IntegralDomain|))
       (|ofCategory| *4 (|CommutativeRing|)) (|ofType| *5 (|PositiveInteger|))
       (|ofType| *6 (|List| (|Symbol|)))
       (|ofType| *7 (|Vector| (|Matrix| *4)))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|))))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|)))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3
    (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| *4)))
   (|isDomain| *5 (|NonNegativeInteger|))
   (|ofCategory| *4 (|PolynomialCategory| *6 *7 *8))
   (|ofCategory| *6 (|GcdDomain|))
   (|ofCategory| *7 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *8 (|OrderedSet|))
   (|isDomain| *2
    (|Record| (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4)
              (|:| |polj| *4)))
   (|isDomain| *1 (|GroebnerInternalPackage| *6 *7 *8 *4))))) 
(((*1 *2 *3 *3)
  (AND
   (|isDomain| *3
    (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|))
              (|:| |poli| *7) (|:| |polj| *7)))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
   (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *7))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7))))) 
(((*1 *2 *3 *4 *4 *2 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *3
        (|Record| (|:| |lcmfij| *6) (|:| |totdeg| (|NonNegativeInteger|))
                  (|:| |poli| *4) (|:| |polj| *4)))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|PolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *4))))) 
(((*1 *2 *3 *4 *4 *2 *2 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|isDomain| *3
        (|Record| (|:| |lcmfij| *6) (|:| |totdeg| (|NonNegativeInteger|))
                  (|:| |poli| *4) (|:| |polj| *4)))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *4 (|PolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3))
       (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6))))) 
(((*1 *2 *2 *2)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |lcmfij| *4) (|:| |totdeg| (|NonNegativeInteger|))
               (|:| |poli| *6) (|:| |polj| *6))))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|))
              (|:| |poli| *2) (|:| |polj| *2)))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6))
   (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2))
   (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|))))) 
(((*1 *2 *3 *4 *2)
  (AND
   (|isDomain| *2
    (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| *3))))
   (|isDomain| *4 (|NonNegativeInteger|))
   (|ofCategory| *3 (|PolynomialCategory| *5 *6 *7))
   (|ofCategory| *5 (|GcdDomain|))
   (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|OrderedSet|))
   (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *3))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|GcdDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *2))
       (|ofCategory| *2 (|PolynomialCategory| *3 *4 *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *3))
       (|ofCategory| *3 (|PolynomialCategory| *5 *6 *7))
       (|ofCategory| *5 (|GcdDomain|))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|isDomain| *2 (|Record| (|:| |poly| *3) (|:| |mult| *5)))
       (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *3))))) 
(((*1 *2 *3 *2)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |lcmfij| *3) (|:| |totdeg| (|NonNegativeInteger|))
               (|:| |poli| *6) (|:| |polj| *6))))
   (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *6 (|PolynomialCategory| *4 *3 *5))
   (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6))))) 
(((*1 *2 *2)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |lcmfij| *4) (|:| |totdeg| (|NonNegativeInteger|))
               (|:| |poli| *6) (|:| |polj| *6))))
   (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
   (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *5 (|OrderedSet|))
   (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6))))) 
(((*1 *2 *3 *2)
  (AND
   (|isDomain| *2
    (|List|
     (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|))
               (|:| |poli| *3) (|:| |polj| *3))))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *3 (|PolynomialCategory| *4 *5 *6))
   (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|))
   (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3))))) 
(((*1 *2 *3 *3 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *4 *3 *5))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *3 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6))
       (|ofCategory| *6 (|PolynomialCategory| *4 *3 *5))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Record| (|:| |lcmfij| *5) (|:| |totdeg| (|NonNegativeInteger|))
              (|:| |poli| *7) (|:| |polj| *7)))
   (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
   (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
   (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *6 (|OrderedSet|))
   (|isDomain| *2 (|Boolean|))
   (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7))))) 
(((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|Integer|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|GcdDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| (|List| *7)))
       (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7))
       (|isDomain| *3 (|List| *7))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|List| *8)))
       (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8))
       (|isDomain| *3 (|List| *8))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| (|List| *7)))
       (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7))
       (|isDomain| *3 (|List| *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|List| *8)))
       (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8))
       (|isDomain| *3 (|List| *8))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|isDomain| *2 (|List| (|List| *7)))
       (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7))
       (|isDomain| *3 (|List| *7))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|)))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *7 (|OrderedSet|))
       (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7))
       (|isDomain| *2 (|List| (|List| *8)))
       (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8))
       (|isDomain| *3 (|List| *8))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|List| *6))
       (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *3 *4 *5 *6))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|EuclideanDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *7))))
 ((*1 *2 *2 *3 *3)
  (AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|))
       (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|EuclideanDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *7))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2 (|PolynomialCategory| *4 *5 *6))
       (|ofCategory| *4 (|EuclideanDomain|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *6 (|OrderedSet|))
       (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *2))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|GaussianFactorizationPackage|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|GaloisGroupUtilities| *3))
       (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|GaloisGroupUtilities| *3))
       (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupUtilities| *3))
       (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupUtilities| *3))
       (|ofCategory| *3 (|FloatingPointSystem|)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|GaloisGroupUtilities| *3))
       (|ofCategory| *3 (|Ring|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|Ring|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|GaloisGroupUtilities| *3)) (|ofCategory| *3 (|Ring|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Integer|))
       (|isDomain| *1 (|GaloisGroupUtilities| *2)) (|ofCategory| *2 (|Ring|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Factored| *6))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|List| *6))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *6))))) 
(((*1 *2 *3 *2)
  (|partial| AND (|isDomain| *3 (|PositiveInteger|))
   (|isDomain| *1 (|GaloisGroupFactorizer| *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *2 *4)
  (|partial| AND (|isDomain| *3 (|PositiveInteger|))
   (|isDomain| *4 (|NonNegativeInteger|))
   (|isDomain| *1 (|GaloisGroupFactorizer| *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *2 *4)
  (|partial| AND (|isDomain| *3 (|PositiveInteger|))
   (|isDomain| *4 (|List| (|NonNegativeInteger|)))
   (|isDomain| *1 (|GaloisGroupFactorizer| *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *2 *4 *5)
  (|partial| AND (|isDomain| *3 (|PositiveInteger|))
   (|isDomain| *4 (|List| (|NonNegativeInteger|)))
   (|isDomain| *5 (|NonNegativeInteger|))
   (|isDomain| *1 (|GaloisGroupFactorizer| *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *2 *4 *5 *6)
  (|partial| AND (|isDomain| *3 (|PositiveInteger|))
   (|isDomain| *4 (|List| (|NonNegativeInteger|)))
   (|isDomain| *5 (|NonNegativeInteger|)) (|isDomain| *6 (|Boolean|))
   (|isDomain| *1 (|GaloisGroupFactorizer| *2))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Factored| *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *2))
       (|ofCategory| *5 (|Ring|))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|Record| (|:| |factor| *4) (|:| |degree| (|Integer|)))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|)))
   (|isDomain| *2 (|Multiset| (|NonNegativeInteger|)))
   (|isDomain| *1 (|GaloisGroupFactorizer| *4))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Factored| *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|Ring|))
       (|isDomain| *2 (|Multiset| (|NonNegativeInteger|)))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *5))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 (|Ring|))
       (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *6))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *6
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *5)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|Ring|))
       (|ofCategory| *2
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *5)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *2))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5
                     (|Join| (|FloatingPointSystem|) (|RetractableTo| *4)
                             (|Field|) (|TranscendentalFunctionCategory|)
                             (|ElementaryFunctionCategory|)))))) 
(((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *4 (|Boolean|))
       (|isDomain| *5 (|Set| (|NonNegativeInteger|)))
       (|isDomain| *6 (|NonNegativeInteger|))
       (|isDomain| *2
        (|Record| (|:| |contp| (|Integer|))
                  (|:| |factors|
                       (|List|
                        (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|)))))))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *2
    (|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| *3))))
   (|isDomain| *1 (|GaloisGroupFactorizer| *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Factored| *3))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|List| (|Record| (|:| |factor| *4) (|:| |degree| (|Integer|)))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|)))
   (|isDomain| *2 (|NonNegativeInteger|))
   (|isDomain| *1 (|GaloisGroupFactorizer| *4))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|GaloisGroupFactorizer| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *1 *2 *3)
  (AND
   (|isDomain| *3
    (|List|
     (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime"))
               (|:| |fctr| *2) (|:| |xpnt| (|Integer|)))))
   (|ofCategory| *2 (|IntegralDomain|)) (|isDomain| *1 (|Factored| *2))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Record| (|:| |contp| (|Integer|))
              (|:| |factors|
                   (|List|
                    (|Record| (|:| |irr| *4) (|:| |pow| (|Integer|)))))))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Integer|)))
   (|isDomain| *2 (|Factored| *4))
   (|isDomain| *1 (|GaloisGroupFactorizer| *4))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")))
   (|isDomain| *1 (|FortranType|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Polynomial| (|Integer|))))
       (|isDomain| *1 (|FortranType|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranType|))))) 
(((*1 *1) (|isDomain| *1 (|FortranType|)))) 
(((*1 *1) (|isDomain| *1 (|FortranType|)))) 
(((*1 *1) (|isDomain| *1 (|FortranType|)))) 
(((*1 *1) (|isDomain| *1 (|FortranType|)))) 
(((*1 *1) (|isDomain| *1 (|FortranType|)))) 
(((*1 *1) (|isDomain| *1 (|FortranType|)))) 
(((*1 *1) (|isDomain| *1 (|FortranType|)))) 
(((*1 *2 *3)
  (|partial| AND (|ofCategory| *5 (|RetractableTo| (|AlgebraicNumber|)))
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|FunctionSpace| *4))
   (|isDomain| *2
    (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))))
   (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|FunctionSpace| *4))
   (|isDomain| *2
    (|Union|
     (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))
     (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|)))
     (|:| |failed| (|Boolean|))))
   (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3)
  (|partial| AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|FunctionSpace| *4))
   (|isDomain| *2
    (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))))
   (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|ofCategory| *5 (|FunctionSpace| *4)) (|isDomain| *2 (|Factored| *3))
   (|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FortranScalarType|))))) 
(((*1 *2)
  (AND
   (|ofCategory| *3 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FunctionSpaceReduce| *3 *4))
   (|ofCategory| *4 (|FunctionSpace| *3))))) 
(((*1 *2 *3)
  (AND
   (|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
   (|isDomain| *2 (|Fraction| (|Integer|)))
   (|isDomain| *1 (|FunctionSpaceReduce| *4 *3))
   (|ofCategory| *3 (|FunctionSpace| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Kernel| *3)) (|ofCategory| *3 (|FunctionSpace| *5))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))))
       (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|FunctionSpaceReduce| *5 *3))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|FourierSeries| *3 *2))
       (|ofCategory| *3
                     (|Join| (|CommutativeRing|)
                             (|Algebra| (|Fraction| (|Integer|)))))
       (|ofCategory| *2 (|Join| (|OrderedSet|) (|AbelianGroup|)))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *1 (|FourierSeries| *3 *2))
       (|ofCategory| *3
                     (|Join| (|CommutativeRing|)
                             (|Algebra| (|Fraction| (|Integer|)))))
       (|ofCategory| *2 (|Join| (|OrderedSet|) (|AbelianGroup|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|IntegrationResult| *3))
       (|isDomain| *1 (|FunctionSpaceComplexIntegration| *5 *3))
       (|ofCategory| *3
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *5)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteSetAggregate| *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|FiniteSetAggregate| *2))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Finite|))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|Finite|))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *3 *2 *4 *5))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))
   (|ofType| *4 (|Symbol|)) (|ofType| *5 *2)))
 ((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)
                         (CATEGORY |domain| (SIGNATURE |coerce| ($ *4)))))
   (|ofCategory| *4 (|OrderedRing|))
   (|ofCategory| *5
                 (|Join| (|UnivariatePowerSeriesCategory| *2 *4) (|Field|)
                         (|TranscendentalFunctionCategory|)
                         (CATEGORY |domain| (SIGNATURE |differentiate| ($ $))
                          (SIGNATURE |integrate| ($ $)))))
   (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *3 *2 *4 *5 *6 *7))
   (|ofCategory| *6 (|PartialTranscendentalFunctions| *5))
   (|ofType| *7 (|Symbol|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)))))
       (|ofCategory| *7 (|OrderedRing|))
       (|ofCategory| *8
                     (|Join| (|UnivariatePowerSeriesCategory| *3 *7) (|Field|)
                             (|TranscendentalFunctionCategory|)
                             (CATEGORY |domain|
                              (SIGNATURE |differentiate| ($ $))
                              (SIGNATURE |integrate| ($ $)))))
       (|isDomain| *2
        (|Union| (|:| |%series| *8)
                 (|:| |%problem|
                      (|Record| (|:| |func| #1=(|String|)) (|:| |prob| #1#)))))
       (|isDomain| *1
        (|FunctionSpaceToUnivariatePowerSeries| *6 *3 *7 *8 *9 *10))
       (|isDomain| *5 (|String|))
       (|ofCategory| *9 (|PartialTranscendentalFunctions| *8))
       (|ofType| *10 (|Symbol|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *6
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *6)
                             (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)))))
       (|ofCategory| *7 (|OrderedRing|))
       (|ofCategory| *8
                     (|Join| (|UnivariatePowerSeriesCategory| *3 *7) (|Field|)
                             (|TranscendentalFunctionCategory|)
                             (CATEGORY |domain|
                              (SIGNATURE |differentiate| ($ $))
                              (SIGNATURE |integrate| ($ $)))))
       (|isDomain| *2
        (|Union| (|:| |%series| *8)
                 (|:| |%problem|
                      (|Record| (|:| |func| #1=(|String|)) (|:| |prob| #1#)))))
       (|isDomain| *1
        (|FunctionSpaceToUnivariatePowerSeries| *6 *3 *7 *8 *9 *10))
       (|isDomain| *5 (|String|))
       (|ofCategory| *9 (|PartialTranscendentalFunctions| *8))
       (|ofType| *10 (|Symbol|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Union| (|:| |%expansion| (|ExponentialExpansion| *5 *3 *6 *7))
                 (|:| |%problem|
                      (|Record| (|:| |func| (|String|))
                                (|:| |prob| (|String|))))))
       (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *5 *3 *6 *7))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))
       (|ofType| *6 (|Symbol|)) (|ofType| *7 *3)))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3))
       (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FunctionSpace| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|FunctionSpace| *4))
       (|ofCategory| *4 (|SetCategory|))))
 ((*1 *1 *2 *1 *1 *1 *1)
  (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1 *1 *1)
  (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1 *1)
  (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (|partial| AND (|ofCategory| *3 (|AbelianSemiGroup|))
   (|ofCategory| *3 (|SetCategory|))
   (|isDomain| *2
    (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| *1))))
   (|ofCategory| *1 (|FunctionSpace| *3))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|FactoredFunctionUtilities| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Vector| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3)))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *1 (|FramedAlgebra| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2)
  (AND (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *2))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *2))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2)
  (AND (|ofCategory| *2 (|CommutativeRing|))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *2))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *2))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))
       (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4))
       (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|FractionalIdeal| *3 *4 *5 *6))
       (|ofCategory| *6 (|RetractableTo| *4))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|FramedAlgebra| *4 *5)) (|ofType| *7 (|Vector| *6))
       (|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *6)) (|ofCategory| *6 (|FramedAlgebra| *4 *5))
       (|ofCategory| *4 (|QuotientFieldCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7)) (|ofType| *7 *2)))) 
(((*1 *1 *1)
  (AND (|ofCategory| *2 (|EuclideanDomain|))
       (|ofCategory| *3 (|QuotientFieldCategory| *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|FractionalIdeal| *2 *3 *4 *5))
       (|ofCategory| *5
                     (|Join| (|FramedAlgebra| *3 *4) (|RetractableTo| *3)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Vector| *2))
       (|ofCategory| *5 (|EuclideanDomain|))
       (|ofCategory| *6 (|QuotientFieldCategory| *5))
       (|ofCategory| *2 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6)))
       (|isDomain| *1 (|FractionalIdeal| *5 *6 *7 *2))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Matrix| *4))
       (|isDomain| *1 (|FramedAlgebra&| *3 *4 *5))
       (|ofCategory| *3 (|FramedAlgebra| *4 *5))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2 (|Matrix| *3))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5))
       (|ofCategory| *4 (|CommutativeRing|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Matrix| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *2 (|Matrix| *3))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *1)
  (AND
   (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| (|Integer|)))))
   (|isDomain| *1 (|FreeGroup| *3)) (|ofCategory| *3 (|SetCategory|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeMonoidCategory| *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |gen| *3) (|:| |exp| (|NonNegativeInteger|)))))))
 ((*1 *2 *1)
  (AND
   (|isDomain| *2
    (|List| (|Record| (|:| |factor| *3) (|:| |exponent| (|Integer|)))))
   (|isDomain| *1 (|Factored| *3)) (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Factored| *3))
       (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|isDomain| *2 (|Union| "nil" "sqfr" "irred" "prime"))
       (|isDomain| *1 (|Factored| *4)) (|ofCategory| *4 (|IntegralDomain|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *2 *3 *4)
  (AND (|isDomain| *3 (|Integer|))
       (|isDomain| *4 (|Union| "nil" "sqfr" "irred" "prime"))
       (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Float|))) (|isDomain| *1 (|DrawOption|))))
 ((*1 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
   (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|))))
 ((*1 *2 *1)
  (AND (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Boolean|))
       (|isDomain| *1 (|Bits|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|has| *1 (ATTRIBUTE |arbitraryPrecision|))
       (|ofCategory| *1 (|FloatingPointSystem|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FloatingPointSystem|))
       (|isDomain| *2 (|PositiveInteger|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|has| *1 (ATTRIBUTE |arbitraryPrecision|))
       (|ofCategory| *1 (|FloatingPointSystem|))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FloatingPointSystem|))
       (|isDomain| *2 (|PositiveInteger|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|))
       (|ofCategory| *1 (|FloatingPointSystem|))
       (|isDomain| *2 (|PositiveInteger|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|))
       (|ofCategory| *1 (|FloatingPointSystem|))
       (|isDomain| *2 (|PositiveInteger|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteFieldCategory|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1 *1)
  (|partial| AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|))
   (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *1 *1) (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|)))
       (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|FullPartialFractionExpansion| *3 *2))
       (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|)))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| *4)
                   (|:| |num| *4))))
       (|isDomain| *1 (|FullPartialFractionExpansion| *3 *4))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|OutputForm|))
       (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofType| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|OutputForm|))
       (|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofType| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|CommutativeRing|))))) 
(((*1 *1 *2 *2 *2)
  (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileNameCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|FreeMonoidCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|FreeMonoidCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *2 (|Record| (|:| |lm| *1) (|:| |mm| *1) (|:| |rm| *1)))
       (|ofCategory| *1 (|FreeMonoidCategory| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Record| (|:| |k| *4) (|:| |c| *3)))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Integer|)))))
       (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| *5)))
       (|isDomain| *1 (|FloatingRealPackage| *5))
       (|ofCategory| *5 (|Join| (|OrderedRing|) (|Field|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Integer|))))
       (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|FloatingRealPackage| *4))
       (|ofCategory| *4 (|Join| (|OrderedRing|) (|Field|)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))
       (|isDomain| *2 (|List| (|Complex| *4)))
       (|isDomain| *1 (|FloatingComplexPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))))
   (|isDomain| *4 (|List| (|Symbol|)))
   (|isDomain| *2 (|List| (|List| (|Complex| *5))))
   (|isDomain| *1 (|FloatingComplexPackage| *5))
   (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *3 *4)
  (AND
   (|isDomain| *3 (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))))
   (|isDomain| *2 (|List| (|List| (|Equation| (|Polynomial| (|Complex| *4))))))
   (|isDomain| *1 (|FloatingComplexPackage| *4))
   (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))))
   (|isDomain| *2 (|List| (|List| (|Equation| (|Polynomial| (|Complex| *4))))))
   (|isDomain| *1 (|FloatingComplexPackage| *4))
   (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))
       (|isDomain| *2 (|List| (|Equation| (|Polynomial| (|Complex| *4)))))
       (|isDomain| *1 (|FloatingComplexPackage| *4))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))))
   (|isDomain| *2 (|List| (|Equation| (|Polynomial| (|Complex| *4)))))
   (|isDomain| *1 (|FloatingComplexPackage| *4))
   (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))) 
(((*1 *2 *1 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Float|))))) 
(((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|DoubleFloat|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|DoubleFloat|))))
 ((*1 *2 *1 *3 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|Float|))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|Float|))))) 
(((*1 *1 *1) (|isDomain| *1 (|DoubleFloat|)))
 ((*1 *1 *1) (|isDomain| *1 (|Float|))) ((*1 *1) (|isDomain| *1 (|Float|)))) 
(((*1 *1 *1) (|isDomain| *1 (|DoubleFloat|)))
 ((*1 *1 *1) (|isDomain| *1 (|Float|))) ((*1 *1) (|isDomain| *1 (|Float|)))) 
(((*1 *1) (|isDomain| *1 (|DoubleFloat|))) ((*1 *1) (|isDomain| *1 (|Float|)))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|Float|))))
 ((*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|Float|))))
 ((*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|Float|))))
 ((*1 *2) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Float|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|Float|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2))
       (|ofCategory| *2
                     (|Join| (|FiniteLinearAggregate| *4)
                             (|ShallowlyMutableAggregate| *4)))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2))
       (|ofCategory| *2
                     (|Join| (|FiniteLinearAggregate| *4)
                             (|ShallowlyMutableAggregate| *4)))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2))
       (|ofCategory| *2
                     (|Join| (|FiniteLinearAggregate| *4)
                             (|ShallowlyMutableAggregate| *4)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *1 (|FreeLieAlgebra| *3 *4))
       (|ofCategory| *4 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4))
       (|ofCategory| *1 (|FiniteLinearAggregate| *4))
       (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *1 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3))
       (|ofCategory| *1 (|ShallowlyMutableAggregate| *3))
       (|ofCategory| *1 (|FiniteLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4))
       (|ofCategory| *1 (|FiniteAggregate| *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4))
       (|ofCategory| *1 (|FiniteAggregate| *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *3 (|BasicType|)) (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4))
       (|ofCategory| *1 (|FiniteAggregate| *4)) (|ofCategory| *4 (|Type|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *3 *1)
  (|partial| AND (|isDomain| *3 (|Mapping| (|Boolean|) *2))
   (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|List| (|Vector| *4)))
       (|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4))
       (|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Vector| *3)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(((*1 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
   (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2))
   (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|ofCategory| *1 (|FileCategory| *2 *4))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|ofCategory| *1 (|FileCategory| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileCategory| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *1 *1) (|ofCategory| *1 (|Conduit|)))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|FileCategory| *2 *3))
       (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileCategory| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|String|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FileCategory| *3 *2))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *1 *2)
  (AND (|ofCategory| *1 (|FileCategory| *3 *2))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|ofCategory| *2
                     (|Join| (|FieldOfPrimeCharacteristic|)
                             (CATEGORY |package| (SIGNATURE |coerce| (*2 *4))
                              (SIGNATURE |lookup| ((|PositiveInteger|) *2))
                              (SIGNATURE |basis|
                               ((|Vector| *2) (|PositiveInteger|)))
                              (SIGNATURE |Frobenius| (*2 *2)))))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage2| *2 *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|PrimitiveArray| (|SparseUnivariatePolynomial| *4)))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|isDomain| *3 (|SparseUnivariatePolynomial| *4))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|FiniteFieldCategory|))
   (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|FiniteFieldCategory|))
   (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|FiniteFieldCategory|))
   (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|FiniteFieldCategory|))
   (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))))) 
(((*1 *2 *2)
  (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
   (|ofCategory| *3 (|FiniteFieldCategory|))
   (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *4))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))
       (|ofCategory| *3 (|FiniteFieldCategory|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))
       (|ofCategory| *3 (|FiniteFieldCategory|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *3))
       (|ofCategory| *3 (|FiniteFieldCategory|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FiniteFieldPolynomialPackage| *4))))) 
(((*1 *2)
  (AND
   (|isDomain| *2
    (|Vector|
     (|List|
      (|Record| (|:| |value| (|PrimeField| *3))
                (|:| |index| (|SingleInteger|))))))
   (|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4))
   (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))
 ((*1 *2)
  (AND
   (|isDomain| *2
    (|Vector|
     (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|))))))
   (|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4))
   (|ofCategory| *3 (|FiniteFieldCategory|))
   (|ofType| *4 (|Union| (|SparseUnivariatePolynomial| *3) *2))))
 ((*1 *2)
  (AND
   (|isDomain| *2
    (|Vector|
     (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|))))))
   (|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4))
   (|ofCategory| *3 (|FiniteFieldCategory|))
   (|ofType| *4 (|PositiveInteger|))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|Matrix| (|PrimeField| *3)))
       (|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Matrix| *3))
       (|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofType| *4
        (|Union| (|SparseUnivariatePolynomial| *3)
                 (|Vector|
                  (|List|
                   (|Record| (|:| |value| *3)
                             (|:| |index| (|SingleInteger|)))))))))
 ((*1 *2)
  (AND (|isDomain| *2 (|Matrix| *3))
       (|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofType| *4 (|PositiveInteger|))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Vector|
     (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|))))))
   (|ofCategory| *4 (|FiniteFieldCategory|))
   (|isDomain| *2 (|NonNegativeInteger|))
   (|isDomain| *1 (|FiniteFieldFunctions| *4))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofType| *4
        (|Union| (|SparseUnivariatePolynomial| *3)
                 (|Vector|
                  (|List|
                   (|Record| (|:| |value| *3)
                             (|:| |index| (|SingleInteger|)))))))))
 ((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofType| *4 (|PositiveInteger|))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|List|
         (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|)))))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *3 (|Integer|))
       (|isDomain| *2 (|Table| (|PositiveInteger|) (|NonNegativeInteger|)))))) 
(((*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|)))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FiniteFieldCategory|))
       (|isDomain| *2 (|Union| "prime" "polynomial" "normal" "cyclic"))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2
        (|Union| (|SparseUnivariatePolynomial| *4)
                 (|Vector|
                  (|List|
                   (|Record| (|:| |value| *4)
                             (|:| |index| (|SingleInteger|)))))))
       (|isDomain| *1 (|FiniteFieldFunctions| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|PositiveInteger|))
   (|isDomain| *2
    (|Vector|
     (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|))))))
   (|isDomain| *1 (|FiniteFieldFunctions| *4))
   (|ofCategory| *4 (|FiniteFieldCategory|))))) 
(((*1 *2 *3)
  (AND
   (|isDomain| *3
    (|Vector|
     (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|))))))
   (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Matrix| *4))
   (|isDomain| *1 (|FiniteFieldFunctions| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|Vector|
         (|List| (|Record| (|:| |value| *4) (|:| |index| (|SingleInteger|))))))
       (|isDomain| *1 (|FiniteFieldFunctions| *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|)))
       (|isDomain| *1 (|FiniteFieldFunctions| *4))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|)))
       (|isDomain| *1 (|FiniteFieldCyclicGroup| *3 *4))
       (|ofType| *3 (|PositiveInteger|)) (|ofType| *4 (|PositiveInteger|))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|)))
       (|isDomain| *1 (|FiniteFieldCyclicGroupExtensionByPolynomial| *3 *4))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofType| *4 (|SparseUnivariatePolynomial| *3))))
 ((*1 *2)
  (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|)))
       (|isDomain| *1 (|FiniteFieldCyclicGroupExtension| *3 *4))
       (|ofCategory| *3 (|FiniteFieldCategory|))
       (|ofType| *4 (|PositiveInteger|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6))
       (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6))
       (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|FunctionFieldCategory&| *4 *3 *5 *6))
       (|ofCategory| *4 (|FunctionFieldCategory| *3 *5 *6))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Vector| *1))
       (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Matrix| (|Fraction| *4)))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Matrix| (|Fraction| *4)))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Matrix| (|Fraction| *4)))))) 
(((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Matrix| (|Fraction| *4)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4)))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Vector| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *5 *5))
       (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|isDomain| *2 (|Record| (|:| |num| (|Matrix| *5)) (|:| |den| *5)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))
 ((*1 *2)
  (|partial| AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *2)))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *2 *5))
   (|ofCategory| *3 (|FunctionFieldCategory| *4 *2 *5))))
 ((*1 *2)
  (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4))
   (|ofCategory| *3 (|UniqueFactorizationDomain|))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2)))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2)
  (|partial| AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *2)))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *2 *5))
   (|ofCategory| *3 (|FunctionFieldCategory| *4 *2 *5))))
 ((*1 *2)
  (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4))
   (|ofCategory| *3 (|UniqueFactorizationDomain|))
   (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2)))
   (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Mapping| *5 *5))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|isDomain| *2
        (|Record| (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5)
                  (|:| |gd| *5)))
       (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *5 (|UniqueFactorizationDomain|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6)))
       (|isDomain| *2 (|List| (|Polynomial| *5)))
       (|isDomain| *1 (|FunctionFieldCategory&| *4 *5 *6 *7))
       (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6))
       (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Polynomial| *4)))))) 
(((*1 *2)
  (AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|isDomain| *2 (|List| (|List| *4)))
       (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6))
       (|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6))))
 ((*1 *2)
  (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|UniqueFactorizationDomain|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|List| (|List| *3)))))) 
(((*1 *1 *2 *3 *3 *3 *4)
  (AND (|ofCategory| *4 (|Field|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|ofCategory| *1 (|FiniteDivisorCategory| *4 *3 *5 *2))
       (|ofCategory| *2 (|FunctionFieldCategory| *4 *3 *5))))
 ((*1 *1 *2 *2 *3)
  (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|Field|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *1 (|FiniteDivisorCategory| *2 *4 *5 *6))
       (|ofCategory| *6 (|FunctionFieldCategory| *2 *4 *5))))
 ((*1 *1 *2 *2)
  (AND (|ofCategory| *2 (|Field|))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3)))
       (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5))
       (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4))))
 ((*1 *1 *2)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2))
       (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|FractionalIdeal| *4 (|Fraction| *4) *5 *6))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Vector| *6))
       (|isDomain| *1 (|FiniteDivisor| *3 *4 *5 *6))
       (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|Field|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4)))
       (|isDomain| *2 (|Vector| *6))
       (|isDomain| *1 (|FiniteDivisor| *3 *4 *5 *6))
       (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|DomainTemplate|)) (|isDomain| *1 (|FunctorData|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))))
       (|isDomain| *1 (|FunctorData|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|PrimitiveArray| (|NonNegativeInteger|)))
       (|isDomain| *1 (|FunctorData|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|FunctorData|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FourierComponent| *3))
       (|ofCategory| *3 (|OrderedSet|))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2))
       (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
       (|ofCategory| *3 (|Finite|))
       (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(((*1 *2 *1 *1)
  (|partial| AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
   (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))
   (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3))
       (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *4 *4))
       (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))))) 
(((*1 *1 *1 *2 *3 *1)
  (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))))) 
(((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|))
       (|ofCategory| *3 (|CommutativeRing|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|FreeAbelianMonoidCategory| *4 *2))
       (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *2 (|CancellationAbelianMonoid|))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| *4 *4))
       (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4))
       (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *4 (|CancellationAbelianMonoid|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3))
       (|ofCategory| *2 (|SetCategory|))
       (|ofCategory| *3 (|CancellationAbelianMonoid|))
       (|ofCategory| *3 (|OrderedAbelianMonoid|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|FactoringUtilities| *4 *5 *2 *6))
       (|ofCategory| *6 (|PolynomialCategory| *2 *4 *5))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *7))
       (|isDomain| *3 (|Integer|))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *6))
       (|ofCategory| *6 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *7))
       (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *7))
       (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5))
       (|ofCategory| *4 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|Ring|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *6))
       (|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *9))
       (|isDomain| *4 (|List| *7)) (|isDomain| *5 (|List| *8))
       (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|Ring|))
       (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *8))
       (|isDomain| *1 (|FactoringUtilities| *6 *7 *8 *9))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5))
       (|ofCategory| *3 (|Field|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3)))) 
(((*1 *2 *3 *3 *3 *4 *5 *4 *6)
  (AND (|isDomain| *3 (|Expression| (|Integer|)))
       (|isDomain| *4 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *5 (|Segment| (|DoubleFloat|))) (|isDomain| *6 (|Integer|))
       (|isDomain| *2 (|TubePlot| (|Plot3D|)))
       (|isDomain| *1 (|ExpressionTubePlot|))))
 ((*1 *2 *3 *3 *3 *4 *5 *4 *6 *7)
  (AND (|isDomain| *3 (|Expression| (|Integer|)))
       (|isDomain| *4 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *5 (|Segment| (|DoubleFloat|))) (|isDomain| *6 (|Integer|))
       (|isDomain| *7 (|String|)) (|isDomain| *2 (|TubePlot| (|Plot3D|)))
       (|isDomain| *1 (|ExpressionTubePlot|))))
 ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
  (AND (|isDomain| *3 (|Expression| (|Integer|)))
       (|isDomain| *4 (|Mapping| #1=(|DoubleFloat|) #1#))
       (|isDomain| *5 (|Segment| #1#)) (|isDomain| *6 (|DoubleFloat|))
       (|isDomain| *7 (|Integer|)) (|isDomain| *2 (|TubePlot| (|Plot3D|)))
       (|isDomain| *1 (|ExpressionTubePlot|))))
 ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
  (AND (|isDomain| *3 (|Expression| (|Integer|)))
       (|isDomain| *4 (|Mapping| #2=(|DoubleFloat|) #2#))
       (|isDomain| *5 (|Segment| #2#)) (|isDomain| *6 (|DoubleFloat|))
       (|isDomain| *7 (|Integer|)) (|isDomain| *8 (|String|))
       (|isDomain| *2 (|TubePlot| (|Plot3D|)))
       (|isDomain| *1 (|ExpressionTubePlot|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| #1=(|DoubleFloat|) #1#))
       (|isDomain| *1 (|ExpressionTubePlot|)) (|isDomain| *3 (|DoubleFloat|))))) 
(((*1 *2 *3 *4 *3 *3)
  (AND (|isDomain| *3 (|Equation| *6)) (|isDomain| *4 (|BasicOperator|))
       (|ofCategory| *6 (|FunctionSpace| *5))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *5 *6))))
 ((*1 *2 *3 *4 *3 *5)
  (AND (|isDomain| *3 (|Equation| *7)) (|isDomain| *4 (|BasicOperator|))
       (|isDomain| *5 (|List| *7)) (|ofCategory| *7 (|FunctionSpace| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *7))))
 ((*1 *2 *3 *4 *5 *3)
  (AND (|isDomain| *3 (|List| (|Equation| *7)))
       (|isDomain| *4 (|List| (|BasicOperator|)))
       (|isDomain| *5 (|Equation| *7)) (|ofCategory| *7 (|FunctionSpace| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *7))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *3 (|List| (|Equation| *8)))
       (|isDomain| *4 (|List| (|BasicOperator|)))
       (|isDomain| *5 (|Equation| *8)) (|isDomain| *6 (|List| *8))
       (|ofCategory| *8 (|FunctionSpace| *7))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *7 *8))))
 ((*1 *2 *3 *4 *5 *3)
  (AND (|isDomain| *3 (|List| *7)) (|isDomain| *4 (|List| (|BasicOperator|)))
       (|isDomain| *5 (|Equation| *7)) (|ofCategory| *7 (|FunctionSpace| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *7))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| (|BasicOperator|)))
       (|isDomain| *6 (|List| (|Equation| *8)))
       (|ofCategory| *8 (|FunctionSpace| *7)) (|isDomain| *5 (|Equation| *8))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *7 *8))))
 ((*1 *2 *3 *4 *3 *5)
  (AND (|isDomain| *3 (|Equation| *5)) (|isDomain| *4 (|BasicOperator|))
       (|ofCategory| *5 (|FunctionSpace| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *5))))
 ((*1 *2 *3 *4 *5 *3)
  (AND (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|Equation| *3))
       (|ofCategory| *3 (|FunctionSpace| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *3))))
 ((*1 *2 *3 *4 *5 *5)
  (AND (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|Equation| *3))
       (|ofCategory| *3 (|FunctionSpace| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *3))))
 ((*1 *2 *3 *4 *5 *6)
  (AND (|isDomain| *4 (|BasicOperator|)) (|isDomain| *5 (|Equation| *3))
       (|isDomain| *6 (|List| *3)) (|ofCategory| *3 (|FunctionSpace| *7))
       (|ofCategory| *7
                     (|Join| (|IntegralDomain|)
                             (|ConvertibleTo| (|InputForm|))))
       (|isDomain| *2 (|Any|))
       (|isDomain| *1 (|ExpressionSpaceODESolver| *7 *3))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Expression| *3))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Expression| *3))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|EuclideanDomain|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|EuclideanDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *1 *1 *1)
  (|partial| AND (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1)))
   (|ofCategory| *1 (|EuclideanDomain|))))
 ((*1 *2 *1 *1)
  (AND
   (|isDomain| *2
    (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1)))
   (|ofCategory| *1 (|EuclideanDomain|))))) 
(((*1 *2 *2 *1)
  (|partial| AND (|isDomain| *2 (|List| *1))
   (|ofCategory| *1 (|EuclideanDomain|))))) 
(((*1 *1 *1 *1)
  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|ExpressionSpace|))
       (|ofCategory| *2 (|Type|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|List| (|Kernel| *1))) (|isDomain| *3 (|List| *1))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Equation| *1)))
       (|ofCategory| *1 (|ExpressionSpace|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Equation| *1)) (|ofCategory| *1 (|ExpressionSpace|))))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|)))
 ((*1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|)))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|Kernel| *1))
   (|ofCategory| *1 (|ExpressionSpace|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Kernel| *1)))
       (|ofCategory| *1 (|ExpressionSpace|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Kernel| *1)))
       (|ofCategory| *1 (|ExpressionSpace|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|List| (|BasicOperator|)))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|Symbol|))
       (|isDomain| *2 (|Boolean|))))
 ((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Kernel| *5)) (|ofCategory| *5 (|FunctionSpace| *4))
       (|ofCategory| *4 (|RetractableTo| (|Integer|)))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *5))
       (|isDomain| *1 (|AlgebraicFunction| *4 *5))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Kernel| *1)) (|ofCategory| *1 (|Ring|))
       (|ofCategory| *1 (|ExpressionSpace|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *1))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Exit|))
       (|isDomain| *1 (|ErrorFunctions|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|Exit|))
       (|isDomain| *1 (|ErrorFunctions|))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Exit|))
       (|isDomain| *1 (|ErrorFunctions|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| (|String|))) (|isDomain| *3 (|String|))
       (|isDomain| *2 (|Exit|)) (|isDomain| *1 (|ErrorFunctions|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|UnivariatePolynomialCategory| *3))
       (|isDomain| *1 (|CommuteUnivariatePolynomialCategory| *3 *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))
 ((*1 *1 *1) (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|AbelianGroup|))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (|partial| AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Monoid|))
   (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (|partial| AND (|isDomain| *1 (|Equation| *2)) (|ofCategory| *2 (|Monoid|))
   (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Equation| *3))) (|isDomain| *1 (|Equation| *3))
       (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Type|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|isDomain| *2
        (|List|
         (|Record|
          (|:| |eigval|
               (|Union| (|Fraction| (|Polynomial| *4))
                        (|SuchThat| (|Symbol|) (|Polynomial| *4))))
          (|:| |eigmult| (|NonNegativeInteger|))
          (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| *4))))))))
       (|isDomain| *1 (|EigenPackage| *4))
       (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4))))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|GcdDomain|))
       (|isDomain| *2
        (|List|
         (|Record|
          (|:| |eigval|
               (|Union| (|Fraction| (|Polynomial| *4))
                        (|SuchThat| (|Symbol|) (|Polynomial| *4))))
          (|:| |geneigvec|
               (|List| (|Matrix| (|Fraction| (|Polynomial| *4))))))))
       (|isDomain| *1 (|EigenPackage| *4))
       (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4))))))) 
(((*1 *2 *3 *4 *5 *5)
  (AND
   (|isDomain| *3
    (|Union| (|Fraction| (|Polynomial| *6))
             (|SuchThat| (|Symbol|) (|Polynomial| *6))))
   (|isDomain| *5 (|NonNegativeInteger|)) (|ofCategory| *6 (|GcdDomain|))
   (|isDomain| *2 (|List| (|Matrix| (|Fraction| (|Polynomial| *6)))))
   (|isDomain| *1 (|EigenPackage| *6))
   (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *6))))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|Record|
     (|:| |eigval|
          (|Union| (|Fraction| (|Polynomial| *5))
                   (|SuchThat| (|Symbol|) (|Polynomial| *5))))
     (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| *4))))
   (|ofCategory| *5 (|GcdDomain|))
   (|isDomain| *2 (|List| (|Matrix| (|Fraction| (|Polynomial| *5)))))
   (|isDomain| *1 (|EigenPackage| *5))
   (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *5))))))) 
(((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|Union| (|Fraction| (|Polynomial| *5))
             (|SuchThat| (|Symbol|) (|Polynomial| *5))))
   (|ofCategory| *5 (|GcdDomain|))
   (|isDomain| *2 (|List| (|Matrix| (|Fraction| (|Polynomial| *5)))))
   (|isDomain| *1 (|EigenPackage| *5))
   (|isDomain| *4 (|Matrix| (|Fraction| (|Polynomial| *5))))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Matrix| (|Fraction| (|Polynomial| *4))))
       (|ofCategory| *4 (|GcdDomain|))
       (|isDomain| *2
        (|List|
         (|Union| (|Fraction| (|Polynomial| *4))
                  (|SuchThat| (|Symbol|) (|Polynomial| *4)))))
       (|isDomain| *1 (|EigenPackage| *4))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Scope|))) (|isDomain| *1 (|Environment|))))) 
(((*1 *2 *3 *3 *1)
  (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| (|SExpression|)))
       (|isDomain| *1 (|Environment|))))) 
(((*1 *1 *2 *2 *3 *1)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|SExpression|))
       (|isDomain| *1 (|Environment|))))) 
(((*1 *2 *3 *1)
  (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|List| (|Property|)))
       (|isDomain| *1 (|Environment|))))) 
(((*1 *1 *2 *3 *1)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|List| (|Property|)))
       (|isDomain| *1 (|Environment|))))) 
(((*1 *1) (|isDomain| *1 (|Environment|)))) 
(((*1 *1) (|isDomain| *1 (|Environment|)))) 
(((*1 *1) (|isDomain| *1 (|Environment|)))) 
(((*1 *2 *1 *3 *3 *2)
  (AND (|isDomain| *3 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5))
       (|ofCategory| *2 (|Type|))
       (|ofCategory| *4 (|FiniteLinearAggregate| *2))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))))
 ((*1 *2 *1 *3 *2)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|EltableAggregate| *3 *2))
       (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Stream| *4)))
       (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *4 *5))
       (|isDomain| *3 (|Stream| *4))
       (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *3 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *3 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(((*1 *2 *2 *3)
  (AND (|ofCategory| *3 (|Field|))
       (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *3 *2))
       (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|UniversalSegment| (|Integer|)))
       (|ofCategory| *1 (|ExtensibleLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|ExtensibleLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|FiniteAggregate| *3))
       (|ofCategory| *1 (|DictionaryOperations| *3))
       (|ofCategory| *3 (|SetCategory|))))
 ((*1 *1 *2 *1)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3))
       (|ofCategory| *1 (|ExtensibleLinearAggregate| *3))
       (|ofCategory| *3 (|Type|))))) 
(((*1 *1 *2 *3 *4)
  (AND (|isDomain| *2 (|InternalRepresentationForm|))
       (|isDomain| *3 (|InternalTypeForm|)) (|isDomain| *4 (|Environment|))
       (|isDomain| *1 (|Elaboration|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|InternalRepresentationForm|))
       (|isDomain| *1 (|Elaboration|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|InternalTypeForm|)) (|isDomain| *1 (|Elaboration|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Environment|)) (|isDomain| *1 (|Elaboration|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Syntax|)) (|isDomain| *1 (|ElaboratedExpression|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|SExpression|))
   (|isDomain| *1 (|ElaboratedExpression|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ElaboratedExpression|))))) 
(((*1 *2 *1)
  (|partial| AND (|isDomain| *2 (|Identifier|))
   (|isDomain| *1 (|ElaboratedExpression|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ElaboratedExpression|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|Fraction| (|Integer|)))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Kernel| *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2))))) 
(((*1 *2 *3 *2 *4)
  (|partial| AND (|isDomain| *3 (|List| (|Kernel| *2)))
   (|isDomain| *4 (|Symbol|))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *5)))
   (|ofCategory| *5
                 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|ElementaryFunctionStructurePackage| *5 *2))))) 
(((*1 *2 *2)
  (AND
   (|ofCategory| *3
                 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|ElementaryFunctionStructurePackage| *3 *2))
   (|ofCategory| *2
                 (|Join| (|AlgebraicallyClosedField|)
                         (|TranscendentalFunctionCategory|)
                         (|FunctionSpace| *3)))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|))
       (|ofCategory| *4
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2))
       (|ofCategory| *2
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *4)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Symbol|))
       (|ofCategory| *5
                     (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2
        (|Record| (|:| |func| *3) (|:| |kers| (|List| (|Kernel| *3)))
                  (|:| |vals| (|List| *3))))
       (|isDomain| *1 (|ElementaryFunctionStructurePackage| *5 *3))
       (|ofCategory| *3
                     (|Join| (|AlgebraicallyClosedField|)
                             (|TranscendentalFunctionCategory|)
                             (|FunctionSpace| *5)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|ElementaryFunction| *4 *3))
       (|ofCategory| *3 (|Join| (|FunctionSpace| *4) (|RadicalCategory|)))))) 
(((*1 *2 *2 *3)
  (|partial| AND
   (|isDomain| *3 (|List| (|Record| (|:| |func| *2) (|:| |pole| (|Boolean|)))))
   (|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|RadicalCategory|)))
   (|ofCategory| *4 (|IntegralDomain|))
   (|isDomain| *1 (|ElementaryFunction| *4 *2))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))))) 
(((*1 *2)
  (AND (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *2)
  (AND (|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|RadicalCategory|)))
       (|isDomain| *1 (|ElementaryFunction| *3 *2))
       (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|ExtAlgBasis|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ExtAlgBasis|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *3 (|DifferentialRing|)) (|ofCategory| *3 (|Ring|))
       (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *4))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Mapping| *1 (|NonNegativeInteger|)))
       (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *3))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Mapping| *1 (|NonNegativeInteger|)))
       (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6))))
 ((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *1 (|DifferentialVariableCategory| *2))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *3))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *4))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|NonNegativeInteger|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3))
       (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *2 (|NonNegativeInteger|))))) 
(((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|List| (|DrawOption|)))
   (|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Any|))
   (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *4)
  (|partial| AND (|isDomain| *3 (|List| (|DrawOption|)))
   (|isDomain| *4 (|Symbol|)) (|isDomain| *1 (|DrawOptionFunctions1| *2))
   (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Float|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *1) (|isDomain| *1 (|Character|)))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Palette|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *3 (|List| (|DrawOption|)))
       (|isDomain| *1 (|DrawOptionFunctions0|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Plot|))
       (|isDomain| *2
        (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|)))))
                  (|:| |xValues| (|Segment| (|DoubleFloat|)))
                  (|:| |yValues| (|Segment| (|DoubleFloat|)))))
       (|isDomain| *1 (|TwoDimensionalPlotClipping|))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|Plot|)) (|isDomain| *4 (|Fraction| (|Integer|)))
       (|isDomain| *2
        (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|)))))
                  (|:| |xValues| (|Segment| (|DoubleFloat|)))
                  (|:| |yValues| (|Segment| (|DoubleFloat|)))))
       (|isDomain| *1 (|TwoDimensionalPlotClipping|))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *2
    (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|)))))
              (|:| |xValues| (|Segment| (|DoubleFloat|)))
              (|:| |yValues| (|Segment| (|DoubleFloat|)))))
   (|isDomain| *1 (|TwoDimensionalPlotClipping|))
   (|isDomain| *3 (|List| (|Point| (|DoubleFloat|))))))
 ((*1 *2 *3)
  (AND
   (|isDomain| *2
    (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|)))))
              (|:| |xValues| (|Segment| (|DoubleFloat|)))
              (|:| |yValues| (|Segment| (|DoubleFloat|)))))
   (|isDomain| *1 (|TwoDimensionalPlotClipping|))
   (|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|)))))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Segment| (|Float|))))
       (|isDomain| *1 (|DrawOption|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DrawOption|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|DrawOption|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|Palette|)) (|isDomain| *1 (|DrawOption|))))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Float|)) (|isDomain| *1 (|DrawOption|))))) 
(((*1 *1 *2)
  (AND
   (|isDomain| *2
    (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)
               (|DoubleFloat|)))
   (|isDomain| *1 (|DrawOption|))))
 ((*1 *1 *2)
  (AND
   (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *1 (|DrawOption|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *1 (|DrawOption|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Segment| (|Fraction| (|Integer|)))))
       (|isDomain| *1 (|DrawOption|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Segment| (|Float|))))
       (|isDomain| *1 (|DrawOption|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|DrawOption|))) (|isDomain| *4 (|Symbol|))
       (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DrawOption|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *3))
       (|ofCategory| *3
                     (|Join| (|ConvertibleTo| (|InputForm|))
                             (|SetCategory|)))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *3))
       (|ofCategory| *3
                     (|Join| (|ConvertibleTo| (|InputForm|))
                             (|SetCategory|)))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|ParametricPlaneCurve| *6))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|ofCategory| *6
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|ParametricPlaneCurve| *5))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|ofCategory| *5
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *5))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|ParametricSpaceCurve| *6))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|ofCategory| *6
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|ParametricSpaceCurve| *5))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|ofCategory| *5
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *5))))
 ((*1 *2 *3 *4 *4 *5)
  (AND (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *3))
       (|ofCategory| *3
                     (|Join| (|ConvertibleTo| (|InputForm|))
                             (|SetCategory|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *3))
       (|ofCategory| *3
                     (|Join| (|ConvertibleTo| (|InputForm|))
                             (|SetCategory|)))))
 ((*1 *2 *3 *4 *4 *5)
  (AND (|isDomain| *3 (|ParametricSurface| *6))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|ofCategory| *6
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *6))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|ParametricSurface| *5))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|ofCategory| *5
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctions| *5))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *4 (|Segment| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|)))
       (|isDomain| *4 (|Segment| (|Float|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3
    (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|TwoDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|TwoDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3
    (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *4 (|Segment| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *4 (|Segment| (|Float|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3
    (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3
    (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3
    (|ParametricSurface|
     (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3
    (|ParametricSurface|
     (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND (|isDomain| *3 (|Equation| *7)) (|isDomain| *4 (|Symbol|))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|ofCategory| *7 (|FunctionSpace| *6))
       (|ofCategory| *6
                     (|Join| (|IntegralDomain|) (|OrderedSet|)
                             (|RetractableTo| (|Integer|))))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForAlgebraicCurves| *6 *7))))
 ((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| (|DoubleFloat|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForPoints|))))
 ((*1 *2 *3 *3 *4)
  (AND (|isDomain| *3 (|List| (|DoubleFloat|)))
       (|isDomain| *4 (|List| (|DrawOption|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForPoints|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|Point| (|DoubleFloat|))))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForPoints|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|List| (|Point| (|DoubleFloat|))))
       (|isDomain| *4 (|List| (|DrawOption|)))
       (|isDomain| *2 (|TwoDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForPoints|))))
 ((*1 *2 *3 *3 *3)
  (AND (|isDomain| *3 (|List| (|DoubleFloat|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForPoints|))))
 ((*1 *2 *3 *3 *3 *4)
  (AND (|isDomain| *3 (|List| (|DoubleFloat|)))
       (|isDomain| *4 (|List| (|DrawOption|)))
       (|isDomain| *2 (|ThreeDimensionalViewport|))
       (|isDomain| *1 (|TopLevelDrawFunctionsForPoints|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|DrawComplex|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DrawComplex|))))) 
(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|DrawComplex|))))) 
(((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3
    (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|DoubleFloat|)))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|DrawComplex|))))) 
(((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3
    (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|DoubleFloat|))) (|isDomain| *5 (|Boolean|))
   (|isDomain| *2 (|ThreeDimensionalViewport|))
   (|isDomain| *1 (|DrawComplex|))))) 
(((*1 *2 *2 *3)
  (AND
   (|isDomain| *2
    (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *3
    (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)
               (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|ParametricSpaceCurve| *6))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|ofCategory| *6
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctions| *6))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|ParametricSpaceCurve| *5))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|ofCategory| *5
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctions| *5))))
 ((*1 *2 *3 *4 *4 *5)
  (AND (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctions| *3))
       (|ofCategory| *3
                     (|Join| (|ConvertibleTo| (|InputForm|))
                             (|SetCategory|)))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctions| *3))
       (|ofCategory| *3
                     (|Join| (|ConvertibleTo| (|InputForm|))
                             (|SetCategory|)))))
 ((*1 *2 *3 *4 *4 *5)
  (AND (|isDomain| *3 (|ParametricSurface| *6))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|ofCategory| *6
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctions| *6))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|ParametricSurface| *5))
       (|isDomain| *4 (|SegmentBinding| (|Float|)))
       (|ofCategory| *5
                     (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctions| *5))))
 ((*1 *2 *3 *4 *5)
  (AND
   (|isDomain| *3
    (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4)
  (AND
   (|isDomain| *3
    (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *5)
  (AND (|isDomain| *3 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *4 (|Segment| (|Float|)))
       (|isDomain| *5 (|List| (|DrawOption|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)))
       (|isDomain| *4 (|Segment| (|Float|)))
       (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
       (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3 (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3
    (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3
    (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4 *5)
  (AND
   (|isDomain| *3
    (|ParametricSurface|
     (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *5 (|List| (|DrawOption|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))
 ((*1 *2 *3 *4 *4)
  (AND
   (|isDomain| *3
    (|ParametricSurface|
     (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))))
   (|isDomain| *4 (|Segment| (|Float|)))
   (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|)))
   (|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|Dequeue| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *1 (|DequeueAggregate| *3))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *2 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *4))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| *4))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6))
       (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *3))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *4))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|List| (|NonNegativeInteger|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|DifferentialVariableCategory| *4))
       (|ofCategory| *6 (|OrderedAbelianMonoidSup|))
       (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *2 *5))
       (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))
       (|ofCategory| *2 (|DifferentialVariableCategory| *4))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *2 *3 *4 *5))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4 (|DifferentialVariableCategory| *3))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *2 *3 *4 *5))
       (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedSet|))
       (|ofCategory| *4 (|DifferentialVariableCategory| *3))
       (|ofCategory| *5 (|OrderedAbelianMonoidSup|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|FunctorData|)) (|isDomain| *1 (|DomainConstructor|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|CategoryConstructor|)) (|isDomain| *1 (|Category|))))
 ((*1 *2 *1)
  (AND (|isDomain| *1 (|ConstructorCall| *2))
       (|ofCategory| *2 (|ConstructorCategory|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|DomainConstructor|)) (|isDomain| *1 (|Domain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|ConstructorCall| (|DomainConstructor|)))
       (|isDomain| *1 (|Domain|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|ConstructorCall| (|DomainConstructor|)))
       (|isDomain| *1 (|Domain|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|Domain|))))) 
(((*1 *2 *3 *3 *2)
  (|partial| AND (|isDomain| *2 (|NonNegativeInteger|))
   (|ofCategory| *3
                 (|Join| (|Monoid|) (|Finite|)
                         (CATEGORY |package|
                          (SIGNATURE ** (*3 *3 (|Integer|))))))
   (|isDomain| *1 (|DiscreteLogarithmPackage| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|DataList| *3))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|DoublyLinkedAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|DisplayPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|Integer|))
       (|isDomain| *1 (|DisplayPackage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|DisplayPackage|))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|String|))) (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|DisplayPackage|))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|Integer|))
       (|isDomain| *1 (|DisplayPackage|))))) 
(((*1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|DisplayPackage|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|Type|))
       (|ofCategory| *1 (|DirectProductCategory| *3 *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Equation| (|Polynomial| (|Integer|))))
       (|isDomain| *2
        (|Record| (|:| |varOrder| (|List| (|Symbol|)))
                  (|:| |inhom|
                       (|Union| (|List| (|Vector| (|NonNegativeInteger|)))
                                "failed"))
                  (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))))
       (|isDomain| *1 (|DiophantineSolutionPackage|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|ofCategory| *1 (|DictionaryOperations| *3))))
 ((*1 *1)
  (AND (|ofCategory| *1 (|DictionaryOperations| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1)
  (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|DoubleFloat|))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|Complex| (|DoubleFloat|)))
       (|isDomain| *1 (|DoubleFloatSpecialFunctions|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DoubleFloat|))))) 
(((*1 *2 *3 *4 *5 *5 *2)
  (|partial| AND (|isDomain| *2 (|Boolean|)) (|isDomain| *3 (|Polynomial| *6))
   (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|OrderedCompletion| *7))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|ofCategory| *7
                 (|Join| (|TranscendentalFunctionCategory|)
                         (|AlgebraicallyClosedFunctionSpace| *6)))
   (|isDomain| *1 (|DefiniteIntegrationTools| *6 *7))))
 ((*1 *2 *3 *4 *4 *2)
  (|partial| AND (|isDomain| *2 (|Boolean|))
   (|isDomain| *3 (|SparseUnivariatePolynomial| *6))
   (|isDomain| *4 (|OrderedCompletion| *6))
   (|ofCategory| *6
                 (|Join| (|TranscendentalFunctionCategory|)
                         (|AlgebraicallyClosedFunctionSpace| *5)))
   (|ofCategory| *5
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|DefiniteIntegrationTools| *5 *6))))) 
(((*1 *2 *3 *4 *2 *2 *5)
  (|partial| AND (|isDomain| *2 (|OrderedCompletion| *4))
   (|isDomain| *3 (|Kernel| *4)) (|isDomain| *5 (|Boolean|))
   (|ofCategory| *4
                 (|Join| (|TranscendentalFunctionCategory|)
                         (|AlgebraicallyClosedFunctionSpace| *6)))
   (|ofCategory| *6
                 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                         (|LinearlyExplicitRingOver| (|Integer|))))
   (|isDomain| *1 (|DefiniteIntegrationTools| *6 *4))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|))
       (|ofCategory| *4
                     (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|DefiniteIntegrationTools| *4 *5))
       (|ofCategory| *5
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *4)))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|AntiSymm| *2 *3)) (|ofCategory| *2 (|Ring|))
       (|ofType| *3 (|List| (|Symbol|)))))
 ((*1 *1 *1)
  (AND (|isDomain| *1 (|DeRhamComplex| *2 *3))
       (|ofCategory| *2 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *3 (|List| (|Symbol|)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AntiSymm| *3 *4))
       (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|List| (|Symbol|)))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|DeRhamComplex| *3 *4))
       (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *4 (|List| (|Symbol|)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Expression| *3))
       (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|)))
       (|isDomain| *1 (|DeRhamComplex| *3 *4))
       (|ofType| *4 (|List| (|Symbol|)))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|DeRhamComplex| *2 *3))
       (|ofCategory| *2 (|Join| (|Ring|) (|OrderedSet|)))
       (|ofType| *3 (|List| (|Symbol|)))))) 
(((*1 *2 *3 *4 *5 *5 *6)
  (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *6 (|Boolean|))
       (|ofCategory| *7
                     (|Join| (|EuclideanDomain|) (|CharacteristicZero|)
                             (|RetractableTo| (|Integer|))
                             (|LinearlyExplicitRingOver| (|Integer|))))
       (|ofCategory| *3
                     (|Join| (|TranscendentalFunctionCategory|)
                             (|PrimitiveFunctionCategory|)
                             (|AlgebraicallyClosedFunctionSpace| *7)))
       (|isDomain| *2
        (|Union| (|:| |f1| #1=(|OrderedCompletion| *3)) (|:| |f2| (|List| #1#))
                 (|:| |fail| "failed") (|:| |pole| "potentialPole")))
       (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *7 *3))
       (|isDomain| *5 (|OrderedCompletion| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|DecimalExpansion|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *2 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| *3))))
       (|isDomain| *1 (|DistinctDegreeFactorize| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|FiniteFieldCategory|))
       (|isDomain| *2
        (|Record| (|:| |cont| *5)
                  (|:| |factors|
                       (|List|
                        (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|)))))))
       (|isDomain| *1 (|DistinctDegreeFactorize| *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Mapping| *2 *2)) (|ofCategory| *5 (|Field|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *2)))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *1 (|DoubleResultantPackage| *5 *2 *6 *3))
       (|ofCategory| *3 (|FunctionFieldCategory| *5 *2 *6))))) 
(((*1 *2 *1 *3 *2)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *1 (|DataArray| *4 *2)) (|ofType| *4 (|PositiveInteger|))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|Integer|))))
       (|isDomain| *1 (|CyclotomicPolynomialPackage|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| (|Integer|))))
       (|isDomain| *1 (|CyclotomicPolynomialPackage|))
       (|isDomain| *3 (|Integer|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|List| (|Integer|)))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| (|PositiveInteger|)))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *3 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *2 (|Fraction| (|Integer|)))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|PositiveInteger|))
       (|isDomain| *2 (|SymmetricPolynomial| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|CycleIndicators|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Vector| (|Matrix| *4)))
       (|ofCategory| *4 (|CommutativeRing|))
       (|isDomain| *2 (|Vector| (|Matrix| (|Polynomial| *4))))
       (|isDomain| *1 (|CoerceVectorMatrixPackage| *4))))) 
(((*1 *1) (|isDomain| *1 (|ConstructorKind|)))) 
(((*1 *1) (|isDomain| *1 (|ConstructorKind|)))) 
(((*1 *1) (|isDomain| *1 (|ConstructorKind|)))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|ConstructorKind|)) (|isDomain| *1 (|CategoryAst|))))
 ((*1 *2 *1)
  (AND (|ofCategory| *1 (|ConstructorCategory|))
       (|isDomain| *2 (|ConstructorKind|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ConstructorCategory|))
       (|isDomain| *2 (|List| (|Boolean|)))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ConstructorCategory|))
       (|isDomain| *2 (|List| (|OverloadSet|)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Syntax|)))
       (|isDomain| *1 (|ConstructorCall| *3))
       (|ofCategory| *3 (|ConstructorCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| (|Constructor|)))
       (|isDomain| *1 (|Constructor|))))) 
(((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|CyclicStreamTools| *3 *2))
       (|ofCategory| *2 (|LazyStreamAggregate| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|CyclicStreamTools| *4 *3))
       (|ofCategory| *3 (|LazyStreamAggregate| *4))))) 
(((*1 *2 *2)
  (|partial| AND (|ofCategory| *3 (|Type|))
   (|isDomain| *1 (|CyclicStreamTools| *3 *2))
   (|ofCategory| *2 (|LazyStreamAggregate| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2
        (|Record| (|:| |start| *3) (|:| |factors| (|Factored| *3))))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Complex| *4))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
(((*1 *2 *3 *2)
  (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *2 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Complex| *3)))))) 
(((*1 *2 *3 *4 *5)
  (AND (|isDomain| *5 (|Boolean|))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *3 *2))
       (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Complex| *3)))))) 
(((*1 *2 *3 *3 *4)
  (AND (|isDomain| *4 (|Boolean|))
       (|ofCategory| *5 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2
        (|List| (|Record| (|:| |factors| (|List| *3)) (|:| |error| *5))))
       (|isDomain| *1 (|ComplexRootFindingPackage| *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *5)))))
 ((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2
        (|List| (|Record| (|:| |factors| (|List| *3)) (|:| |error| *4))))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *2 (|List| (|Complex| *4)))
       (|isDomain| *1 (|ComplexRootPackage| *3 *4))
       (|ofCategory| *3
                     (|UnivariatePolynomialCategory| (|Complex| (|Integer|))))
       (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))))
 ((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2 (|List| (|Complex| *4)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))
 ((*1 *2 *3 *4)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|OrderedRing|)))
       (|isDomain| *2 (|List| (|Complex| *4)))
       (|isDomain| *1 (|ComplexRootFindingPackage| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|CRApackage| *3))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|EuclideanDomain|))
       (|isDomain| *1 (|CRApackage| *3))))) 
(((*1 *2 *3 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Mapping| (|Point| *3) (|Point| *3)))
       (|isDomain| *1 (|CoordinateSystems| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))
       (|isDomain| *1 (|CoordinateSystems| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))
       (|isDomain| *1 (|CoordinateSystems| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))
       (|isDomain| *1 (|CoordinateSystems| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))
       (|isDomain| *1 (|CoordinateSystems| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))
       (|isDomain| *1 (|CoordinateSystems| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))
       (|isDomain| *1 (|CoordinateSystems| *3))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Point| *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|TranscendentalFunctionCategory|)
                             (|RadicalCategory|)))
       (|isDomain| *1 (|CoordinateSystems| *3))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Binding|))) (|isDomain| *1 (|Contour|))))) 
(((*1 *1 *2 *1) (AND (|isDomain| *2 (|Binding|)) (|isDomain| *1 (|Contour|))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *3 (|Stream| *2)) (|ofCategory| *2 (|EuclideanDomain|))
       (|isDomain| *1 (|ContinuedFraction| *2))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *1 *1)
  (AND (|isDomain| *1 (|ContinuedFraction| *2))
       (|ofCategory| *2 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| (|Fraction| *3)))
       (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| (|Fraction| *3)))
       (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|ContinuedFraction| *3))
       (|ofCategory| *3 (|EuclideanDomain|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SubSpaceComponentProperty|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|SubSpaceComponentProperty|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *3 (|Environment|))
       (|isDomain| *1 (|CompilerPackage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|SpadAst|)) (|isDomain| *2 (|Maybe| (|Elaboration|)))
       (|isDomain| *1 (|CompilerPackage|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|String|))
       (|isDomain| *2 (|List| (|Maybe| (|Elaboration|))))
       (|isDomain| *1 (|CompilerPackage|))))) 
(((*1 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *1 *2 *2)
  (AND (|ofCategory| *1 (|ComplexCategory| *2))
       (|ofCategory| *2 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|ComplexCategory| *3))
       (|ofCategory| *3 (|CommutativeRing|))
       (|ofCategory| *3 (|RealNumberSystem|))
       (|ofCategory| *3 (|TranscendentalFunctionCategory|))
       (|isDomain| *2 (|Record| (|:| |r| *3) (|:| |phi| *3)))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|))
       (|isDomain| *1 (|CommutativeOperation| *3))))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|Commutator|)))
 ((*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Commutator|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *2 (|FunctionSpace| *4))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|CombinatorialOpsCategory|))
       (|isDomain| *2 (|Symbol|))))
 ((*1 *1 *1) (|ofCategory| *1 (|CombinatorialOpsCategory|)))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *2 (|FunctionSpace| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|SegmentBinding| *2))
       (|ofCategory| *2 (|FunctionSpace| *4))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|SegmentBinding| *1))
       (|ofCategory| *1 (|CombinatorialOpsCategory|))))
 ((*1 *1 *1 *2)
  (AND (|ofCategory| *1 (|CombinatorialOpsCategory|))
       (|isDomain| *2 (|Symbol|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *2 *2)
  (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|)))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *2 *2 *2)
  (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|IntegerNumberSystem|))
       (|isDomain| *1 (|IntegerCombinatoricFunctions| *2))))) 
(((*1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|)))
 ((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))
 ((*1 *2 *2)
  (AND (|isDomain| *1 (|IntegerCombinatoricFunctions| *2))
       (|ofCategory| *2 (|IntegerNumberSystem|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *4 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *4 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *4 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *4 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *4 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|FunctionSpace| *4))
       (|isDomain| *1 (|CombinatorialFunction| *4 *2))
       (|ofCategory| *4 (|IntegralDomain|))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|CombinatorialFunction| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))))) 
(((*1 *1) (|isDomain| *1 (|Color|)))) 
(((*1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|Color|))))) 
(((*1 *2 *3 *4 *4 *4 *4)
  (AND (|isDomain| *4 (|DoubleFloat|))
       (|isDomain| *2
        (|Record| (|:| |brans| (|List| (|List| (|Point| *4))))
                  (|:| |xValues| (|Segment| *4))
                  (|:| |yValues| (|Segment| *4))))
       (|isDomain| *1 (|TwoDimensionalPlotClipping|))
       (|isDomain| *3 (|List| (|List| (|Point| *4))))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|Plot|))
       (|isDomain| *2
        (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|)))))
                  (|:| |xValues| (|Segment| (|DoubleFloat|)))
                  (|:| |yValues| (|Segment| (|DoubleFloat|)))))
       (|isDomain| *1 (|TwoDimensionalPlotClipping|))))
 ((*1 *2 *3 *4 *4)
  (AND (|isDomain| *3 (|Plot|)) (|isDomain| *4 (|Fraction| (|Integer|)))
       (|isDomain| *2
        (|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|)))))
                  (|:| |xValues| (|Segment| (|DoubleFloat|)))
                  (|:| |yValues| (|Segment| (|DoubleFloat|)))))
       (|isDomain| *1 (|TwoDimensionalPlotClipping|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|PositiveInteger|))
       (|isDomain| *1 (|CliffordAlgebra| *3 *4 *5)) (|ofType| *3 *2)
       (|ofCategory| *4 (|Field|)) (|ofType| *5 (|QuadraticForm| *3 *4))))) 
(((*1 *1 *1)
  (AND (|ofCategory| *1 (|FiniteAggregate| *2))
       (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|))
       (|ofCategory| *2 (|BasicType|))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2
        (|Record| (|:| |func| *3) (|:| |poly| *3) (|:| |c1| (|Fraction| *5))
                  (|:| |c2| (|Fraction| *5))
                  (|:| |deg| (|NonNegativeInteger|))))
       (|isDomain| *1 (|ChangeOfVariable| *4 *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *5)))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *2 (|UniqueFactorizationDomain|))
       (|isDomain| *1 (|ChangeOfVariable| *2 *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4)))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|Fraction| *6))
       (|ofCategory| *5 (|UniqueFactorizationDomain|))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| *5))
       (|isDomain| *2
        (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| *3)
                  (|:| |radicand| *6)))
       (|isDomain| *1 (|ChangeOfVariable| *5 *6 *7))
       (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *7 (|UnivariatePolynomialCategory| *3))))) 
(((*1 *2 *3)
  (|partial| AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
   (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
   (|isDomain| *2
    (|Record| (|:| |radicand| (|Fraction| *5))
              (|:| |deg| (|NonNegativeInteger|))))
   (|isDomain| *1 (|ChangeOfVariable| *4 *5 *3))
   (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *5)))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|UniqueFactorizationDomain|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Record| (|:| |coef| (|Fraction| *5)) (|:| |poly| *3)))
       (|isDomain| *1 (|ChangeOfVariable| *4 *5 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *5)))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Character|))))) 
(((*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Character|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Character|))))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *1) (|isDomain| *1 (|Character|)))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Character|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Character|)))
       (|isDomain| *1 (|CharacterClass|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|CharacterClass|))))) 
(((*1 *1) (|isDomain| *1 (|CharacterClass|)))) 
(((*1 *1) (|isDomain| *1 (|CharacterClass|)))) 
(((*1 *1) (|isDomain| *1 (|CharacterClass|)))) 
(((*1 *1) (|isDomain| *1 (|CharacterClass|)))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|OperatorSignature|)))
       (|isDomain| *1 (|Category|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|ConstructorCall| (|CategoryConstructor|))))
       (|isDomain| *1 (|Category|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|ConstructorCall| (|CategoryConstructor|))))
       (|isDomain| *1 (|Category|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| (|Integer|)))
       (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|))
       (|ofType| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|CommutativeRing|))))) 
(((*1 *1)
  (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|CommutativeRing|))))) 
(((*1 *1)
  (AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 (|Integer|))
       (|ofType| *3 (|NonNegativeInteger|))
       (|ofCategory| *4 (|CommutativeRing|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|CartesianTensor| *3 *4 *5))
       (|ofType| *3 (|Integer|)) (|ofType| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|CommutativeRing|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *5)) (|ofCategory| *5 (|CommutativeRing|))
       (|isDomain| *1 (|CartesianTensor| *3 *4 *5)) (|ofType| *3 (|Integer|))
       (|ofType| *4 (|NonNegativeInteger|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|CardinalNumber|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|))))) 
(((*1 *2) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|))))) 
(((*1 *2 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CardinalNumber|))))) 
(((*1 *2 *1 *3)
  (AND (|ofCategory| *1 (|CachableSet|)) (|isDomain| *3 (|NonNegativeInteger|))
       (|isDomain| *2 (|Void|))))) 
(((*1 *2 *1 *1)
  (AND (|isDomain| *2 (|Maybe| *1))
       (|ofCategory| *1 (|CancellationAbelianMonoid|))))) 
(((*1 *1) (|isDomain| *1 (|ByteOrder|)))) 
(((*1 *1) (|isDomain| *1 (|ByteOrder|)))) 
(((*1 *1) (|isDomain| *1 (|ByteOrder|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ByteBuffer|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ByteBuffer|))))) 
(((*1 *2 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ByteBuffer|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Byte|))))) 
(((*1 *1 *1 *2 *1)
  (AND (|isDomain| *1 (|BinaryTree| *2)) (|ofCategory| *2 (|SetCategory|))))
 ((*1 *1 *2)
  (AND (|isDomain| *1 (|BinaryTree| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|BinaryTournament| *3))))) 
(((*1 *1 *1 *2 *1)
  (AND (|ofCategory| *1 (|BinaryTreeCategory| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|Boolean|)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|)))) 
(((*1 *1 *1 *1) (|isDomain| *1 (|Boolean|)))
 ((*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|)))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|))
       (|isDomain| *1 (|BinarySearchTree| *3))))) 
(((*1 *1 *2 *1)
  (AND (|isDomain| *1 (|BinarySearchTree| *2))
       (|ofCategory| *2 (|OrderedSet|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BrillhartTests| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|BrillhartTests| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *2)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|BrillhartTests| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BrillhartTests| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))
 ((*1 *2 *3 *2)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BrillhartTests| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|)))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|BinaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *1 *1 *1)
  (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2))
       (|ofCategory| *1 (|BinaryRecursiveAggregate| *2))
       (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|Join| (|Field|) (|RetractableTo| (|Fraction| *2))))
       (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|BoundIntegerRoots| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
(((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|BasicOperator|))
   (|isDomain| *1 (|BasicOperatorFunctions1| *2))
   (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|))
       (|isDomain| *1 (|BasicOperatorFunctions1| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|))
       (|isDomain| *3 (|List| (|Mapping| *4 (|List| *4))))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|BasicOperatorFunctions1| *4))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *4 *4))
       (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *1 (|BasicOperatorFunctions1| *4))))
 ((*1 *2 *3)
  (|partial| AND (|isDomain| *3 (|BasicOperator|))
   (|isDomain| *2 (|List| (|Mapping| *4 (|List| *4))))
   (|isDomain| *1 (|BasicOperatorFunctions1| *4))
   (|ofCategory| *4 (|SetCategory|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|List| (|Property|))) (|isDomain| *1 (|Binding|))))
 ((*1 *2 *1)
  (AND (|isDomain| *2 (|AssociationList| (|String|) (|None|)))
       (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *2 *1)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) #1=(|BasicOperator|) #1#))
       (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| (|Boolean|) #1=(|BasicOperator|) #1#))
       (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Boolean|))
       (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|None|))
       (|isDomain| *1 (|BasicOperator|))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|String|)) (|isDomain| *3 (|None|))
       (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|AssociationList| (|String|) (|None|)))
       (|isDomain| *1 (|BasicOperator|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|BinaryOperation| *3))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|List| (|Property|)))
       (|isDomain| *1 (|Binding|))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|ofCategory| *1 (|BagAggregate| *3))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *1)
  (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(((*1 *2 *3)
  (AND (|has| *2 (ATTRIBUTE (|commutative| "*")))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *6 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|BezoutMatrix| *2 *3 *4 *5 *6))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *4 (|MatrixCategory| *2 *5 *6))))) 
(((*1 *2 *3 *3)
  (AND (|has| *2 (ATTRIBUTE (|commutative| "*")))
       (|ofCategory| *5 (|FiniteLinearAggregate| *2))
       (|ofCategory| *6 (|FiniteLinearAggregate| *2))
       (|ofCategory| *2 (|Ring|))
       (|isDomain| *1 (|BezoutMatrix| *2 *3 *4 *5 *6))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))
       (|ofCategory| *4 (|MatrixCategory| *2 *5 *6))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6))
       (|isDomain| *1 (|BezoutMatrix| *4 *3 *2 *5 *6))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6))
       (|isDomain| *1 (|BezoutMatrix| *4 *3 *2 *5 *6))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *6 (|FiniteLinearAggregate| *4))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|BalancedBinaryTree| *3))
       (|ofCategory| *3 (|SetCategory|))))) 
(((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|BalancedBinaryTree| *3))))) 
(((*1 *1 *1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3 *3 *3 *3))
       (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|BalancedBinaryTree| *3))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Mapping| *2 *2 *2))
       (|isDomain| *1 (|BalancedBinaryTree| *2))
       (|ofCategory| *2 (|SetCategory|))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| (|List| *2) *2 *2 *2))
       (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|BalancedBinaryTree| *2))))
 ((*1 *1 *1 *2 *3)
  (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *2 (|SetCategory|))
       (|isDomain| *1 (|BalancedBinaryTree| *2))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *3)
  (AND (|ofCategory| *4 (|Join| (|GcdDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|BalancedFactorisation| *4 *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))
 ((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|List| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))
       (|ofCategory| *5 (|Join| (|GcdDomain|) (|CharacteristicZero|)))
       (|isDomain| *2 (|Factored| *3))
       (|isDomain| *1 (|BalancedFactorisation| *5 *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3 (|Integer|))) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|Automorphism| *3))))
 ((*1 *1 *2 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|Automorphism| *3))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|Ring|))
       (|isDomain| *1 (|Automorphism| *3))))) 
(((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|))
       (|isDomain| *1 (|ArrayStack| *3))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |minor| (|List| #1=(|PositiveInteger|))) (|:| |eq| *3)
                  (|:| |minors| (|List| (|List| #1#)))
                  (|:| |ops| (|List| *3))))
       (|isDomain| *1 (|AssociatedEquations| *5 *3))
       (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|Vector| (|Matrix| *4)))
       (|isDomain| *1 (|AssociatedEquations| *4 *5))
       (|isDomain| *3 (|Matrix| *4))
       (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
(((*1 *2 *3 *4)
  (AND (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *2
        (|Record| (|:| |mat| (|Matrix| *5))
                  (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))))
       (|isDomain| *1 (|AssociatedEquations| *5 *3))
       (|isDomain| *4 (|PositiveInteger|))
       (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|OneDimensionalArray| *3)) (|ofCategory| *3 (|Type|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|))
       (|isDomain| *1 (|OneDimensionalArray| *3))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *3 *5))
       (|ofCategory| *4 (|Type|))
       (|ofCategory| *3 (|FiniteLinearAggregate| *4))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))))) 
(((*1 *1 *1 *2 *3)
  (AND (|isDomain| *2 (|Integer|))
       (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *5 *3))
       (|ofCategory| *4 (|Type|))
       (|ofCategory| *5 (|FiniteLinearAggregate| *4))
       (|ofCategory| *3 (|FiniteLinearAggregate| *4))))) 
(((*1 *1) (|isDomain| *1 (|Arity|)))) 
(((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5
                     (|Join| (|Ring|) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|isDomain| *1 (|ApplyRules| *4 *5 *2))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|List| (|RewriteRule| *4 *5 *2)))
       (|ofCategory| *4 (|SetCategory|))
       (|ofCategory| *5
                     (|Join| (|Ring|) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *5) (|PatternMatchable| *4)
                             (|ConvertibleTo| (|Pattern| *4))))
       (|isDomain| *1 (|ApplyRules| *4 *5 *2))))
 ((*1 *2 *3 *2 *4)
  (AND (|isDomain| *3 (|List| (|RewriteRule| *5 *6 *2)))
       (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|SetCategory|))
       (|ofCategory| *6
                     (|Join| (|Ring|) (|PatternMatchable| *5)
                             (|ConvertibleTo| (|Pattern| *5))))
       (|ofCategory| *2
                     (|Join| (|FunctionSpace| *6) (|PatternMatchable| *5)
                             (|ConvertibleTo| (|Pattern| *5))))
       (|isDomain| *1 (|ApplyRules| *5 *6 *2))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *3 (|None|))
       (|isDomain| *1 (|Any|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|Any|))))) 
(((*1 *2 *1) (AND (|isDomain| *2 (|None|)) (|isDomain| *1 (|Any|))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Matrix| *3)))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Matrix| *3)))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *2 (|List| (|Matrix| *3)))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|AlgebraPackage| *4 *3))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *3))
       (|isDomain| *1 (|AlgebraPackage| *4 *3))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(((*1 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *4))
       (|isDomain| *1 (|AlgebraPackage| *3 *4))
       (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|AlgebraPackage| *4 *3))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|AlgebraPackage| *4 *3))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|AlgebraPackage| *4 *3))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|AlgebraPackage| *4 *3))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|NonNegativeInteger|))
       (|isDomain| *1 (|AlgebraPackage| *4 *3))
       (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4))))) 
(((*1 *2 *3 *2 *4)
  (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|NonNegativeInteger|))
       (|ofCategory| *5 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))))
       (|ofCategory| *5 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *5 *2))
       (|ofCategory| *2 (|FunctionSpace| *5))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *5
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *5
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *5
                                                                (|Kernel|
                                                                 $)))))))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *3
                                                                (|Kernel|
                                                                 $)))))))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *3
                                                                (|Kernel|
                                                                 $)))))))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))))
       (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *3 *2))
       (|ofCategory| *2 (|FunctionSpace| *3))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *3
                                                                (|Kernel|
                                                                 $)))))))))) 
(((*1 *2 *3)
  (AND (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|SparseUnivariatePolynomial| *3))
       (|isDomain| *1 (|AlgebraicManipulations| *4 *3))
       (|ofCategory| *3
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *4
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *4
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *4
                                                                (|Kernel|
                                                                 $)))))))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *3
                                                                (|Kernel|
                                                                 $)))))))))
 ((*1 *2 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *3
                                                                (|Kernel|
                                                                 $)))))))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *4
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *4
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *4
                                                                (|Kernel|
                                                                 $)))))))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *4 *2))))
 ((*1 *2 *2 *3)
  (AND (|isDomain| *3 (|List| (|Kernel| *2)))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *4
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *4
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *4
                                                                (|Kernel|
                                                                 $)))))))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *4 *2))))) 
(((*1 *2 *2)
  (AND (|ofCategory| *3 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicManipulations| *3 *2))
       (|ofCategory| *2
                     (|Join| (|Field|) (|ExpressionSpace|)
                             (CATEGORY |domain|
                              (SIGNATURE |numer|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |denom|
                               ((|SparseMultivariatePolynomial| *3
                                                                (|Kernel| $))
                                $))
                              (SIGNATURE |coerce|
                               ($
                                (|SparseMultivariatePolynomial| *3
                                                                (|Kernel|
                                                                 $)))))))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|))
       (|ofCategory| *5 (|UnivariatePolynomialCategory| *4))
       (|isDomain| *2 (|Void|))
       (|isDomain| *1 (|AlgebraicFunctionField| *4 *5 *6 *7))
       (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5)))
       (|ofType| *7 *6)))) 
(((*1 *2 *3)
  (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AlgFactor| *3))
       (|ofCategory| *3 (|UnivariatePolynomialCategory| (|AlgebraicNumber|)))))) 
(((*1 *2 *3 *1)
  (AND (|ofCategory| *1 (|AssociationListAggregate| *3 *4))
       (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))
       (|isDomain| *2 (|Maybe| (|Record| (|:| |key| *3) (|:| |entry| *4))))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|Boolean|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *2 (|FunctionSpace| *3))
       (|isDomain| *1 (|AlgebraicFunction| *3 *2))
       (|ofCategory| *3 (|RetractableTo| *4))
       (|ofCategory| *3 (|IntegralDomain|))))) 
(((*1 *2 *3)
  (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 (|FunctionSpace| *4))
       (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|OutputForm|))
       (|isDomain| *1 (|AlgebraicFunction| *4 *5))))) 
(((*1 *2 *3 *2)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2))
       (|ofCategory| *2 (|FunctionSpace| *4))
       (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *1 (|AlgebraicFunction| *4 *2))))) 
(((*1 *1 *2 *3 *3 *4 *4)
  (AND (|isDomain| *2 (|Polynomial| (|Integer|))) (|isDomain| *3 (|Symbol|))
       (|isDomain| *4 (|Segment| (|Fraction| (|Integer|))))
       (|isDomain| *1 (|PlaneAlgebraicCurvePlot|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))
       (|isDomain| *2 (|List| *1))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))
       (|isDomain| *2 (|List| *1))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))
       (|isDomain| *2 (|List| *1))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3))))) 
(((*1 *1 *2 *3)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|isDomain| *3 (|Symbol|))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))))
 ((*1 *1 *2)
  (AND (|isDomain| *2 (|Polynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))))
 ((*1 *1 *1 *2)
  (AND (|isDomain| *2 (|Symbol|))
       (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3))
       (|ofCategory| *3 (|IntegralDomain|))))
 ((*1 *1 *1)
  (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2))
       (|ofCategory| *2 (|IntegralDomain|))))) 
(((*1 *2 *3 *4)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
       (|isDomain| *4 (|Symbol|))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))
       (|isDomain| *2 (|List| *1))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))
       (|isDomain| *2 (|List| *1))))
 ((*1 *2 *3)
  (AND (|isDomain| *3 (|Polynomial| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedField|))
       (|isDomain| *2 (|List| *1))))
 ((*1 *2 *1 *3)
  (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|))
       (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *4))))
 ((*1 *2 *1)
  (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *1))
       (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3))))) 
(((*1 *2 *1 *1)
  (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|))))) 
((|opposite?| . 1288287) (|zerosOf| . 1287440) (|zeroOf| . 1286754)
 (|rootsOf| . 1285907) (|makeSketch| . 1285690) (|inrootof| . 1285472)
 (|droot| . 1285255) (|iroot| . 1285020) (|eq?| . 1284933) (|assoc| . 1284702)
 (|doublyTransitive?| . 1284539) (|knownInfBasis| . 1284195)
 (|rootSplit| . 1283188) (|ratDenom| . 1279076) (|ratPoly| . 1278012)
 (|rootPower| . 1276881) (|rootProduct| . 1275750) (|rootSimp| . 1274619)
 (|rootKerSimp| . 1273402) (|leftRank| . 1273187) (|rightRank| . 1272972)
 (|doubleRank| . 1272757) (|weakBiRank| . 1272542) (|biRank| . 1272327)
 (|basisOfCommutingElements| . 1272133) (|basisOfLeftAnnihilator| . 1271936)
 (|basisOfRightAnnihilator| . 1271739) (|basisOfLeftNucleus| . 1271545)
 (|basisOfRightNucleus| . 1271351) (|basisOfMiddleNucleus| . 1271157)
 (|basisOfNucleus| . 1270963) (|basisOfCenter| . 1270769)
 (|basisOfLeftNucloid| . 1270557) (|basisOfRightNucloid| . 1270345)
 (|basisOfCentroid| . 1270133) (|radicalOfLeftTraceForm| . 1269939)
 (|obj| . 1269868) (|dom| . 1269790) (|any| . 1269675) (|applyRules| . 1268684)
 (|localUnquote| . 1268228) (|arbitrary| . 1268189) (|setColumn!| . 1267923)
 (|setRow!| . 1267657) (|oneDimensionalArray| . 1267387)
 (|associatedSystem| . 1267014) (|uncouplingMatrices| . 1266740)
 (|associatedEquations| . 1266278) (|arrayStack| . 1266151)
 (|morphism| . 1265756) (|balancedFactorisation| . 1265231)
 (|before?| . 1265144) (|mapDown!| . 1264827) (|mapUp!| . 1264512)
 (|setleaves!| . 1264374) (|balancedBinaryTree| . 1264218)
 (|sylvesterMatrix| . 1263894) (|bezoutMatrix| . 1263570)
 (|bezoutResultant| . 1263189) (|bezoutDiscriminant| . 1262811)
 (|inspect| . 1262722) (|extract!| . 1262633) (|bag| . 1262509)
 (|binding| . 1262378) (|binaryOperation| . 1262244)
 (|setProperties| . 1262120) (|setProperty| . 1261872)
 (|deleteProperty!| . 1261694) (|has?| . 1261567) (|comparison| . 1261434)
 (|equality| . 1261301) (|nary?| . 1261215) (|unary?| . 1261129)
 (|nullary?| . 1261043) (|properties| . 1260834) (|derivative| . 1260223)
 (|constantOperator| . 1260070) (|constantOpIfCan| . 1259915)
 (|integerBound| . 1259680) (|setright!| . 1259511) (|setleft!| . 1259342)
 (|brillhartIrreducible?| . 1259021) (|brillhartTrials| . 1258670)
 (|noLinearFactor?| . 1258510) (|insertRoot!| . 1258403)
 (|binarySearchTree| . 1258271) (|nor| . 1258172) (|nand| . 1258073)
 (|node| . 1257958) (|binaryTournament| . 1257826) (|binaryTree| . 1257638)
 (|byte| . 1257550) (|setLength!| . 1257453) (|capacity| . 1257359)
 (|byteBuffer| . 1257265) (|unknownEndian| . 1257222) (|bigEndian| . 1257179)
 (|littleEndian| . 1257136) (|subtractIfCan| . 1257025)
 (|setPosition| . 1256893) (|generalizedContinuumHypothesisAssumed| . 1256806)
 (|generalizedContinuumHypothesisAssumed?| . 1256724) (|countable?| . 1256637)
 (|Aleph| . 1256532) (|unravel| . 1256320) (|ravel| . 1256108)
 (|leviCivitaSymbol| . 1255927) (|kroneckerDelta| . 1255746)
 (|reindex| . 1255515) (|parents| . 1255386) (|principalAncestors| . 1255257)
 (|exportedOperators| . 1255150) (|alphanumeric| . 1255102)
 (|alphabetic| . 1255054) (|hexDigit| . 1255006) (|digit| . 1254958)
 (|charClass| . 1254769) (|alphanumeric?| . 1254689) (|lowerCase?| . 1254609)
 (|upperCase?| . 1254529) (|alphabetic?| . 1254449) (|hexDigit?| . 1254369)
 (|digit?| . 1254289) (|escape| . 1254246) (|verticalTab| . 1254203)
 (|horizontalTab| . 1254160) (|backspace| . 1254117) (|formfeed| . 1254074)
 (|linefeed| . 1254031) (|carriageReturn| . 1253988) (|newline| . 1253945)
 (|underscore| . 1253902) (|char| . 1253732) (|ord| . 1253639)
 (|mkIntegral| . 1253300) (|radPoly| . 1252926) (|rootPoly| . 1252455)
 (|goodPoint| . 1252192) (|chvar| . 1251730) (|removeDuplicates| . 1251556)
 (|e| . 1251354) (|clipParametric| . 1250655) (|clipWithRanges| . 1250294)
 (|numberOfHues| . 1250213) (|yellow| . 1250174) (|iifact| . 1250012)
 (|iibinom| . 1249822) (|iiperm| . 1249632) (|iipow| . 1249442)
 (|iidsum| . 1249252) (|iidprod| . 1249062) (|ipow| . 1248872)
 (|factorial| . 1248521) (|multinomial| . 1248365) (|permutation| . 1248005)
 (|stirling1| . 1247877) (|stirling2| . 1247749) (|summation| . 1247126)
 (|factorials| . 1246607) (|mkcomm| . 1246478)
 (|commutativeOperation| . 1246334) (|polarCoordinates| . 1246056)
 (|complex| . 1245943) (|imaginary| . 1245836) (|elaborateFile| . 1245684)
 (|elaborate| . 1245547) (|macroExpand| . 1245417) (|solid| . 1245309)
 (|solid?| . 1245204) (|denominators| . 1245064) (|numerators| . 1244924)
 (|convergents| . 1244764) (|approximants| . 1244604) (|reducedForm| . 1244494)
 (|partialQuotients| . 1244354) (|partialDenominators| . 1244214)
 (|partialNumerators| . 1244074) (|reducedContinuedFraction| . 1243931)
 (|push| . 1243850) (|bindings| . 1243761) (|cartesian| . 1243511)
 (|polar| . 1243261) (|cylindrical| . 1243011) (|spherical| . 1242761)
 (|parabolic| . 1242511) (|parabolicCylindrical| . 1242261)
 (|paraboloidal| . 1242011) (|ellipticCylindrical| . 1241736)
 (|prolateSpheroidal| . 1241461) (|oblateSpheroidal| . 1241186)
 (|bipolar| . 1240911) (|bipolarCylindrical| . 1240636) (|toroidal| . 1240361)
 (|conical| . 1240083) (|modTree| . 1239949) (|multiEuclideanTree| . 1239815)
 (|complexZeros| . 1239022) (|divisorCascade| . 1238370) (|graeffe| . 1238161)
 (|pleskenSplit| . 1237623) (|reciprocalPolynomial| . 1237414)
 (|rootRadius| . 1236995) (|schwerpunkt| . 1236760) (|setErrorBound| . 1236551)
 (|startPolynomial| . 1236251) (|cycleElt| . 1236095)
 (|computeCycleLength| . 1235902) (|computeCycleEntry| . 1235752)
 (|findConstructor| . 1235616) (|arguments| . 1235461) (|operations| . 1235347)
 (|dualSignature| . 1235237) (|kind| . 1235038) (|package| . 1234989)
 (|domain| . 1234940) (|category| . 1234891) (|coerceP| . 1234662)
 (|powerSum| . 1234487) (|elementary| . 1234309) (|alternating| . 1234131)
 (|cyclic| . 1233956) (|dihedral| . 1233781) (|cap| . 1233598)
 (|cup| . 1233463) (|wreath| . 1233328) (|SFunction| . 1233144)
 (|skewSFunction| . 1232965) (|cyclotomicDecomposition| . 1232783)
 (|cyclotomicFactorization| . 1232597) (|qsetelt| . 1232410)
 (|doubleResultant| . 1232064) (|distdfact| . 1231651)
 (|separateDegrees| . 1231365) (|trace2PowMod| . 1231129)
 (|tracePowMod| . 1230893) (|irreducible?| . 1230681) (|decimal| . 1230572)
 (|innerint| . 1229745) (|exteriorDifferential| . 1229582)
 (|totalDifferential| . 1229378) (|homogeneous?| . 1229034)
 (|leadingBasisTerm| . 1228746) (|ignore?| . 1228274) (|computeInt| . 1227768)
 (|checkForZero| . 1226707) (|nan?| . 1226625) (|logGamma| . 1226393)
 (|hypergeometric0F1| . 1226155) (|rotatez| . 1225984) (|rotatey| . 1225813)
 (|rotatex| . 1225642) (|identity| . 1225474) (|dictionary| . 1225229)
 (|dioSolve| . 1224794) (|directProduct| . 1224656) (|newLine| . 1224575)
 (|copies| . 1224451) (|say| . 1224208) (|sayLength| . 1223959)
 (|setnext!| . 1223793) (|setprevious!| . 1223627) (|next| . 1223522)
 (|previous| . 1223417) (|datalist| . 1223293)
 (|shanksDiscLogAlgorithm| . 1222987) (|showSummary| . 1222913)
 (|reflect| . 1222797) (|reify| . 1222681) (|constructor| . 1222391)
 (|functorData| . 1222297) (|separant| . 1222027) (|initial| . 1221757)
 (|leader| . 1221487) (|isobaric?| . 1221182) (|weights| . 1220531)
 (|differentialVariables| . 1220226) (|extractBottom!| . 1220133)
 (|extractTop!| . 1220040) (|insertBottom!| . 1219944) (|insertTop!| . 1219848)
 (|bottom!| . 1219755) (|top!| . 1219662) (|dequeue| . 1219324)
 (|makeObject| . 1214256) (|recolor| . 1213957) (|drawComplex| . 1213675)
 (|drawComplexVectorField| . 1213424) (|setRealSteps| . 1213342)
 (|setImagSteps| . 1213260) (|setClipValue| . 1213172) (|draw| . 1203972)
 (|option?| . 1203812) (|range| . 1203581) (|colorFunction| . 1203154)
 (|curveColor| . 1202996) (|pointColor| . 1202838) (|clip| . 1201276)
 (|clipBoolean| . 1201133) (|style| . 1200913) (|toScale| . 1200691)
 (|pointColorPalette| . 1200548) (|curveColorPalette| . 1200405)
 (|var1Steps| . 1200158) (|var2Steps| . 1199911) (|space| . 1199597)
 (|tubePoints| . 1199350) (|tubeRadius| . 1199132) (|option| . 1198788)
 (|weight| . 1197786) (|makeVariable| . 1196915) (|Nul| . 1196820)
 (|exponents| . 1196727) (|iisqrt2| . 1196542) (|iisqrt3| . 1196357)
 (|iiexp| . 1196169) (|iilog| . 1195981) (|iisin| . 1195793)
 (|iicos| . 1195605) (|iitan| . 1195417) (|iicot| . 1195229)
 (|iisec| . 1195041) (|iicsc| . 1194853) (|iiasin| . 1194665)
 (|iiacos| . 1194477) (|iiatan| . 1194289) (|iiacot| . 1194101)
 (|iiasec| . 1193913) (|iiacsc| . 1193725) (|iisinh| . 1193537)
 (|iicosh| . 1193349) (|iitanh| . 1193161) (|iicoth| . 1192973)
 (|iisech| . 1192785) (|iicsch| . 1192597) (|iiasinh| . 1192409)
 (|iiacosh| . 1192221) (|iiatanh| . 1192033) (|iiacoth| . 1191845)
 (|iiasech| . 1191657) (|iiacsch| . 1191469) (|specialTrigs| . 1191193)
 (|localReal?| . 1190977) (|rischNormalize| . 1190346)
 (|realElementary| . 1189422) (|validExponential| . 1188905)
 (|rootNormalize| . 1188408) (|tanQ| . 1187900) (|callForm?| . 1187807)
 (|getIdentifier| . 1187698) (|variable?| . 1187605) (|getConstant| . 1187495)
 (|type| . 1187403) (|environment| . 1187315) (|typeForm| . 1187222)
 (|irForm| . 1187112) (|elaboration| . 1186920) (|select!| . 1186548)
 (|delete!| . 1186235) (|sn| . 1186044) (|cn| . 1185853) (|dn| . 1185662)
 (|sncndn| . 1185395) (|qsetelt!| . 1184929) (|categoryFrame| . 1184884)
 (|interactiveEnv| . 1184839) (|currentEnv| . 1184794)
 (|putProperties| . 1184656) (|getProperties| . 1184521)
 (|putProperty| . 1184386) (|getProperty| . 1184244) (|scopes| . 1184153)
 (|eigenvalues| . 1183839) (|eigenvector| . 1183488)
 (|generalizedEigenvector| . 1182625) (|generalizedEigenvectors| . 1182160)
 (|eigenvectors| . 1181664) (|factorAndSplit| . 1181496) (|rightOne| . 1181371)
 (|leftOne| . 1181246) (|rightZero| . 1181121) (|leftZero| . 1180996)
 (|swap| . 1180672) (|error| . 1180155) (|minPoly| . 1179674)
 (|freeOf?| . 1179456) (|operators| . 1179344) (|tower| . 1179236)
 (|kernels| . 1179128) (|mainKernel| . 1179023) (|distribute| . 1178914)
 (|subst| . 1178437) (|multiEuclidean| . 1178331)
 (|extendedEuclidean| . 1178034) (|euclideanSize| . 1177926)
 (|sizeLess?| . 1177833) (|simplifyPower| . 1177666) (|number?| . 1177502)
 (|seriesSolve| . 1173503) (|constantToUnaryFunction| . 1173350)
 (|tubePlot| . 1171971) (|exponentialOrder| . 1171756)
 (|completeEval| . 1171321) (|lowerPolynomial| . 1170955)
 (|raisePolynomial| . 1170589) (|normalDeriv| . 1170242) (|ran| . 1169955)
 (|highCommonTerms| . 1169728) (|mapCoef| . 1169510) (|nthCoef| . 1169298)
 (|binomThmExpt| . 1169048) (|pomopo!| . 1168886) (|mapExponents| . 1168689)
 (|linearAssociatedLog| . 1168286) (|linearAssociatedOrder| . 1168086)
 (|linearAssociatedExp| . 1167876) (|createNormalElement| . 1167736)
 (|sin?| . 1167604) (|lookupFunction| . 1167517)
 (|encodingDirectory| . 1167396) (|attributeData| . 1167265)
 (|domainTemplate| . 1167174) (|lSpaceBasis| . 1166837)
 (|finiteBasis| . 1166500) (|principal?| . 1166155) (|divisor| . 1164496)
 (|rationalPoints| . 1163791) (|nonSingularModel| . 1163001)
 (|algSplitSimple| . 1162566) (|hyperelliptic| . 1161986)
 (|elliptic| . 1161133) (|integralDerivationMatrix| . 1160750)
 (|integralRepresents| . 1160443) (|integralCoordinates| . 1160101)
 (|yCoordinates| . 1159759) (|inverseIntegralMatrixAtInfinity| . 1159445)
 (|integralMatrixAtInfinity| . 1159131) (|inverseIntegralMatrix| . 1158817)
 (|integralMatrix| . 1158503) (|reduceBasisAtInfinity| . 1158199)
 (|normalizeAtInfinity| . 1157895) (|complementaryBasis| . 1157591)
 (|integral?| . 1156683) (|integralAtInfinity?| . 1156381)
 (|integralBasisAtInfinity| . 1156080) (|ramified?| . 1155478)
 (|ramifiedAtInfinity?| . 1155179) (|singular?| . 1154577)
 (|singularAtInfinity?| . 1154278) (|branchPoint?| . 1153676)
 (|branchPointAtInfinity?| . 1153377) (|rationalPoint?| . 1152707)
 (|absolutelyIrreducible?| . 1152049) (|genus| . 1151369)
 (|getZechTable| . 1150684) (|createZechTable| . 1150450)
 (|createMultiplicationTable| . 1150156)
 (|createMultiplicationMatrix| . 1149902)
 (|createLowComplexityTable| . 1149632)
 (|createLowComplexityNormalBasis| . 1149234) (|representationType| . 1149099)
 (|createPrimitiveElement| . 1149044) (|tableForDiscreteLogarithm| . 1148874)
 (|factorsOfCyclicGroupSize| . 1148695) (|sizeMultiplication| . 1147607)
 (|getMultiplicationMatrix| . 1146795) (|getMultiplicationTable| . 1145927)
 (|primitive?| . 1145625) (|numberOfIrreduciblePoly| . 1145457)
 (|numberOfPrimitivePoly| . 1145289) (|numberOfNormalPoly| . 1145121)
 (|createIrreduciblePoly| . 1144896) (|createPrimitivePoly| . 1144671)
 (|createNormalPoly| . 1144446) (|createNormalPrimitivePoly| . 1144221)
 (|createPrimitiveNormalPoly| . 1143996) (|nextIrreduciblePoly| . 1143812)
 (|nextPrimitivePoly| . 1143628) (|nextNormalPoly| . 1143444)
 (|nextNormalPrimitivePoly| . 1143260) (|nextPrimitiveNormalPoly| . 1143076)
 (|leastAffineMultiple| . 1142894) (|reducedQPowers| . 1142636)
 (|rootOfIrreduciblePoly| . 1142030) (|write!| . 1141887) (|read!| . 1141747)
 (|iomode| . 1141573) (|close!| . 1141389) (|reopen!| . 1141219)
 (|open| . 1140911) (|rightUnit| . 1140745) (|leftUnit| . 1140579)
 (|rightMinimalPolynomial| . 1140352) (|leftMinimalPolynomial| . 1140125)
 (|associatorDependence| . 1139679) (|lieAlgebra?| . 1139313)
 (|jordanAlgebra?| . 1138947) (|noncommutativeJordanAlgebra?| . 1138581)
 (|jordanAdmissible?| . 1138215) (|lieAdmissible?| . 1137849)
 (|jacobiIdentity?| . 1137483) (|powerAssociative?| . 1137332)
 (|alternative?| . 1136966) (|flexible?| . 1136600)
 (|rightAlternative?| . 1136234) (|leftAlternative?| . 1135868)
 (|antiAssociative?| . 1135502) (|associative?| . 1135136)
 (|antiCommutative?| . 1134770) (|commutative?| . 1134404)
 (|rightCharacteristicPolynomial| . 1134221)
 (|leftCharacteristicPolynomial| . 1134038) (|rightNorm| . 1133912)
 (|leftNorm| . 1133786) (|rightTrace| . 1133660) (|leftTrace| . 1133534)
 (|someBasis| . 1133381) (|find| . 1133230) (|count| . 1132868)
 (|every?| . 1132688) (|any?| . 1132508) (|sort!| . 1132095)
 (|copyInto!| . 1131891) (|sorted?| . 1131531) (|LiePoly| . 1131345)
 (|quickSort| . 1131040) (|heapSort| . 1130735) (|shellSort| . 1130430)
 (|outputSpacing| . 1130309) (|outputGeneral| . 1130120)
 (|outputFixed| . 1129931) (|outputFloating| . 1129742) (|exp1| . 1129661)
 (|log10| . 1129537) (|log2| . 1129413) (|rationalApproximation| . 1128827)
 (|relerror| . 1128748) (|complexSolve| . 1127579) (|complexRoots| . 1127020)
 (|realRoots| . 1126516) (|leadingTerm| . 1126322) (|overlap| . 1126134)
 (|hcrf| . 1126022) (|hclf| . 1125910) (|writable?| . 1125819)
 (|readable?| . 1125728) (|exists?| . 1125637) (|extension| . 1125547)
 (|directory| . 1125457) (|filename| . 1125361) (|shallowExpand| . 1125120)
 (|deepExpand| . 1124879) (|fracPart| . 1124520) (|polyPart| . 1124313)
 (|fullPartialFraction| . 1124067) (|primeFrobenius| . 1123882)
 (|discreteLog| . 1123644) (|decreasePrecision| . 1123456)
 (|increasePrecision| . 1123268) (|precision| . 1123004) (|bits| . 1122616)
 (|mantissa| . 1122522) (|unitNormalize| . 1122429) (|unit| . 1122084)
 (|flagFactor| . 1121888) (|sqfrFactor| . 1121757) (|primeFactor| . 1121626)
 (|nthFlag| . 1121433) (|nthExponent| . 1121302)
 (|irreducibleFactor| . 1121171) (|factors| . 1120598) (|nilFactor| . 1120467)
 (|regularRepresentation| . 1120007) (|traceMatrix| . 1119298)
 (|randomLC| . 1118908) (|minimize| . 1118576) (|module| . 1117840)
 (|rightRegularRepresentation| . 1117494)
 (|leftRegularRepresentation| . 1117148) (|rightTraceMatrix| . 1116599)
 (|leftTraceMatrix| . 1116050) (|rightDiscriminant| . 1115591)
 (|leftDiscriminant| . 1115132) (|represents| . 1113895)
 (|mergeFactors| . 1113743) (|isMult| . 1113506) (|applyQuote| . 1112791)
 (|ground| . 1112536) (|ground?| . 1112218) (|exprToXXP| . 1111428)
 (|exprToUPS| . 1110151) (|exprToGenUPS| . 1108874) (|localAbs| . 1107467)
 (|universe| . 1107332) (|complement| . 1107194) (|cardinality| . 1107039)
 (|internalIntegrate0| . 1106486) (|makeCos| . 1106212) (|makeSin| . 1105938)
 (|iiGamma| . 1105772) (|iiabs| . 1105606) (|bringDown| . 1105038)
 (|newReduc| . 1104822) (|logical?| . 1104732) (|character?| . 1104642)
 (|doubleComplex?| . 1104552) (|complex?| . 1104462) (|double?| . 1104372)
 (|ffactor| . 1104066) (|qfactor| . 1103690) (|UP2ifCan| . 1103205)
 (|anfactor| . 1102778) (|fortranCharacter| . 1102733)
 (|fortranDoubleComplex| . 1102688) (|fortranComplex| . 1102643)
 (|fortranLogical| . 1102598) (|fortranInteger| . 1102553)
 (|fortranDouble| . 1102508) (|fortranReal| . 1102463) (|external?| . 1102381)
 (|dimensionsOf| . 1102266) (|scalarTypeOf| . 1102120) (|makeFR| . 1101507)
 (|musserTrials| . 1101148) (|stopMusserTrials| . 1100789)
 (|numberOfFactors| . 1100384) (|modularFactor| . 1100158)
 (|useSingleFactorBound?| . 1099994) (|useSingleFactorBound| . 1099827)
 (|useEisensteinCriterion?| . 1099663) (|useEisensteinCriterion| . 1099496)
 (|eisensteinIrreducible?| . 1099329) (|tryFunctionalDecomposition?| . 1099165)
 (|tryFunctionalDecomposition| . 1098998) (|btwFact| . 1098507)
 (|beauzamyBound| . 1098063) (|bombieriNorm| . 1097194) (|rootBound| . 1096750)
 (|singleFactorBound| . 1095815) (|quadraticNorm| . 1095399)
 (|infinityNorm| . 1094983) (|scaleRoots| . 1094804) (|shiftRoots| . 1094625)
 (|degreePartition| . 1094072) (|factorOfDegree| . 1092565)
 (|factorsOfDegree| . 1092283) (|pascalTriangle| . 1092111)
 (|rangePascalTriangle| . 1091834) (|sizePascalTriangle| . 1091696)
 (|fillPascalTriangle| . 1091572) (|safeCeiling| . 1091400)
 (|safeFloor| . 1091228) (|safetyMargin| . 1090853) (|sumSquares| . 1090701)
 (|euclideanNormalForm| . 1090382) (|euclideanGroebner| . 1089375)
 (|factorGroebnerBasis| . 1088557) (|groebnerFactorize| . 1086917)
 (|credPol| . 1086610) (|redPol| . 1086303) (|gbasis| . 1085965)
 (|critT| . 1085545) (|critM| . 1085245) (|critB| . 1084939)
 (|critBonD| . 1084532) (|critMTonD1| . 1084128) (|critMonD1| . 1083721)
 (|redPo| . 1083348) (|hMonic| . 1083079) (|updatF| . 1082679)
 (|sPol| . 1082290) (|updatD| . 1081883) (|minGbasis| . 1081579)
 (|lepol| . 1081282) (|prinshINFO| . 1080988) (|prindINFO| . 1080528)
 (|fprindINFO| . 1080065) (|prinpolINFO| . 1079736) (|prinb| . 1079414)
 (|critpOrder| . 1078991) (|makeCrit| . 1078484) (|virtualDegree| . 1078176)
 (|lcm| . 1078045) (|conditionsForIdempotents| . 1076674)
 (|genericRightDiscriminant| . 1076328) (|genericRightTraceForm| . 1075976)
 (|genericLeftDiscriminant| . 1075630) (|genericLeftTraceForm| . 1075278)
 (|genericRightNorm| . 1074929) (|genericRightTrace| . 1074580)
 (|genericRightMinimalPolynomial| . 1074216) (|rightRankPolynomial| . 1073387)
 (|genericLeftNorm| . 1073038) (|genericLeftTrace| . 1072689)
 (|genericLeftMinimalPolynomial| . 1072325) (|leftRankPolynomial| . 1071496)
 (|generic| . 1069632) (|rightUnits| . 1069003) (|leftUnits| . 1068374)
 (|compBound| . 1068122) (|tablePow| . 1067834) (|solveid| . 1067588)
 (|testModulus| . 1067354) (|HenselLift| . 1067012)
 (|completeHensel| . 1066755) (|multMonom| . 1066170) (|build| . 1065585)
 (|leadingIndex| . 1065006) (|leadingExponent| . 1064427)
 (|GospersMethod| . 1063839) (|nextSubsetGray| . 1063690)
 (|firstSubsetGray| . 1063537) (|clipPointsDefault| . 1063364)
 (|drawToScale| . 1063191) (|adaptive| . 1062798) (|figureUnits| . 1062628)
 (|putColorInfo| . 1062466) (|appendPoint| . 1062334) (|component| . 1061773)
 (|ranges| . 1061280) (|pointLists| . 1061158) (|makeGraphImage| . 1060498)
 (|graphImage| . 1060454) (|groebSolve| . 1060044) (|testDim| . 1059718)
 (|genericPosition| . 1059237) (|lfunc| . 1059152) (|inHallBasis?| . 1059026)
 (|reorder| . 1058262) (|parameters| . 1058061) (|headAst| . 1057926)
 (|heap| . 1057806) (|gcdprim| . 1057654) (|gcdcofact| . 1057495)
 (|gcdcofactprim| . 1057336) (|lintgcd| . 1057149) (|hex| . 1057036)
 (|host| . 1056958) (|trueEqual| . 1056862) (|factorList| . 1056230)
 (|listConjugateBases| . 1055619) (|matrixGcd| . 1055157)
 (|divideIfCan!| . 1054703) (|leastPower| . 1054274) (|idealiser| . 1053433)
 (|idealiserMatrix| . 1053013) (|moduleSum| . 1052524)
 (|mapUnivariate| . 1051788) (|mapUnivariateIfCan| . 1051410)
 (|mapMatrixIfCan| . 1050988) (|mapBivariate| . 1050580)
 (|fullDisplay| . 1049666) (|relationsIdeal| . 1049188) (|saturate| . 1048637)
 (|groebner?| . 1048351) (|groebnerIdeal| . 1048058) (|ideal| . 1047043)
 (|leadingIdeal| . 1046785) (|backOldPos| . 1046388)
 (|generalPosition| . 1045932) (|quotient| . 1045412) (|zeroDim?| . 1044804)
 (|inRadical?| . 1044515) (|in?| . 1044226) (|element?| . 1043937)
 (|zeroDimPrime?| . 1043352) (|zeroDimPrimary?| . 1042767)
 (|radical| . 1042213) (|primaryDecomp| . 1041178) (|contract| . 1040149)
 (|gensym| . 1040105) (|leadingSupport| . 1039951) (|combineWithIf| . 1039688)
 (|term| . 1039543) (|shrinkable| . 1039256) (|physicalLength!| . 1038972)
 (|physicalLength| . 1038663) (|flexibleArray| . 1038376)
 (|elseBranch| . 1038300) (|thenBranch| . 1038224)
 (|generalizedInverse| . 1037938) (|imports| . 1037847) (|sequence| . 1037771)
 (|readBytes!| . 1037628) (|readUInt32!| . 1037521) (|readInt32!| . 1037415)
 (|readUInt16!| . 1037308) (|readInt16!| . 1037202) (|readUInt8!| . 1037096)
 (|readInt8!| . 1036991) (|readByte!| . 1036886) (|setFieldInfo| . 1036624)
 (|pol| . 1036410) (|xn| . 1036180) (|dAndcExp| . 1035930) (|repSq| . 1035724)
 (|expPot| . 1035520) (|qPot| . 1035325) (|lookup| . 1035038)
 (|normal?| . 1034462) (|basis| . 1032620) (|normalElement| . 1032282)
 (|minimalPolynomial| . 1031453) (|position!| . 1031356) (|eof?| . 1031268)
 (|inputBinaryFile| . 1031094) (|increment| . 1030926)
 (|incrementBy| . 1030755) (|charpol| . 1030460) (|solve1| . 1030164)
 (|innerEigenvectors| . 1029606) (|compile| . 1029476) (|declare| . 1029349)
 (|parseString| . 1029270) (|unparse| . 1029191) (|flatten| . 1029145)
 (|lambda| . 1029052) (|binary| . 1028850) (|packageCall| . 1028692)
 (|interpret| . 1028487) (|innerSolve1| . 1027895) (|innerSolve| . 1027539)
 (|makeEq| . 1027185) (|modularGcdPrimitive| . 1026893)
 (|modularGcd| . 1026601) (|reduction| . 1025994) (|signAround| . 1025219)
 (|invmod| . 1025158) (|powmod| . 1025094) (|mulmod| . 1025030)
 (|submod| . 1024966) (|addmod| . 1024902) (|mask| . 1024844) (|dec| . 1024786)
 (|inc| . 1024728) (|symmetricRemainder| . 1024667)
 (|positiveRemainder| . 1024606) (|bit?| . 1024509) (|algint| . 1024036)
 (|algintegrate| . 1023433) (|palgintegrate| . 1022830)
 (|palginfieldint| . 1022360) (|bitLength| . 1022278) (|bitCoef| . 1022191)
 (|bitTruth| . 1022069) (|contains?| . 1021822) (|inf| . 1021613)
 (|qinterval| . 1021401) (|interval| . 1020727) (|unit?| . 1020638)
 (|associates?| . 1020546) (|unitCanonical| . 1020493) (|unitNormal| . 1020337)
 (|lfextendedint| . 1019766) (|lflimitedint| . 1019071)
 (|lfinfieldint| . 1018569) (|lfintegrate| . 1017993) (|lfextlimint| . 1017347)
 (|BasicMethod| . 1017184) (|PollardSmallFactor| . 1017054)
 (|palgint0| . 1015722) (|palgextint0| . 1014408) (|palglimint0| . 1012846)
 (|palgRDE0| . 1011520) (|palgLODE0| . 1009876) (|chineseRemainder| . 1008807)
 (|divisors| . 1008655) (|eulerPhi| . 1008547) (|fibonacci| . 1008439)
 (|harmonic| . 1008283) (|jacobi| . 1008172) (|moebiusMu| . 1008064)
 (|numberOfDivisors| . 1007956) (|sumOfDivisors| . 1007848)
 (|sumOfKthPowerDivisors| . 1007698) (|HermiteIntegrate| . 1006854)
 (|palgint| . 1006254) (|palgextint| . 1005659) (|palglimint| . 1004940)
 (|palgRDE| . 1004335) (|palgLODE| . 1003548) (|splitConstant| . 1003001)
 (|pmComplexintegrate| . 1002305) (|pmintegrate| . 1000939)
 (|infieldint| . 1000632) (|extendedint| . 1000232) (|limitedint| . 999716)
 (|integerIfCan| . 999567) (|internalIntegrate| . 998618)
 (|infieldIntegrate| . 998306) (|limitedIntegrate| . 997770)
 (|extendedIntegrate| . 997339) (|varselect| . 997116) (|kmax| . 996893)
 (|ksec| . 996630) (|vark| . 996372) (|removeConstantTerm| . 996144)
 (|mkPrim| . 995865) (|intPatternMatch| . 995089) (|primintegrate| . 994583)
 (|expintegrate| . 994054) (|tanintegrate| . 993577)
 (|primextendedint| . 993020) (|expextendedint| . 992440)
 (|primlimitedint| . 991775) (|explimitedint| . 991091)
 (|primextintfrac| . 990752) (|primlimintfrac| . 990297)
 (|primintfldpoly| . 990005) (|expintfldpoly| . 989653)
 (|monomialIntegrate| . 989245) (|monomialIntPoly| . 988957)
 (|inverseLaplace| . 988371) (|inputOutputBinaryFile| . 988185)
 (|closed| . 988145) (|bothWays| . 988105) (|input| . 987797)
 (|resolve| . 987665) (|bytes| . 987562) (|ip4Address| . 987482)
 (|iprint| . 987358) (|elem?| . 987230) (|notelem| . 987056)
 (|logpart| . 986745) (|ratpart| . 986652) (|mkAnswer| . 986257)
 (|irDef| . 986105) (|irCtor| . 985956) (|irVar| . 985807)
 (|perfectNthPower?| . 985621) (|perfectNthRoot| . 985265)
 (|approxNthRoot| . 985107) (|perfectSquare?| . 984970)
 (|perfectSqrt| . 984855) (|approxSqrt| . 984746)
 (|generateIrredPoly| . 984525) (|complexExpand| . 983710)
 (|complexIntegrate| . 982788)
 (|dimensionOfIrreducibleRepresentation| . 982626)
 (|irreducibleRepresentation| . 982009) (|checkRur| . 981505)
 (|cAcsch| . 981329) (|cAsech| . 981153) (|cAcoth| . 980977)
 (|cAtanh| . 980801) (|cAcosh| . 980625) (|cAsinh| . 980449) (|cCsch| . 980273)
 (|cSech| . 980097) (|cCoth| . 979921) (|cTanh| . 979745) (|cCosh| . 979569)
 (|cSinh| . 979393) (|cAcsc| . 979217) (|cAsec| . 979041) (|cAcot| . 978865)
 (|cAtan| . 978689) (|cAcos| . 978513) (|cAsin| . 978337) (|cCsc| . 978161)
 (|cSec| . 977985) (|cCot| . 977809) (|cTan| . 977633) (|cCos| . 977457)
 (|cSin| . 977281) (|cLog| . 977105) (|cExp| . 976929)
 (|cRationalPower| . 976731) (|cPower| . 976552)
 (|seriesToOutputForm| . 976169) (|iCompose| . 976052)
 (|taylorQuoByVar| . 975938) (|iExquo| . 975781) (|getStream| . 975587)
 (|getRef| . 975402) (|makeSeries| . 975134) (|mappingMode| . 975017)
 (|categoryMode| . 974967) (|voidMode| . 974917) (|noValueMode| . 974867)
 (|jokerMode| . 974817) (GF2FG . 974289) (FG2F . 973799) (F2FG . 973309)
 (|explogs2trigs| . 972788) (|trigs2explogs| . 972203) (|swap!| . 971972)
 (|fill!| . 971550) (|minIndex| . 971382) (|maxIndex| . 971214)
 (|entry?| . 970961) (|indices| . 970791) (|index?| . 970618)
 (|entries| . 970448) (|categories| . 970216) (|jvmInterface| . 970164)
 (|jvmSuper| . 970112) (|jvmNameAndTypeConstantTag| . 970064)
 (|jvmInterfaceMethodConstantTag| . 970016)
 (|jvmMethodrefConstantTag| . 969968) (|jvmFieldrefConstantTag| . 969920)
 (|jvmStringConstantTag| . 969872) (|jvmClassConstantTag| . 969824)
 (|jvmDoubleConstantTag| . 969776) (|jvmLongConstantTag| . 969728)
 (|jvmFloatConstantTag| . 969680) (|jvmIntegerConstantTag| . 969632)
 (|jvmUTF8ConstantTag| . 969584) (|jvmTransient| . 969536)
 (|jvmVolatile| . 969488) (|jvmStrict| . 969439) (|jvmAbstract| . 969340)
 (|jvmNative| . 969291) (|jvmSynchronized| . 969242) (|jvmFinal| . 969097)
 (|jvmStatic| . 969002) (|jvmProtected| . 968907) (|jvmPrivate| . 968812)
 (|jvmPublic| . 968667) (|search| . 968515) (|keys| . 968337) (|key?| . 968156)
 (|symbolIfCan| . 968028) (|kernel| . 967463) (|argument| . 967070)
 (|constantKernel| . 966898) (|constantIfCan| . 966717) (|kovacic| . 965761)
 (|unknown| . 965707) (|laplace| . 965155) (|trailingCoefficient| . 964982)
 (|normalizeIfCan| . 964527) (|polCase| . 964143) (|distFact| . 963400)
 (|identification| . 963059) (|LyndonCoordinates| . 962706)
 (|LyndonBasis| . 962332) (|zeroDimensional?| . 961840) (|fglmIfCan| . 961399)
 (|groebner| . 959762) (|lexTriangular| . 959436)
 (|squareFreeLexTriangular| . 958639) (|belong?| . 956851) (|erf| . 956513)
 (|dilog| . 956175) (|li| . 955837) (|Ci| . 955499) (|Si| . 955161)
 (|Ei| . 954823) (|linGenPos| . 954447) (|groebgen| . 954066)
 (|totolex| . 953766) (|minPol| . 953063) (|computeBasis| . 952835)
 (|coord| . 952158) (|anticoord| . 951825) (|intcompBasis| . 951545)
 (|choosemon| . 951257) (|transform| . 950970) (|pack!| . 950824)
 (|library| . 950745) (|complexLimit| . 949606) (|limit| . 946780)
 (|linearlyDependent?| . 946529) (|linearDependence| . 946278)
 (|solveLinear| . 945692) (|linearElement| . 945524) (|reducedSystem| . 945079)
 (|leftReducedSystem| . 944664) (|linearForm| . 944506)
 (|setDifference| . 944383) (|setIntersection| . 944260) (|setUnion| . 944137)
 (|append| . 944057) (|null| . 943943) (|nil| . 943869) (|substitute| . 943755)
 (|duplicates?| . 943619) (|mapGen| . 942914) (|mapExpon| . 942372)
 (|commutativeEquality| . 942173) (|plus| . 941830) (|leftMult| . 941659)
 (|rightMult| . 941488) (|makeUnit| . 941323) (|reverse!| . 940903)
 (|reverse| . 940458) (|nthFactor| . 939655) (|nthExpon| . 939145)
 (|makeMulti| . 938911) (|makeTerm| . 938740) (|listOfMonoms| . 938499)
 (|insert| . 938235) (|delete| . 937956) (|symmetricSquare| . 937802)
 (|factor1| . 937190) (|symmetricProduct| . 936796) (|symmetricPower| . 936310)
 (|directSum| . 935916) (|\\/| . 935869) (|/\\| . 935822) (~ . 935778)
 (|solveLinearPolynomialEquationByFractions| . 935510)
 (|hasSolution?| . 934805) (|linSolve| . 934284) (|LyndonWordsList| . 934062)
 (|LyndonWordsList1| . 933816) (|lyndonIfCan| . 933671) (|lyndon| . 933532)
 (|lyndon?| . 933358) (|numberOfComputedEntries| . 933216) (|rst| . 933113)
 (|frst| . 933010) (|lazyEvaluate| . 932907) (|lazy?| . 932776)
 (|explicitlyEmpty?| . 932645) (|explicitEntries?| . 932514) (|iter| . 932311)
 (|arg1| . 932154) (|arg2| . 931997) (|comp| . 931718) (|mappingAst| . 931588)
 (|nullary| . 931453) (|fixedPoint| . 931093) (|id| . 930989)
 (|recur| . 930597) (|const| . 930415) (|curry| . 930199) (|diag| . 929980)
 (|curryRight| . 929714) (|curryLeft| . 929448) (|constantRight| . 929185)
 (|constantLeft| . 928922) (|twist| . 928656) (|setsubMatrix!| . 928407)
 (|subMatrix| . 928155) (|swapColumns!| . 927909) (|swapRows!| . 927663)
 (|vertConcat| . 927455) (|horizConcat| . 927247) (|squareTop| . 927042)
 (|elRow1!| . 926717) (|elRow2!| . 926389) (|elColumn2!| . 926061)
 (|fractionFreeGauss!| . 925726) (|invertIfCan| . 925401) (|copy!| . 925254)
 (|plus!| . 925104) (|minus!| . 924809) (|leftScalarTimes!| . 924659)
 (|rightScalarTimes!| . 924509) (|times!| . 924359) (|power!| . 924157)
 (|nothing| . 924082) (|just| . 924004) (|duplicates| . 923784)
 (|removeDuplicates!| . 923539) (|linears| . 923361) (|ddFact| . 923104)
 (|separateFactors| . 922513) (|exptMod| . 922095) (|meshPar2Var| . 920953)
 (|meshFun2Var| . 920489) (|meshPar1Var| . 920122) (|ptFunc| . 919741)
 (|rowEch| . 919590) (|rowEchLocal| . 919436) (|rowEchelonLocal| . 919279)
 (|normalizedDivide| . 918668) (|binaryFunction| . 918362)
 (|makeFloatFunction| . 917869) (|function| . 917104) (|makeRecord| . 916911)
 (|unaryFunction| . 916646) (|compiledFunction| . 916068) (|corrPoly| . 915482)
 (|lifting| . 914872) (|lifting1| . 914122) (|exprex| . 914000)
 (|coerceL| . 913878) (|coerceS| . 913756) (|frobenius| . 913560)
 (|computePowers| . 913348) (|pow| . 913136) (|An| . 912952)
 (|UnVectorise| . 912768) (|Vectorise| . 912584) (|setPoly| . 912437)
 (|index| . 911685) (|exponent| . 910925) (|exQuo| . 909911)
 (|moebius| . 909810) (|rightRecip| . 909581) (|leftRecip| . 909352)
 (|leftPower| . 909154) (|rightPower| . 908956)
 (|derivationCoordinates| . 908642) (|generator| . 907459) (|one?| . 906936)
 (|monoidOperation| . 906794) (|neutralValue| . 906683)
 (|splitSquarefree| . 906347) (|normalDenom| . 906102) (|reshape| . 905291)
 (|totalfract| . 904666) (|pushdterm| . 904083) (|pushucoef| . 903485)
 (|pushuconst| . 902997) (|numberOfMonomials| . 902452) (|unique| . 902327)
 (|multiset| . 902029) (|systemCommand| . 901907) (|mergeDifference| . 901778)
 (|squareFreePrim| . 901472) (|compdegd| . 901042) (|univcase| . 900733)
 (|consnewpol| . 900156) (|nsqfree| . 899464) (|intChoose| . 898668)
 (|coefChoose| . 898331) (|myDegree| . 897865) (|normDeriv2| . 897503)
 (|plenaryPower| . 897341) (|antiCommutator| . 897282) (|commutator| . 897178)
 (|associator| . 897116) (|complexEigenvalues| . 896861)
 (|complexEigenvectors| . 896465) (|isConnected?| . 896327)
 (|connectTo| . 895952) (|shift| . 895539) (|normalizedAssociate| . 895188)
 (|normalize| . 893800) (|outputArgs| . 893384) (|normInvertible?| . 892941)
 (|normFactors| . 892554) (|npcoef| . 891715) (|listexp| . 891345)
 (|characteristicPolynomial| . 889198) (|realEigenvalues| . 888970)
 (|realEigenvectors| . 888613) (|halfExtendedResultant2| . 888343)
 (|halfExtendedResultant1| . 888073) (|extendedResultant| . 887768)
 (|subResultantsChain| . 887548) (|lazyPseudoQuotient| . 887434)
 (|lazyPseudoRemainder| . 887320) (|bernoulliB| . 887082) (|eulerE| . 886844)
 (|numeric| . 885125) (|complexNumeric| . 881083) (|numericIfCan| . 879650)
 (|complexNumericIfCan| . 876449) (|FormatArabic| . 876321)
 (|ScanArabic| . 876193) (|FormatRoman| . 876065) (|ScanRoman| . 875937)
 (|ScanFloatIgnoreSpaces| . 875819) (|ScanFloatIgnoreSpacesIfCan| . 875695)
 (|rk4| . 875077) (|rk4a| . 874764) (|rk4qc| . 873897) (|rk4f| . 873590)
 (|aromberg| . 873248) (|asimpson| . 872906) (|atrapezoidal| . 872564)
 (|romberg| . 872225) (|simpson| . 871886) (|trapezoidal| . 871547)
 (|rombergo| . 871208) (|simpsono| . 870869) (|trapezoidalo| . 870530)
 (|sup| . 870258) (|inv| . 868984) (|imagE| . 868873) (|imagk| . 868762)
 (|imagj| . 868651) (|imagi| . 868540) (|octon| . 868272)
 (|constDsolve| . 867556) (|expint| . 867009) (|diff| . 866424)
 (|algDsolve| . 865740) (|denomLODE| . 864727) (|indicialEquations| . 862543)
 (|indicialEquation| . 861543) (|denomRicDE| . 861042)
 (|leadingCoefficientRicDE| . 860478) (|constantCoefficientRicDE| . 859847)
 (|changeVar| . 858887) (|ratDsolve| . 856599)
 (|indicialEquationAtInfinity| . 855775) (|reduceLODE| . 855310)
 (|singRicDE| . 853798) (|polyRicDE| . 852370) (|ricDsolve| . 848072)
 (|triangulate| . 847226) (|solveInField| . 846117)
 (|wronskianMatrix| . 845616) (|variationOfParameters| . 845381)
 (|lexico| . 844992) (|po| . 844820) (|op| . 844648) (|infinity| . 844438)
 (|makeop| . 844106) (|opeval| . 843802) (|evaluateInverse| . 843505)
 (|evaluate| . 842433) (|conjug| . 842127) (|adjoint| . 840984)
 (|arity| . 840851) (|getDatabase| . 840714) (|whatInfinity| . 840567)
 (|infinite?| . 840300) (|finite?| . 839948) (|minusInfinity| . 839740)
 (|plusInfinity| . 839532) (|pureLex| . 839309) (|totalLex| . 839086)
 (|reverseLex| . 838863) (|min| . 838333) (|leftLcm| . 838013)
 (|rightExtendedGcd| . 837769) (|rightGcd| . 837622)
 (|rightExactQuotient| . 837469) (|rightRemainder| . 837322)
 (|rightQuotient| . 837175) (|rightLcm| . 837028) (|leftExtendedGcd| . 836784)
 (|leftGcd| . 836464) (|leftExactQuotient| . 836136) (|leftRemainder| . 835816)
 (|leftQuotient| . 835496) (|times| . 835225) (|apply| . 834408)
 (|monicLeftDivide| . 833833) (|monicRightDivide| . 833258)
 (|leftDivide| . 832453) (|rightDivide| . 831896) (|hermiteH| . 831725)
 (|laguerreL| . 831382) (|legendreP| . 831149) (|outputList| . 831026)
 (|writeBytes!| . 830882) (|writeUInt8!| . 830746) (|writeInt8!| . 830612)
 (|writeByte!| . 830478) (|isOpen?| . 830211) (|outputBinaryFile| . 830035)
 (|not| . 829939) (|or| . 829837) (|and| . 829735) (|quo| . 829574)
 (|rem| . 829413) (|div| . 829163) (>= . 829026) (> . 828889) (~= . 828754)
 (|blankSeparate| . 828659) (|semicolonSeparate| . 828564)
 (|commaSeparate| . 828469) (|pile| . 828374) (|paren| . 828094)
 (|bracket| . 827954) (|prod| . 827808) (|overlabel| . 827758)
 (|overbar| . 827711) (|prime| . 827569) (|quote| . 827481)
 (|supersub| . 827383) (|presuper| . 827333) (|presub| . 827283)
 (|super| . 827233) (|sub| . 827183) (|rarrow| . 827133) (|assign| . 827083)
 (|slash| . 827033) (|over| . 826983) (|zag| . 826933) (|box| . 826746)
 (|label| . 826696) (|infix?| . 826615) (|postfix| . 826565) (|infix| . 826416)
 (|prefix| . 826318) (|vconcat| . 826175) (|hconcat| . 826032)
 (|rspace| . 825946) (|vspace| . 825865) (|hspace| . 825784)
 (|superHeight| . 825703) (|subHeight| . 825622) (|height| . 824676)
 (|width| . 824312) (|doubleFloatFormat| . 824232) (|messagePrint| . 824118)
 (|message| . 824038) (|members| . 823802) (|padecf| . 823483)
 (|pade| . 822524) (|root| . 822257) (|quotientByP| . 822195)
 (|moduloP| . 822090) (|modulus| . 820814) (|digits| . 820123)
 (|continuedFraction| . 819114) (|pair| . 818995) (|light| . 818919)
 (|pastel| . 818843) (|bright| . 818547) (|dim| . 818471) (|dark| . 818395)
 (|getSyntaxFormsFromFile| . 818274) (|surface| . 818176)
 (|coordinate| . 817751) (|conjugates| . 817618) (|shuffle| . 817446)
 (|shufflein| . 817274) (|sequences| . 816935) (|permutations| . 816775)
 (|lists| . 816519) (|makeResult| . 816215) (|is?| . 814997) (|Is| . 813629)
 (|addMatchRestricted| . 813438) (|insertMatch| . 813250) (|addMatch| . 813062)
 (|getMatch| . 812875) (|failed| . 812535) (|failed?| . 812133)
 (|optpair| . 811991) (|getBadValues| . 811862) (|resetBadValues| . 811773)
 (|hasTopPredicate?| . 811649) (|topPredicate| . 811470)
 (|setTopPredicate| . 811308) (|patternVariable| . 811148)
 (|withPredicates| . 811016) (|setPredicates| . 810884) (|predicates| . 810755)
 (|hasPredicate?| . 810631) (|optional?| . 810507) (|multiple?| . 810383)
 (|generic?| . 810259) (|quoted?| . 810135) (|inR?| . 810011)
 (|isList| . 809869) (|isQuotient| . 809691) (|isOp| . 809296)
 (|Zero| . 808974) (|satisfy?| . 808315) (|addBadValue| . 808024)
 (|badValues| . 807822) (|retractable?| . 806934) (|ListOfTerms| . 806183)
 (|One| . 805706) (|leftFactor| . 805531) (|rightFactorCandidate| . 805319)
 (D . 803987) (|ptree| . 803800) (|coerceImages| . 803672)
 (|fixedPoints| . 803516) (|odd?| . 803153) (|even?| . 802790)
 (|numberOfCycles| . 802651) (|cyclePartition| . 802521)
 (|coerceListOfPairs| . 802384) (|coercePreimagesImages| . 802247)
 (|listRepresentation| . 802062) (|permanent| . 801746) (|cycles| . 801599)
 (|cycle| . 801461) (|initializeGroupForWordProblem| . 801162) (<= . 800891)
 (< . 800481) (|support| . 800214) (|wordInGenerators| . 800016)
 (|wordInStrongGenerators| . 799818) (|orbits| . 799671) (|orbit| . 799060)
 (|permutationGroup| . 798904) (|wordsForStrongGenerators| . 798735)
 (|strongGenerators| . 798579) (|base| . 798214) (|generators| . 797774)
 (|bivariateSLPEBR| . 797357)
 (|solveLinearPolynomialEquationByRecursion| . 796608)
 (|factorByRecursion| . 795837) (|factorSquareFreeByRecursion| . 795066)
 (|randomR| . 794265) (|factorSFBRlcUnit| . 793463) (|charthRoot| . 793147)
 (|conditionP| . 792809) (|solveLinearPolynomialEquation| . 791771)
 (|factorSquareFreePolynomial| . 791566) (|factorPolynomial| . 791061)
 (|squareFreePolynomial| . 790556) (|gcdPolynomial| . 789951)
 (|torsion?| . 788969) (|torsionIfCan| . 787955) (|getGoodPrime| . 787654)
 (|badNum| . 787086) (|mix| . 786748) (|doubleDisc| . 786490)
 (|polyred| . 786263) (|padicFraction| . 786155) (|padicallyExpand| . 785987)
 (|numberOfFractionalTerms| . 785851) (|nthFractionalTerm| . 785712)
 (|firstNumer| . 785604) (|firstDenom| . 785464) (|compactFraction| . 785356)
 (|partialFraction| . 784656) (|gcdPrimitive| . 783767)
 (|symmetricGroup| . 783432) (|alternatingGroup| . 783097)
 (|abelianGroup| . 782920) (|cyclicGroup| . 782585) (|dihedralGroup| . 782250)
 (|mathieu11| . 781961) (|mathieu12| . 781672) (|mathieu22| . 781383)
 (|mathieu23| . 781094) (|mathieu24| . 780805) (|janko2| . 780516)
 (|rubiksGroup| . 780394) (|youngGroup| . 780065) (|lexGroebner| . 779877)
 (|totalGroebner| . 779689) (|expressIdealMember| . 779546)
 (|principalIdeal| . 779364) (|LagrangeInterpolation| . 779153)
 (|psolve| . 770580) (|wrregime| . 769750) (|rdregime| . 768864)
 (|bsolve| . 767612) (|dmp2rfi| . 766321) (|se2rfi| . 765868)
 (|pr2dmp| . 765480) (|hasoln| . 764968) (|ParCondList| . 764142)
 (|redpps| . 763584) (|B1solve| . 762760) (|factorset| . 762378)
 (|maxrank| . 761676) (|minrank| . 760974) (|minset| . 760583)
 (|nextSublist| . 760145) (|overset?| . 759688) (|ParCond| . 759100)
 (|redmat| . 758685) (|regime| . 757578) (|sqfree| . 757231)
 (|inconsistent?| . 756384) (|debug| . 756309) (|numFunEvals| . 756237)
 (|setAdaptive| . 756162) (|adaptive?| . 756090)
 (|setScreenResolution| . 756015) (|screenResolution| . 755772)
 (|setMaxPoints| . 755697) (|maxPoints| . 755454) (|setMinPoints| . 755379)
 (|minPoints| . 755136) (|parametric?| . 755061) (|plotPolar| . 754379)
 (|debug3D| . 754302) (|numFunEvals3D| . 754228) (|setAdaptive3D| . 754151)
 (|adaptive3D?| . 754077) (|setScreenResolution3D| . 754000)
 (|screenResolution3D| . 753926) (|setMaxPoints3D| . 753849)
 (|maxPoints3D| . 753775) (|setMinPoints3D| . 753698) (|minPoints3D| . 753624)
 (|tValues| . 753516) (|tRange| . 753330) (|plot| . 751328)
 (|pointPlot| . 750623) (|calcRanges| . 750442) (|assert| . 749974)
 (|optional| . 749671) (|multiple| . 749368) (|fixPredicate| . 749033)
 (|patternMatch| . 744310) (|patternMatchTimes| . 743791)
 (|bernoulli| . 743447) (|chebyshevT| . 743101) (|chebyshevU| . 742755)
 (|cyclotomic| . 742233) (|euler| . 741937) (|fixedDivisor| . 741760)
 (|laguerre| . 741583) (|legendre| . 741284) (|dmpToHdmp| . 741012)
 (|hdmpToDmp| . 740740) (|pToHdmp| . 740501) (|hdmpToP| . 740262)
 (|dmpToP| . 740034) (|pToDmp| . 739806) (|sylvesterSequence| . 739598)
 (|sturmSequence| . 739393) (|boundOfCauchy| . 739182)
 (|sturmVariationsOf| . 738897) (|lazyVariations| . 738571)
 (|content| . 737812) (|primitiveMonomials| . 737590) (|totalDegree| . 737074)
 (|minimumDegree| . 736098) (|monomials| . 735541) (|isPlus| . 734461)
 (|isTimes| . 733388) (|isExpt| . 731557) (|isPower| . 730583)
 (|rroot| . 729880) (|qroot| . 729129) (|froot| . 728387) (|nthr| . 727675)
 (|port| . 727586) (|firstUncouplingMatrix| . 727312) (|integral| . 726202)
 (|primitiveElement| . 723931) (|nextPrime| . 723814) (|prevPrime| . 723697)
 (|primes| . 723549) (|print| . 723353) (|selectsecond| . 723220)
 (|selectfirst| . 723087) (|makeprod| . 722951) (|property| . 722569)
 (|disjunction| . 722457) (|conjunction| . 722345) (|isEquiv| . 722159)
 (|isImplies| . 721973) (|isOr| . 721787) (|isAnd| . 721601) (|isNot| . 721431)
 (|isAtom| . 721293) (|atoms| . 720842) (|dual| . 720410) (|equiv| . 720350)
 (|implies| . 720290) (|false| . 720236) (|true| . 720182) (|merge!| . 719758)
 (|max| . 719230) (|resultantEuclidean| . 718951)
 (|semiResultantEuclidean2| . 718697) (|semiResultantEuclidean1| . 718443)
 (|indiceSubResultant| . 718212) (|indiceSubResultantEuclidean| . 717881)
 (|semiIndiceSubResultantEuclidean| . 717575) (|degreeSubResultant| . 717344)
 (|degreeSubResultantEuclidean| . 717013)
 (|semiDegreeSubResultantEuclidean| . 716707)
 (|lastSubResultantEuclidean| . 716425)
 (|semiLastSubResultantEuclidean| . 716168)
 (|subResultantGcdEuclidean| . 715895)
 (|semiSubResultantGcdEuclidean2| . 715647)
 (|semiSubResultantGcdEuclidean1| . 715399) (|discriminantEuclidean| . 715120)
 (|semiDiscriminantEuclidean| . 714866) (|chainSubResultants| . 714656)
 (|schema| . 714419) (|resultantReduit| . 714205)
 (|resultantReduitEuclidean| . 713870)
 (|semiResultantReduitEuclidean| . 713578) (|divide| . 712829)
 (|Lazard| . 712598) (|Lazard2| . 712364) (|nextsousResultant2| . 712176)
 (|resultantnaif| . 711994) (|resultantEuclideannaif| . 711715)
 (|semiResultantEuclideannaif| . 711461) (|pdct| . 711371) (|powers| . 711237)
 (|partitions| . 711096) (|parts| . 710990) (|partition| . 710761)
 (|complete| . 710124) (|pole?| . 709779) (|monomial| . 706528)
 (|leadingMonomial| . 705276) (|zRange| . 705151) (|yRange| . 704903)
 (|xRange| . 704655) (|listBranches| . 704375) (|triangular?| . 704037)
 (|rewriteIdealWithRemainder| . 703689)
 (|rewriteIdealWithHeadRemainder| . 703341) (|remainder| . 702937)
 (|headRemainder| . 702560) (|roughUnitIdeal?| . 702222)
 (|roughEqualIdeals?| . 701881) (|roughSubIdeal?| . 701540)
 (|roughBase?| . 701202) (|trivialIdeal?| . 700901) (|sort| . 700102)
 (|collectUpper| . 699833) (|collect| . 699564) (|collectUnder| . 699295)
 (|mainVariable?| . 698991) (|mainVariables| . 698690)
 (|removeSquaresIfCan| . 698366) (|unprotectedRemoveRedundantFactors| . 698046)
 (|removeRedundantFactors| . 696372) (|certainlySubVariety?| . 696017)
 (|possiblyNewVariety?| . 695625) (|probablyZeroDim?| . 695273)
 (|selectPolynomials| . 694802) (|selectOrPolynomials| . 694322)
 (|selectAndPolynomials| . 693842) (|quasiMonicPolynomials| . 693424)
 (|univariate?| . 693107) (|univariatePolynomials| . 692689)
 (|linear?| . 692372) (|linearPolynomials| . 691954) (|bivariate?| . 691637)
 (|bivariatePolynomials| . 691219)
 (|removeRoughlyRedundantFactorsInPols| . 690536)
 (|removeRoughlyRedundantFactorsInPol| . 690209) (|interReduce| . 689885)
 (|roughBasicSet| . 689450) (|crushedSet| . 689126)
 (|rewriteSetByReducingWithParticularGenerators| . 688653)
 (|rewriteIdealWithQuasiMonicGenerators| . 688226)
 (|squareFreeFactors| . 687877) (|univariatePolynomialsGcds| . 687136)
 (|removeRoughlyRedundantFactorsInContents| . 686777)
 (|removeRedundantFactorsInContents| . 686418)
 (|removeRedundantFactorsInPols| . 686059) (|irreducibleFactors| . 685642)
 (|lazyIrreducibleFactors| . 685225)
 (|removeIrreducibleRedundantFactors| . 684805) (|normalForm| . 684159)
 (|changeBase| . 683938) (|companionBlocks| . 683666) (|xCoord| . 683543)
 (|yCoord| . 683420) (|zCoord| . 683297) (|rCoord| . 683174)
 (|thetaCoord| . 683051) (|phiCoord| . 682928) (|color| . 682731)
 (|hue| . 682460) (|shade| . 682261) (|nthRootIfCan| . 682070)
 (|expIfCan| . 681924) (|logIfCan| . 681778) (|sinIfCan| . 681632)
 (|cosIfCan| . 681486) (|tanIfCan| . 681340) (|cotIfCan| . 681194)
 (|secIfCan| . 681048) (|cscIfCan| . 680902) (|asinIfCan| . 680756)
 (|acosIfCan| . 680610) (|atanIfCan| . 680464) (|acotIfCan| . 680318)
 (|asecIfCan| . 680172) (|acscIfCan| . 680026) (|sinhIfCan| . 679880)
 (|coshIfCan| . 679734) (|tanhIfCan| . 679588) (|cothIfCan| . 679442)
 (|sechIfCan| . 679296) (|cschIfCan| . 679150) (|asinhIfCan| . 679004)
 (|acoshIfCan| . 678858) (|atanhIfCan| . 678712) (|acothIfCan| . 678566)
 (|asechIfCan| . 678420) (|acschIfCan| . 678274) (|pushdown| . 676661)
 (|pushup| . 675048) (|reducedDiscriminant| . 674733)
 (|idealSimplify| . 674477) (|definingInequation| . 674221)
 (|definingEquations| . 673930) (|setStatus| . 673617)
 (|quasiAlgebraicSet| . 673323) (|radicalSimplify| . 672795)
 (|random| . 671464) (|denominator| . 671210) (|numerator| . 670966)
 (|denom| . 669505) (|numer| . 668024) (|quadraticForm| . 667852)
 (|back| . 667761) (|front| . 667670) (|rotate!| . 667579)
 (|dequeue!| . 667488) (|enqueue!| . 667394) (|quatern| . 667272)
 (|imagK| . 667050) (|imagJ| . 666828) (|imagI| . 666606)
 (|conjugate| . 666067) (|queue| . 665945) (|nthRoot| . 665519)
 (|fractRadix| . 665384) (|wholeRadix| . 665252) (|cycleRagits| . 665120)
 (|prefixRagits| . 664988) (|fractRagits| . 664854) (|wholeRagits| . 664722)
 (|radix| . 664560) (|randnum| . 664383) (|reseed| . 664260) (|seed| . 664172)
 (|rational| . 662689) (|rational?| . 661337) (|rationalIfCan| . 659854)
 (|setvalue!| . 659698) (|setchildren!| . 659507) (|node?| . 659342)
 (|child?| . 659177) (|distance| . 659044) (|leaves| . 658914)
 (|nodes| . 658784) (|rename| . 658688) (|rename!| . 658592)
 (|mainValue| . 658467) (|mainDefiningPolynomial| . 658342)
 (|mainForm| . 658236) (|sqrt| . 657722) (|rischDE| . 656645)
 (|rischDEsys| . 655789) (|monomRDE| . 655320) (|baseRDE| . 654927)
 (|polyRDE| . 654313) (|monomRDEsys| . 653806) (|baseRDEsys| . 653438)
 (|weighted| . 653213) (|rdHack1| . 652957) (|midpoint| . 652688)
 (|midpoints| . 652363) (|realZeros| . 649798)
 (|mainCharacterization| . 649440) (|algebraicOf| . 649058)
 (|ReduceOrder| . 648608) (|setref| . 648521) (|deref| . 648439)
 (|ref| . 648357) (= . 647927) (|radicalEigenvectors| . 647534)
 (|radicalEigenvector| . 647273) (|radicalEigenvalues| . 647076)
 (|eigenMatrix| . 646872) (|normalise| . 646747) (|gramschmidt| . 646613)
 (|orthonormalBasis| . 646405) (|antisymmetricTensors| . 645945)
 (|createGenericMatrix| . 645743) (|symmetricTensors| . 645376)
 (|tensorProduct| . 644822) (|permutationRepresentation| . 643958)
 (|completeEchelonBasis| . 643776) (|createRandomElement| . 643593)
 (|cyclicSubmodule| . 643317) (|standardBasisOfCyclicSubmodule| . 643059)
 (|areEquivalent?| . 642323) (|isAbsolutelyIrreducible?| . 641875)
 (|meatAxe| . 640663) (|scanOneDimSubspaces| . 640381) (|double| . 640129)
 (|expt| . 639877) (|lift| . 637991) (|solveRetract| . 637614)
 (|variables| . 635504) (|mainVariable| . 634615) (|univariate| . 631361)
 (|multivariate| . 629347) (|uniform01| . 629255) (|normal01| . 629163)
 (|exponential1| . 629071) (|chiSquare1| . 628930) (|normal| . 628787)
 (|exponential| . 628422) (|chiSquare| . 628262) (F . 628099) (|t| . 627939)
 (|factorFraction| . 627699) (|componentUpperBound| . 627596) (|blue| . 627453)
 (|green| . 627310) (|red| . 627167) (|whitePoint| . 627064)
 (|uniform| . 626587) (|binomial| . 625992) (|poisson| . 625841)
 (|geometric| . 625690) (|ridHack1| . 625575) (|interpolate| . 624845)
 (|nullSpace| . 622895) (|nullity| . 621568) (|rank| . 618739)
 (|rowEchelon| . 616913) (|column| . 616379) (|row| . 615845) (|qelt| . 614994)
 (|ncols| . 614444) (|nrows| . 613894) (|maxColIndex| . 613366)
 (|minColIndex| . 612838) (|maxRowIndex| . 612310) (|minRowIndex| . 611782)
 (|antisymmetric?| . 611274) (|symmetric?| . 610766) (|diagonal?| . 610258)
 (|square?| . 609750) (|matrix| . 608628) (|rectangularMatrix| . 608405)
 (|annihilate?| . 608326) (|characteristic| . 606439) (|round| . 606384)
 (|fractionPart| . 605713) (|wholePart| . 605250) (|floor| . 605033)
 (|ceiling| . 604816) (|norm| . 600952) (|mightHaveRoots| . 600705)
 (|refine| . 598803) (|middle| . 598594) (|size| . 596591) (|right| . 595970)
 (|left| . 595349) (|roman| . 595184) (|mainSquareFreePart| . 594949)
 (|mainPrimitivePart| . 594714) (|mainContent| . 594479)
 (|primitivePart!| . 594244) (|gcd| . 591954) (|nextsubResultant2| . 591705)
 (|LazardQuotient2| . 591410) (|LazardQuotient| . 591118)
 (|subResultantChain| . 590840) (|halfExtendedSubResultantGcd2| . 590258)
 (|halfExtendedSubResultantGcd1| . 589676) (|extendedSubResultantGcd| . 589051)
 (|exactQuotient!| . 588567) (|exactQuotient| . 588083)
 (|primPartElseUnitCanonical!| . 587843) (|primPartElseUnitCanonical| . 587603)
 (|retract| . 585066) (|retractIfCan| . 582078) (|lazyResidueClass| . 581473)
 (|monicModulo| . 581155) (|lazyPseudoDivide| . 580135)
 (|lazyPremWithDefault| . 579458) (|lazyPquo| . 579045) (|lazyPrem| . 578632)
 (|pquo| . 578219) (|prem| . 577806) (|supRittWu?| . 577572)
 (|RittWuCompare| . 577336) (|mainMonomials| . 577105)
 (|mainCoefficients| . 576874) (|leastMonomial| . 576671)
 (|mainMonomial| . 576468) (|quasiMonic?| . 576237) (|monic?| . 575804)
 (|leadingCoefficient| . 573523) (|deepestInitial| . 573320)
 (|iteratedInitials| . 573089) (|deepestTail| . 572886) (|head| . 572419)
 (|mdeg| . 572170) (|mvar| . 571703) (|iterators| . 571522)
 (|relativeApprox| . 570912) (|rootOf| . 569374) (|allRootsOf| . 568249)
 (|definingPolynomial| . 567197) (|positive?| . 566618) (|negative?| . 566040)
 (|zero?| . 565352) (|augment| . 564010) (|lastSubResultant| . 563074)
 (|lastSubResultantElseSplit| . 562735) (|invertibleSet| . 562412)
 (|invertible?| . 561711) (|invertibleElseSplit?| . 561366)
 (|purelyAlgebraicLeadingMonomial?| . 561043)
 (|algebraicCoefficients?| . 560720) (|purelyTranscendental?| . 560397)
 (|purelyAlgebraic?| . 559756) (|prepareSubResAlgo| . 559300)
 (|internalLastSubResultant| . 558300) (|integralLastSubResultant| . 557861)
 (|toseLastSubResultant| . 557422) (|toseInvertible?| . 556575)
 (|toseInvertibleSet| . 556179) (|toseSquareFreePart| . 555743)
 (|expression| . 555266) (|quotedOperators| . 554805) (|pattern| . 554380)
 (|suchThat| . 552163) (|rule| . 551284) (|rules| . 550813)
 (|ruleset| . 550342) (|rur| . 548427) (|create| . 548372)
 (|clearCache| . 548250) (|cache| . 548125) (|enterInCache| . 547832)
 (|currentCategoryFrame| . 547793) (|currentScope| . 547754)
 (|pushNewContour| . 547675) (|findBinding| . 547417) (|contours| . 547330)
 (|structuralConstants| . 545985) (|coordinates| . 543313) (|bounds| . 543221)
 (|equation| . 542687) (|incr| . 542560) (|high| . 542468) (|low| . 542376)
 (|hi| . 542284) (|lo| . 542192) (BY . 542062) (|body| . 541142)
 (|union| . 540489) (|subset?| . 540355) (|symmetricDifference| . 540249)
 (|difference| . 540039) (|intersect| . 538013) (|set| . 537784)
 (|brace| . 537417) (|part?| . 537283) (|latex| . 537198) (|hash| . 537106)
 (|delta| . 536897) (|member?| . 536380) (|enumerate| . 536168)
 (|setOfMinN| . 535968) (|elements| . 535676) (|replaceKthElement| . 535511)
 (|incrementKthElement| . 535349) (|cdr| . 535077) (|car| . 534805)
 (|expr| . 534533) (|float| . 534025) (|integer| . 533615) (|symbol| . 533343)
 (|destruct| . 532823) (|float?| . 532523) (|integer?| . 531988)
 (|symbol?| . 531566) (|string?| . 531266) (|list?| . 530966)
 (|pair?| . 530666) (|atom?| . 530366) (|null?| . 530066) (|eq| . 529677)
 (|startTable!| . 528841) (|stopTable!| . 528077)
 (|supDimElseRittWu?| . 527295) (|algebraicSort| . 526519)
 (|moreAlgebraic?| . 525737) (|subTriSet?| . 524955) (|subPolSet?| . 524117)
 (|internalSubPolSet?| . 523279) (|internalInfRittWu?| . 522441)
 (|internalSubQuasiComponent?| . 521687) (|subQuasiComponent?| . 520055)
 (|removeSuperfluousQuasiComponents| . 519279) (|subCase?| . 518361)
 (|removeSuperfluousCases| . 517529) (|prepareDecompose| . 516323)
 (|branchIfCan| . 515289) (|startTableGcd!| . 514427)
 (|stopTableGcd!| . 513637) (|startTableInvSet!| . 512775)
 (|stopTableInvSet!| . 511985) (|stosePrepareSubResAlgo| . 511511)
 (|stoseInternalLastSubResultant| . 510479)
 (|stoseIntegralLastSubResultant| . 510022) (|stoseLastSubResultant| . 509565)
 (|stoseInvertible?sqfreg| . 509094) (|stoseInvertibleSetsqfreg| . 508680)
 (|stoseInvertible?reg| . 508209) (|stoseInvertibleSetreg| . 507795)
 (|stoseInvertible?| . 506912) (|stoseInvertibleSet| . 506498)
 (|stoseSquareFreePart| . 506044) (|coleman| . 505868)
 (|inverseColeman| . 505692) (|listYoungTableaus| . 505505)
 (|makeYoungTableau| . 505280) (|nextColeman| . 505104)
 (|nextLatticePermutation| . 504894) (|nextPartition| . 504537)
 (|numberOfImproperPartitions| . 504419) (|subSet| . 504254)
 (|unrankImproperPartitions0| . 504089) (|unrankImproperPartitions1| . 503924)
 (|semiGroupOperation| . 503782) (|subresultantSequence| . 503516)
 (|SturmHabichtSequence| . 503250) (|SturmHabichtCoefficients| . 503012)
 (|SturmHabicht| . 502774) (|countRealRoots| . 502539)
 (|SturmHabichtMultiple| . 502262) (|countRealRootsMultiple| . 501988)
 (|source| . 501808) (|target| . 501413) (|signature| . 500934)
 (|signatureAst| . 500806) (|xor| . 500656) (|depth| . 500386) (|top| . 500295)
 (|pop!| . 500204) (|push!| . 500110) (|map!| . 499957) (|minordet| . 499145)
 (|determinant| . 498049) (|diagonalProduct| . 497407) (|trace| . 496506)
 (|diagonal| . 496279) (|diagonalMatrix| . 495432) (|scalarMatrix| . 494953)
 (|hermite| . 494500) (|completeHermite| . 494152) (|smith| . 493874)
 (|completeSmith| . 493494) (|diophantineSystem| . 493086) (|csubst| . 492728)
 (|particularSolution| . 491558) (|mapSolve| . 491015) (|linear| . 490332)
 (|quadratic| . 489646) (|cubic| . 488957) (|quartic| . 488265)
 (|aLinear| . 487952) (|aQuadratic| . 487636) (|aCubic| . 487317)
 (|aQuartic| . 486995) (|radicalSolve| . 484631) (|radicalRoots| . 484036)
 (|contractSolve| . 483293) (|decomposeFunc| . 483087) (|unvectorise| . 482601)
 (|bubbleSort!| . 481919) (|insertionSort!| . 481237) (|check| . 480711)
 (|objects| . 480362) (|lprop| . 480205) (|llprop| . 480039) (|lllp| . 479881)
 (|lllip| . 479713) (|lp| . 479573) (|mesh?| . 479443) (|mesh| . 478037)
 (|polygon?| . 477907) (|polygon| . 477348) (|closedCurve?| . 477218)
 (|closedCurve| . 476659) (|curve?| . 476529) (|curve| . 475775)
 (|point?| . 475645) (|enterPointData| . 475456) (|composites| . 475326)
 (|components| . 475196) (|numberOfComposites| . 475055)
 (|numberOfComponents| . 474236) (|create3Space| . 474010) (|parse| . 473885)
 (|outputAsFortran| . 473466) (|outputAsScript| . 473203)
 (|outputAsTex| . 472940) (|abs| . 472192) (|Beta| . 471514)
 (|digamma| . 471058) (|polygamma| . 470505) (|Gamma| . 469773)
 (|besselJ| . 469305) (|besselY| . 468837) (|besselI| . 468369)
 (|besselK| . 467901) (|airyAi| . 467445) (|airyBi| . 466989)
 (|subNode?| . 466710) (|infLex?| . 466380) (|setEmpty!| . 466188)
 (|setStatus!| . 465965) (|setCondition!| . 465770) (|setValue!| . 465575)
 (|copy| . 464993) (|status| . 464490) (|value| . 463960) (|empty?| . 463371)
 (|splitNodeOf!| . 462809) (|remove!| . 461444) (|remove| . 460386)
 (|subNodeOf?| . 460060) (|nodeOf?| . 459790) (|result| . 459523)
 (|conditions| . 459303) (|updateStatus!| . 459111)
 (|extractSplittingLeaf| . 458917) (|squareMatrix| . 458746)
 (|transpose| . 457817) (|rightTrim| . 457617) (|leftTrim| . 457417)
 (|trim| . 457217) (|split| . 454987) (|position| . 454028)
 (|replace| . 453904) (|match?| . 453771) (|match| . 452318)
 (|substring?| . 452187) (|suffix?| . 452094) (|prefix?| . 452001)
 (|upperCase!| . 451947) (|upperCase| . 451803) (|lowerCase!| . 451749)
 (|lowerCase| . 451605) (|KrullNumber| . 450653) (|numberOfVariables| . 449701)
 (|algebraicDecompose| . 448489) (|transcendentalDecompose| . 446045)
 (|internalDecompose| . 442262) (|decompose| . 439028)
 (|upDateBranches| . 437594) (|printInfo| . 436590) (|preprocess| . 435524)
 (|internalZeroSetSplit| . 434674) (|internalAugment| . 433269)
 (|stack| . 433154) (|size?| . 432978) (|possiblyInfinite?| . 432851)
 (|explicitlyFinite?| . 432724) (|nextItem| . 432637) (|init| . 432389)
 (|step| . 432311) (|upperBound| . 432221) (|lowerBound| . 432143)
 (|iterationVar| . 431985) (|infiniteProduct| . 431002)
 (|evenInfiniteProduct| . 430019) (|oddInfiniteProduct| . 429036)
 (|generalInfiniteProduct| . 427930) (|filterUntil| . 427657)
 (|filterWhile| . 427384) (|generate| . 426856) (|showAll?| . 426709)
 (|showAllElements| . 426556) (|output| . 425950) (|cons| . 425790)
 (|delay| . 425660) (|findCycle| . 425396) (|repeating?| . 425208)
 (|repeating| . 425092) (|exquo| . 423515) (|recip| . 422290)
 (|integers| . 422106) (|oddintegers| . 421922) (|int| . 421086)
 (|mapmult| . 420943) (|deriv| . 420803) (|gderiv| . 420610)
 (|compose| . 420299) (|addiag| . 420111) (|lazyIntegrate| . 419857)
 (|nlde| . 419607) (|powern| . 419383) (|mapdiv| . 419205)
 (|lazyGintegrate| . 418932) (|power| . 418754) (|sincos| . 418499)
 (|sinhcosh| . 418234) (|asin| . 416946) (|acos| . 415658) (|atan| . 414278)
 (|acot| . 412990) (|asec| . 411702) (|acsc| . 410414) (|sinh| . 409132)
 (|cosh| . 407850) (|tanh| . 406568) (|coth| . 405286) (|sech| . 404004)
 (|csch| . 402722) (|asinh| . 401437) (|acosh| . 400152) (|atanh| . 398867)
 (|acoth| . 397582) (|asech| . 396297) (|acsch| . 395012)
 (|subresultantVector| . 394789) (|primitivePart| . 393514)
 (|pointData| . 393349) (|parent| . 393222) (|level| . 392973)
 (|extractProperty| . 392793) (|extractClosed| . 392638)
 (|extractIndex| . 392465) (|extractPoint| . 392309) (|traverse| . 392124)
 (|defineProperty| . 391883) (|closeComponent| . 391667)
 (|modifyPoint| . 391012) (|addPointLast| . 390801) (|addPoint2| . 390642)
 (|addPoint| . 389990) (|merge| . 389046) (|deepCopy| . 388919)
 (|shallowCopy| . 388792) (|numberOfChildren| . 388619) (|children| . 388313)
 (|child| . 388137) (|birth| . 388010) (|internal?| . 387855)
 (|root?| . 387700) (|leaf?| . 387417) (|rhs| . 386411) (|lhs| . 385405)
 (|construct| . 380550) (|predicate| . 380253) (|sum| . 377073)
 (|outputForm| . 376072) (|list| . 375897) (|string| . 375274)
 (|argscript| . 375180) (|superscript| . 375086) (|subscript| . 374992)
 (|script| . 374550) (|scripts| . 374123) (|scripted?| . 374046)
 (|name| . 372962) (|resetNew| . 372891) (|symFunc| . 372559)
 (|symbolTableOf| . 372431) (|argumentListOf| . 372299)
 (|returnTypeOf| . 372108) (|printHeader| . 371794) (|returnType!| . 371192)
 (|argumentList!| . 370752) (|endSubProgram| . 370671)
 (|currentSubProgram| . 370590) (|newSubProgram| . 370472)
 (|clearTheSymbolTable| . 370277) (|showTheSymbolTable| . 370229)
 (|symbolTable| . 370074) (|printTypes| . 369879) (|newTypeLists| . 369791)
 (|typeLists| . 369472) (|externalList| . 369380) (|typeList| . 369007)
 (|parametersOf| . 368915) (|fortranTypeOf| . 368790) (|declare!| . 367972)
 (|empty| . 367278) (|case| . 361218) (|compound?| . 361141)
 (|getOperands| . 360928) (|getOperator| . 360669) (|nil?| . 360592)
 (|buildSyntax| . 360376) (|autoCoerce| . 356897) (|solve| . 339825)
 (|triangularSystems| . 339554) (|loadNativeModule| . 339444)
 (|nativeModuleExtension| . 339371) (|hostByteOrder| . 339295)
 (|hostPlatform| . 339222) (|rootDirectory| . 339149) (|bumprow| . 338829)
 (|bumptab| . 338586) (|bumptab1| . 338399) (|untab| . 338203)
 (|bat1| . 338003) (|bat| . 337816) (|tab1| . 337616) (|tab| . 337445)
 (|lex| . 337305) (|slex| . 337137) (|inverse| . 335308) (|maxrow| . 334970)
 (|mr| . 334622) (|listOfLists| . 333965) (|tableau| . 333832)
 (|operator| . 331489) (|tanSum| . 331361) (|tanAn| . 331165)
 (|tanNa| . 331034) (|table| . 330680) (|initTable!| . 330498)
 (|printInfo!| . 330283) (|startStats!| . 330071) (|printStats!| . 329889)
 (|clearTable!| . 329707) (|usingTable?| . 329522) (|printingInfo?| . 329337)
 (|makingStats?| . 329152) (|extractIfCan| . 328990) (|insert!| . 328050)
 (|setPrologue!| . 327957) (|setTex!| . 327864) (|setEpilogue!| . 327771)
 (|prologue| . 327681) (|new| . 326280) (|tex| . 326190) (|epilogue| . 326100)
 (|display| . 324929) (|endOfFile?| . 324850) (|readIfCan!| . 324663)
 (|readLineIfCan!| . 324573) (|readLine!| . 324495) (|writeLine!| . 324338)
 (|sign| . 321510) (|nonQsign| . 321382) (|direction| . 321233)
 (|createThreeSpace| . 321119) (|pi| . 320836) (|cyclicParents| . 320706)
 (|cyclicEqual?| . 320582) (|cyclicEntries| . 320452) (|cyclicCopy| . 320366)
 (|tree| . 320030) (|cyclic?| . 319781) (|cos| . 318394) (|cot| . 317109)
 (|csc| . 315824) (|sec| . 314539) (|sin| . 313152) (|tan| . 311867)
 (|complexNormalize| . 310178) (|complexElementary| . 308489)
 (|trigs| . 307712) (|real| . 306570) (|imag| . 305648) (|real?| . 304721)
 (|complexForm| . 303861) (|UpTriBddDenomInv| . 303570)
 (|LowTriBddDenomInv| . 303279) (|simplify| . 302334) (|htrigs| . 302077)
 (|simplifyExp| . 301820) (|simplifyLog| . 301563) (|expandPower| . 301306)
 (|expandLog| . 301049) (|cos2sec| . 300792) (|cosh2sech| . 300535)
 (|cot2trig| . 300278) (|coth2trigh| . 300021) (|csc2sin| . 299764)
 (|csch2sinh| . 299507) (|sec2cos| . 299250) (|sech2cosh| . 298993)
 (|sin2csc| . 298736) (|sinh2csch| . 298479) (|tan2trig| . 298222)
 (|tanh2trigh| . 297965) (|tan2cot| . 297708) (|tanh2coth| . 297451)
 (|cot2tan| . 297194) (|coth2tanh| . 296937) (|removeCosSq| . 296680)
 (|removeSinSq| . 296423) (|removeCoshSq| . 296166) (|removeSinhSq| . 295909)
 (|expandTrigProducts| . 295438) (|fintegrate| . 294820)
 (|coefficient| . 291576) (|coHeight| . 291218) (|extendIfCan| . 290938)
 (|algebraicVariables| . 290620) (|zeroSetSplitIntoTriangularSystems| . 290209)
 (|zeroSetSplit| . 285802) (|reduceByQuasiMonic| . 285516)
 (|collectQuasiMonic| . 285233) (|removeZero| . 284947)
 (|initiallyReduce| . 284457) (|headReduce| . 283967)
 (|stronglyReduce| . 283681) (|rewriteSetWithReduction| . 283264)
 (|autoReduced?| . 282881) (|initiallyReduced?| . 281745)
 (|headReduced?| . 280609) (|stronglyReduced?| . 279972) (|reduced?| . 279096)
 (|normalized?| . 277960) (|quasiComponent| . 277584) (|initials| . 277266)
 (|basicSet| . 276361) (|infRittWu?| . 274972) (|getCurve| . 274859)
 (|listLoops| . 274679) (|closed?| . 274435) (|open?| . 274294)
 (|setClosed| . 274150) (|tube| . 273713) (|point| . 272618)
 (|unitVector| . 271758) (|cosSinInfo| . 271608) (|loopPoints| . 271375)
 (|select| . 270489) (|generalTwoFactor| . 270166) (|generalSqFr| . 269843)
 (|twoFactor| . 269489) (|setOrder| . 269138) (|getOrder| . 268948)
 (|less?| . 268419) (|userOrdered?| . 268272) (|largest| . 267885)
 (|more?| . 267525) (|setVariableOrder| . 267244) (|getVariableOrder| . 267059)
 (|resetVariableOrder| . 266958) (|prime?| . 265979) (|sample| . 265104)
 (|bitior| . 264771) (|bitand| . 264438) (|rationalFunction| . 263949)
 (|taylorIfCan| . 263752) (|taylor| . 258588) (|removeZeroes| . 257414)
 (|taylorRep| . 257222) (|factor| . 244459) (|factorSquareFree| . 242716)
 (|henselFact| . 241950) (|hasHi| . 241824) (|segment| . 241379)
 (SEGMENT . 241102) (|fmecg| . 240107) (|commonDenominator| . 239146)
 (|clearDenominator| . 238155) (|splitDenominator| . 236333)
 (|monicRightFactorIfCan| . 236058) (|rightFactorIfCan| . 235780)
 (|leftFactorIfCan| . 235544) (|monicDecomposeIfCan| . 235248)
 (|monicCompleteDecompose| . 234985) (|divideIfCan| . 234718)
 (|noKaratsuba| . 234528) (|karatsubaOnce| . 234338) (|karatsuba| . 234103)
 (|separate| . 233327) (|pseudoDivide| . 232518) (|pseudoQuotient| . 232366)
 (|composite| . 231889) (|subResultantGcd| . 231316) (|resultant| . 230506)
 (|discriminant| . 228980) (|differentiate| . 226889)
 (|pseudoRemainder| . 226774) (|shiftLeft| . 226613) (|shiftRight| . 226452)
 (|karatsubaDivide| . 226223) (|monicDivide| . 225760)
 (|divideExponents| . 225597) (|unmakeSUP| . 225428) (|makeSUP| . 225259)
 (|vectorise| . 225068) (|eval| . 218088) (|extend| . 215600)
 (|approximate| . 214344) (|truncate| . 213966) (|order| . 209218)
 (|center| . 208644) (|terms| . 207758) (|squareFreePart| . 206772)
 (|BumInSepFFE| . 206335) (|multiplyExponents| . 205807)
 (|laurentIfCan| . 205609) (|laurent| . 201429) (|laurentRep| . 201236)
 (|rationalPower| . 200995) (|puiseux| . 196814) (|dominantTerm| . 195824)
 (|limitPlus| . 194707) (|split!| . 194504) (|setlast!| . 194336)
 (|setrest!| . 194048) (|setelt| . 191815) (|setfirst!| . 191647)
 (|cycleSplit!| . 191482) (|concat!| . 190764) (|cycleTail| . 190657)
 (|cycleLength| . 190511) (|cycleEntry| . 190404) (|third| . 190297)
 (|second| . 190076) (|tail| . 189665) (|last| . 188946) (|rest| . 188102)
 (|elt| . 180551) (|first| . 179379) (|concat| . 178590)
 (|invmultisect| . 178218) (|multisect| . 177846) (|revert| . 177556)
 (|generalLambert| . 177184) (|evenlambert| . 176894) (|oddlambert| . 176604)
 (|lambert| . 176314) (|lagrange| . 176024) (|univariatePolynomial| . 175510)
 (|integrate| . 163971) (** . 158122) (|polynomial| . 157244)
 (|multiplyCoefficients| . 156753) (|quoByVar| . 156639)
 (|coefficients| . 155730) (|series| . 148295) (|stFunc1| . 147984)
 (|stFunc2| . 147656) (|stFuncN| . 147327) (|fixedPointExquo| . 147117)
 (|ode1| . 146866) (|ode2| . 146609) (|ode| . 146321) (|mpsode| . 145982)
 (UP2UTS . 145681) (UTS2UP . 145338) (LODO2FUN . 144987) (RF2UTS . 144610)
 (|variable| . 143694) (|magnitude| . 143531) (|length| . 142064)
 (|cross| . 141737) (|outerProduct| . 141579) (|dot| . 141035) (- . 138775)
 (|zero| . 138343) (+ . 136024) (|vector| . 135908) (|scan| . 133709)
 (|reduce| . 126869) (|map| . 101942) (|graphCurves| . 101292)
 (|drawCurves| . 100760) (|update| . 100588) (|show| . 100420)
 (|scale| . 99892) (|connect| . 99724) (|region| . 99556) (|points| . 99388)
 (|units| . 98719) (|getGraph| . 98575) (|putGraph| . 98403) (|graphs| . 98092)
 (|graphStates| . 97551) (|graphState| . 97282) (|makeViewport2D| . 97077)
 (|viewport2D| . 97021) (|getPickedPoints| . 96896) (|key| . 96620)
 (|close| . 96330) (|write| . 95640) (|colorDef| . 95507) (|reset| . 95323)
 (|intensity| . 95193) (|lighting| . 95057) (|clipSurface| . 94926)
 (|showClipRegion| . 94795) (|showRegion| . 94664) (|hitherPlane| . 94534)
 (|eyeDistance| . 94404) (|perspective| . 94273) (|translate| . 93797)
 (|zoom| . 93240) (|rotate| . 92974) (|drawStyle| . 92843)
 (|outlineRender| . 92712) (|diagonals| . 92581) (|axes| . 92117)
 (|controlPanel| . 91859) (|viewpoint| . 89672) (|dimensions| . 89286)
 (|title| . 88810) (|resize| . 88528) (|move| . 88240) (|options| . 87780)
 (|modifyPointData| . 87411) (|subspace| . 86908) (|makeViewport3D| . 86518)
 (|viewport3D| . 86460) (|viewDeltaYDefault| . 86275)
 (|viewDeltaXDefault| . 86090) (|viewZoomDefault| . 85905)
 (|viewPhiDefault| . 85720) (|viewThetaDefault| . 85535)
 (|pointColorDefault| . 85356) (|lineColorDefault| . 85177)
 (|axesColorDefault| . 84998) (|unitsColorDefault| . 84819)
 (|pointSizeDefault| . 84610) (|viewPosDefault| . 84377)
 (|viewSizeDefault| . 84150) (|viewDefaults| . 84064)
 (|viewWriteDefault| . 83855) (|viewWriteAvailable| . 83751)
 (|var1StepsDefault| . 83542) (|var2StepsDefault| . 83333)
 (|tubePointsDefault| . 83124) (|tubeRadiusDefault| . 82897) (|void| . 82859)
 (|dimension| . 81355) (|crest| . 81103) (|cfirst| . 80851)
 (|sts2stst| . 80601) (|clikeUniv| . 80333) (|weierstrass| . 80103)
 (|qqq| . 79817) (|integralBasis| . 77755) (|localIntegralBasis| . 76008)
 (|qualifier| . 75929) (|mainExpression| . 75850) (|condition| . 75507)
 (|changeWeightLevel| . 74818) (|characteristicSerie| . 73941)
 (|characteristicSet| . 73234) (|medialSet| . 72527) (|Hausdorff| . 72232)
 (|Frobenius| . 71579) (|transcendenceDegree| . 71232)
 (|extensionDegree| . 70484) (|inGroundField?| . 70357)
 (|transcendent?| . 70230) (|algebraic?| . 69784) (|varList| . 68593)
 (|sh| . 68189) (|mirror| . 67435) (|monomial?| . 66439) (|monom| . 65945)
 (|rquo| . 65068) (|lquo| . 64191) (|mindegTerm| . 63969) (|log| . 61558)
 (|exp| . 59245) (|product| . 58089) (|LiePolyIfCan| . 57699)
 (|coerce| . 45959) (|trunc| . 45583) (|degree| . 41161) (/ . 37328)
 (|quasiRegular| . 37062) (|quasiRegular?| . 36733) (|constant| . 35948)
 (|constant?| . 35406) (|coef| . 34753) (|mindeg| . 34439) (|maxdeg| . 34122)
 (|#| . 33312) (|reductum| . 31135) (* . 23431) (|RemainderList| . 23017)
 (|unexpand| . 22675) (|expand| . 20495) (|shape| . 20408)
 (|youngDiagram| . 20299) (Y . 19838) (|triangSolve| . 18514)
 (|univariateSolve| . 15694) (|realSolve| . 13158) (|positiveSolve| . 11340)
 (|squareFree| . 8213) (|convert| . 795) (|linearlyDependentOverZ?| . 518)
 (|linearDependenceOverZ| . 282) (|solveLinearlyOverQ| . 30))