TSTP Solution File: GRP592-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:56:30 EDT 2022
% Result : Unsatisfiable 15.05s 15.14s
% Output : Proof 15.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP592-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.13/0.14 % Command : moca.sh %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 12:16:48 EDT 2022
% 0.14/0.36 % CPUTime :
% 15.05/15.14 % SZS status Unsatisfiable
% 15.05/15.14 % SZS output start Proof
% 15.05/15.14 The input problem is unsatisfiable because
% 15.05/15.14
% 15.05/15.14 [1] the following set of Horn clauses is unsatisfiable:
% 15.05/15.14
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C
% 15.05/15.14 multiply(A, B) = inverse(double_divide(B, A))
% 15.05/15.14 multiply(a, b) = multiply(b, a) ==> \bottom
% 15.05/15.14
% 15.05/15.14 This holds because
% 15.05/15.14
% 15.05/15.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 15.05/15.14
% 15.05/15.14 E:
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C
% 15.05/15.14 f1(multiply(a, b)) = true__
% 15.05/15.14 f1(multiply(b, a)) = false__
% 15.05/15.14 multiply(A, B) = inverse(double_divide(B, A))
% 15.05/15.14 G:
% 15.05/15.14 true__ = false__
% 15.05/15.14
% 15.05/15.14 This holds because
% 15.05/15.14
% 15.05/15.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 15.05/15.14
% 15.05/15.14 double_divide(X0, double_divide(X1, inverse(X1))) = inverse(X0)
% 15.05/15.14 double_divide(X1, Y1) = double_divide(Y1, inverse(inverse(X1)))
% 15.05/15.14 double_divide(X1, inverse(X1)) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(Y0, Y1) = double_divide(Y1, Y0)
% 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y0)), Y2)
% 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y2)), Y0)
% 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) = double_divide(double_divide(Y2, inverse(Y0)), Y2)
% 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) = double_divide(double_divide(Y2, inverse(Y2)), Y0)
% 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y0)), Y2)
% 15.05/15.14 double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(double_divide(Y2, inverse(Y2)), Y0)
% 15.05/15.14 double_divide(Y0, double_divide(inverse(X0), X0)) = inverse(Y0)
% 15.05/15.14 double_divide(Y0, double_divide(inverse(X0), inverse(inverse(Y0)))) = double_divide(X0, double_divide(X1, inverse(X1)))
% 15.05/15.14 double_divide(Y0, inverse(X0)) = double_divide(inverse(X0), Y0)
% 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))) = double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1)
% 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))) = double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0) = double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1)
% 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0) = double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(X0, double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))), X0) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(inverse(Y1), inverse(inverse(Y1)))
% 15.05/15.14 double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(X0), inverse(inverse(X1)))) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(double_divide(X1, inverse(X1)), double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1)) = double_divide(X0, inverse(X0))
% 15.05/15.14 double_divide(double_divide(Y0, X0), Y0) = double_divide(double_divide(X0, double_divide(X1, inverse(X1))), double_divide(Y2, inverse(Y2)))
% 15.05/15.14 double_divide(double_divide(Y0, X0), Y0) = double_divide(double_divide(false__, inverse(false__)), double_divide(X0, double_divide(false__, inverse(false__))))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(X0, double_divide(X1, inverse(X1)))), double_divide(inverse(Y0), X0)) = double_divide(Y2, inverse(Y2))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), Y0) = double_divide(double_divide(X0, inverse(X0)), double_divide(Y2, inverse(Y2)))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y0) = double_divide(Y2, inverse(Y2))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y0) = double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y0) = double_divide(Y2, inverse(Y2))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y0) = double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y0) = double_divide(Y2, inverse(Y2))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y0) = double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(Y0, double_divide(inverse(X0), inverse(X1))), Y0) = double_divide(double_divide(X0, X1), double_divide(Y2, inverse(Y2)))
% 15.05/15.14 double_divide(double_divide(Y0, inverse(X0)), Y0) = double_divide(X0, double_divide(X1, inverse(X1)))
% 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), X0) = double_divide(X0, double_divide(X1, inverse(X1)))
% 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), X0) = double_divide(X0, double_divide(false__, inverse(false__)))
% 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(Y2, inverse(Y2))
% 15.05/15.14 double_divide(double_divide(Y1, inverse(Y1)), Y0) = inverse(Y0)
% 15.05/15.14 double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), Y1) = double_divide(Y1, double_divide(Y2, inverse(Y2)))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), Y1) = double_divide(Y1, double_divide(false__, inverse(false__)))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), Y1) = double_divide(Y1, double_divide(Y2, inverse(Y2)))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), Y1) = double_divide(Y1, double_divide(false__, inverse(false__)))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(X2, inverse(X2))) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), Y1), double_divide(X0, inverse(Y1))) = double_divide(Y2, inverse(Y2))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), Y1), Y1) = double_divide(Y2, inverse(Y2))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), Y1) = double_divide(Y1, double_divide(Y2, inverse(Y2)))
% 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), Y1) = double_divide(Y1, double_divide(false__, inverse(false__)))
% 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), X0) = double_divide(X0, double_divide(false__, inverse(false__)))
% 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), Y1) = inverse(Y1)
% 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(double_divide(inverse(Y0), inverse(inverse(Y0))), double_divide(X1, inverse(X1))) = double_divide(X0, inverse(X0))
% 15.05/15.14 double_divide(false__, double_divide(inverse(X0), X0)) = inverse(false__)
% 15.05/15.14 double_divide(false__, inverse(false__)) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(inverse(X0), X0) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 double_divide(inverse(X0), X0) = double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(Y0))) = inverse(double_divide(X0, inverse(X0)))
% 15.05/15.14 double_divide(inverse(double_divide(Y0, double_divide(X1, inverse(X1)))), inverse(Y0)) = double_divide(X0, inverse(X0))
% 15.05/15.14 inverse(double_divide(Y1, inverse(Y1))) = double_divide(X0, inverse(X0))
% 15.05/15.14 inverse(double_divide(Y1, inverse(Y1))) = inverse(double_divide(X0, inverse(X0)))
% 15.05/15.14 inverse(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(Y1, inverse(Y1))
% 15.05/15.14 inverse(false__) = double_divide(false__, double_divide(Y1, inverse(Y1)))
% 15.05/15.14 inverse(inverse(double_divide(Y1, inverse(Y1)))) = double_divide(X0, inverse(X0))
% 15.05/15.14 double_divide(X0, double_divide(X0, inverse(inverse(Y1)))) -> Y1
% 15.05/15.14 double_divide(X0, inverse(inverse(double_divide(Y1, X0)))) -> Y1
% 15.05/15.14 double_divide(X1, double_divide(inverse(inverse(X1)), inverse(inverse(Y0)))) -> Y0
% 15.05/15.14 double_divide(X1, double_divide(inverse(inverse(Y1)), inverse(inverse(X1)))) -> Y1
% 15.05/15.14 double_divide(Y0, double_divide(Y0, false__)) -> false__
% 15.05/15.14 double_divide(Y0, double_divide(false__, Y0)) -> false__
% 15.05/15.14 double_divide(Y1, double_divide(Y0, Y1)) -> Y0
% 15.05/15.14 double_divide(Y1, double_divide(Y1, Y0)) -> Y0
% 15.05/15.14 double_divide(double_divide(X0, X1), double_divide(inverse(inverse(Y1)), double_divide(inverse(inverse(X0)), inverse(inverse(X1))))) -> Y1
% 15.05/15.14 double_divide(double_divide(X0, double_divide(X1, inverse(X1))), double_divide(inverse(inverse(Y1)), inverse(X0))) -> Y1
% 15.05/15.14 double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(X0), inverse(inverse(X1)))) -> double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(X0, inverse(inverse(Y1))), X0) -> Y1
% 15.05/15.14 double_divide(double_divide(X1, inverse(X1)), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), double_divide(inverse(X0), inverse(X1))) -> double_divide(X0, X1)
% 15.05/15.14 double_divide(double_divide(Y0, inverse(Y0)), double_divide(inverse(X0), inverse(inverse(X1)))) -> double_divide(X0, inverse(X1))
% 15.05/15.14 double_divide(double_divide(Y2, Y1), Y1) -> Y2
% 15.05/15.14 double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(X0), inverse(inverse(X1)))), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(Y1, inverse(Y1))), Y0), double_divide(inverse(X0), inverse(X1))) -> double_divide(X0, X1)
% 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y0), inverse(Y2)) -> Y2
% 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y0), inverse(Y2)) -> Y2
% 15.05/15.14 double_divide(double_divide(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y0), inverse(Y2)) -> Y2
% 15.05/15.14 double_divide(double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(X2, inverse(X2))), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(double_divide(false__, Y1), Y1) -> false__
% 15.05/15.14 double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))) -> double_divide(false__, inverse(false__))
% 15.05/15.14 double_divide(double_divide(inverse(X0), X0), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(Y1, inverse(Y1))) -> double_divide(X0, X1)
% 15.05/15.14 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(double_divide(Y1, double_divide(Y2, inverse(Y2))), Y1)) -> double_divide(X0, X1)
% 15.05/15.14 double_divide(false__, double_divide(false__, inverse(inverse(Y1)))) -> Y1
% 15.05/15.14 double_divide(inverse(X1), double_divide(inverse(inverse(Y1)), inverse(inverse(inverse(X1))))) -> Y1
% 15.05/15.14 double_divide(inverse(X1), inverse(inverse(double_divide(Y1, inverse(X1))))) -> Y1
% 15.05/15.14 double_divide(inverse(X2), inverse(inverse(double_divide(double_divide(X0, inverse(Y1)), inverse(double_divide(X0, inverse(X2))))))) -> Y1
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(Y1, double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1)))), Y1)) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(Y1, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), Y1)) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(Y1, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), Y1)) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(double_divide(X0, X1), double_divide(inverse(X0), inverse(X1))), double_divide(false__, inverse(false__)))) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(X2, inverse(X2)))) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), double_divide(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0), double_divide(false__, inverse(false__)))) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)))) -> Y0
% 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(inverse(double_divide(X1, Y0))))) -> inverse(X1)
% 15.05/15.14 double_divide(inverse(Y0), inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0))))))) -> Y0
% 15.05/15.14 double_divide(inverse(Y1), double_divide(X1, inverse(X1))) -> Y1
% 15.05/15.14 double_divide(inverse(Y1), double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))) -> Y1
% 15.05/15.14 double_divide(inverse(Y1), inverse(inverse(double_divide(X0, inverse(X0))))) -> Y1
% 15.05/15.14 double_divide(inverse(Y1), inverse(inverse(inverse(double_divide(X0, inverse(X0)))))) -> Y1
% 15.05/15.14 double_divide(inverse(double_divide(X1, inverse(Y2))), inverse(X1)) -> Y2
% 15.05/15.14 double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(double_divide(X0, inverse(X2))))), inverse(Y2))))), Y1) -> Y2
% 15.05/15.14 double_divide(inverse(double_divide(Y0, X0)), inverse(Y0)) -> double_divide(X0, double_divide(false__, inverse(false__)))
% 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(Y0))), inverse(Y3)) -> Y3
% 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X1, inverse(Y0))), inverse(Y3))))), inverse(X1)) -> Y3
% 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(double_divide(double_divide(X0, Y2), inverse(double_divide(X0, inverse(X2))))), inverse(Y0))))), inverse(Y3))))), Y2) -> Y3
% 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, Y2), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), inverse(Y0))))), inverse(Y3))))), Y2) -> Y3
% 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y2), inverse(Y0))), inverse(Y3))))), Y2) -> Y3
% 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, inverse(Y0)), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), Y2), inverse(X3))), inverse(Y3))))), Y2) -> Y3
% 15.05/15.14 double_divide(inverse(double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y0)), inverse(double_divide(X0, inverse(X2))))), Y2), inverse(X2))), inverse(Y3))))), Y2) -> Y3
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) -> C
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0)), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y1), inverse(Y2))), Y1) -> Y2
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X1, inverse(Y2)), inverse(double_divide(X1, inverse(X0))))), inverse(X3))))), Y1), inverse(X3))), Y1) -> Y2
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(Y1, inverse(Y2))), Y3), inverse(Y2))), Y3) -> Y1
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(double_divide(X0, inverse(X2))))), Y1), inverse(X2))), Y1) -> Y2
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(double_divide(X0, inverse(X2))))), inverse(Y1)), inverse(X2))), Y3), inverse(Y2))), Y3) -> Y1
% 15.05/15.14 double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), Y1), inverse(Y2))), Y1) -> Y2
% 15.05/15.14 double_divide(inverse(double_divide(inverse(double_divide(double_divide(Y1, Y2), inverse(double_divide(Y1, inverse(inverse(double_divide(X0, inverse(X0)))))))), inverse(Y3))), Y2) -> Y3
% 15.05/15.14 double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(inverse(inverse(double_divide(X1, Y1))), inverse(inverse(X1))) -> Y1
% 15.05/15.14 double_divide(inverse(inverse(inverse(double_divide(X0, inverse(X0))))), inverse(Y1)) -> Y1
% 15.05/15.14 double_divide(inverse(inverse(inverse(inverse(double_divide(X0, inverse(X0)))))), inverse(Y1)) -> Y1
% 15.05/15.14 f1(double_divide(inverse(a), inverse(b))) -> false__
% 15.05/15.14 f1(double_divide(inverse(b), inverse(a))) -> true__
% 15.05/15.14 f1(inverse(double_divide(a, b))) -> false__
% 15.05/15.14 f1(inverse(double_divide(b, a))) -> true__
% 15.05/15.14 f1(multiply(a, b)) -> true__
% 15.05/15.14 f1(multiply(b, a)) -> false__
% 15.05/15.14 inverse(double_divide(X1, Y0)) -> double_divide(inverse(X1), inverse(Y0))
% 15.05/15.14 inverse(double_divide(Y0, double_divide(X1, inverse(X1)))) -> Y0
% 15.05/15.14 inverse(double_divide(Y0, double_divide(double_divide(X0, double_divide(X1, inverse(X1))), X0))) -> Y0
% 15.05/15.14 inverse(double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))))) -> Y0
% 15.05/15.14 inverse(double_divide(Y0, inverse(X1))) -> double_divide(inverse(Y0), inverse(inverse(X1)))
% 15.05/15.14 inverse(double_divide(Y1, inverse(double_divide(X0, inverse(X0))))) -> Y1
% 15.05/15.14 inverse(inverse(Y1)) -> Y1
% 15.05/15.14 multiply(A, B) -> inverse(double_divide(B, A))
% 15.05/15.14 true__ -> false__
% 15.05/15.14 with the LPO induced by
% 15.05/15.14 a > b > f1 > multiply > inverse > double_divide > true__ > false__
% 15.05/15.14
% 15.05/15.14 % SZS output end Proof
% 15.05/15.14
%------------------------------------------------------------------------------