TSTP Solution File: GRP586-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP586-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 10:56:27 EDT 2022
% Result : Unsatisfiable 117.69s 117.86s
% Output : Proof 117.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP586-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : moca.sh %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 23:45:02 EDT 2022
% 0.11/0.33 % CPUTime :
% 117.69/117.86 % SZS status Unsatisfiable
% 117.69/117.86 % SZS output start Proof
% 117.69/117.86 The input problem is unsatisfiable because
% 117.69/117.86
% 117.69/117.86 [1] the following set of Horn clauses is unsatisfiable:
% 117.69/117.86
% 117.69/117.86 double_divide(A, inverse(double_divide(inverse(double_divide(double_divide(A, B), inverse(C))), B))) = C
% 117.69/117.86 multiply(A, B) = inverse(double_divide(B, A))
% 117.69/117.86 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom
% 117.69/117.86
% 117.69/117.86 This holds because
% 117.69/117.86
% 117.69/117.86 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 117.69/117.86
% 117.69/117.86 E:
% 117.69/117.86 double_divide(A, inverse(double_divide(inverse(double_divide(double_divide(A, B), inverse(C))), B))) = C
% 117.69/117.86 f1(a2) = false__
% 117.69/117.86 f1(multiply(multiply(inverse(b2), b2), a2)) = true__
% 117.69/117.86 multiply(A, B) = inverse(double_divide(B, A))
% 117.69/117.86 G:
% 117.69/117.86 true__ = false__
% 117.69/117.86
% 117.69/117.86 This holds because
% 117.69/117.86
% 117.69/117.86 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 117.69/117.86
% 117.69/117.86 double_divide(Y0, inverse(Y0)) = double_divide(X0, inverse(X0))
% 117.69/117.86 double_divide(Y0, inverse(double_divide(inverse(X2), Y1))) = double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1)
% 117.69/117.86 double_divide(Y0, inverse(double_divide(inverse(double_divide(double_divide(double_divide(inverse(Y1), X2), X3), inverse(X1))), X3))) = double_divide(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), Y3), inverse(Y1))), Y3)
% 117.69/117.86 double_divide(double_divide(X0, double_divide(false__, inverse(false__))), X0) = double_divide(Y1, inverse(Y1))
% 117.69/117.86 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(Y1, inverse(Y1))
% 117.69/117.86 double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))) = double_divide(false__, inverse(false__))
% 117.69/117.86 double_divide(double_divide(Y0, inverse(Y0)), X0) = double_divide(X0, double_divide(false__, inverse(false__)))
% 117.69/117.86 double_divide(double_divide(false__, inverse(false__)), double_divide(X1, inverse(X1))) = double_divide(X0, inverse(X0))
% 117.69/117.86 double_divide(inverse(Y0), inverse(inverse(Y0))) = inverse(double_divide(X0, inverse(X0)))
% 117.69/117.86 double_divide(inverse(double_divide(X2, inverse(Y2))), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1))) = double_divide(inverse(double_divide(double_divide(Y0, Y3), inverse(Y2))), Y3)
% 117.69/117.86 double_divide(inverse(double_divide(X2, inverse(Y3))), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1))) = double_divide(Y0, inverse(double_divide(inverse(Y3), Y1)))
% 117.69/117.86 double_divide(inverse(double_divide(Y0, double_divide(X1, inverse(X1)))), inverse(Y0)) = double_divide(X0, inverse(X0))
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(X2, Y2), inverse(Y3))), Y2) = double_divide(Y0, inverse(double_divide(inverse(Y3), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1)))))
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(Y0, Y1), inverse(X2))), Y1) = double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1)
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), X3), inverse(Y1))), X3) = double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(Y1))), Y3)
% 117.69/117.86 inverse(double_divide(Y1, inverse(Y1))) = double_divide(X0, inverse(X0))
% 117.69/117.86 inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))) = double_divide(Y1, inverse(Y1))
% 117.69/117.86 double_divide(A, inverse(double_divide(inverse(double_divide(double_divide(A, B), inverse(C))), B))) -> C
% 117.69/117.86 double_divide(X1, inverse(double_divide(inverse(Y2), inverse(X1)))) -> Y2
% 117.69/117.86 double_divide(Y0, inverse(double_divide(inverse(double_divide(X2, inverse(Y2))), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1))))) -> Y2
% 117.69/117.86 double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(inverse(Y2), X1))))) -> Y2
% 117.69/117.86 double_divide(double_divide(X1, inverse(X1)), inverse(Y1)) -> Y1
% 117.69/117.86 double_divide(double_divide(double_divide(X0, double_divide(false__, inverse(false__))), X0), inverse(Y1)) -> Y1
% 117.69/117.86 double_divide(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1))), inverse(Y1)) -> Y1
% 117.69/117.86 double_divide(double_divide(inverse(X1), inverse(inverse(Y1))), inverse(X1)) -> Y1
% 117.69/117.86 double_divide(inverse(X1), inverse(inverse(double_divide(Y1, inverse(X1))))) -> Y1
% 117.69/117.86 double_divide(inverse(Y0), double_divide(X1, inverse(X1))) -> Y0
% 117.69/117.86 double_divide(inverse(Y0), inverse(inverse(inverse(double_divide(X0, inverse(X0)))))) -> Y0
% 117.69/117.86 double_divide(inverse(Y1), double_divide(false__, inverse(false__))) -> Y1
% 117.69/117.86 double_divide(inverse(Y1), inverse(inverse(double_divide(X0, inverse(X0))))) -> Y1
% 117.69/117.86 double_divide(inverse(double_divide(X0, inverse(X1))), inverse(double_divide(inverse(double_divide(X1, inverse(Y2))), inverse(X0)))) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(X2, inverse(X2))), inverse(Y2)) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(X2, inverse(double_divide(Y0, inverse(Y2))))), inverse(double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1))) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(X2, inverse(double_divide(double_divide(Y0, Y1), inverse(Y3))))), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1))) -> Y3
% 117.69/117.86 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
% 117.69/117.86 double_divide(inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), Y1), inverse(double_divide(double_divide(X0, X1), inverse(X3))))), inverse(Y2))))), Y1) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(Y1, inverse(Y2))), inverse(Y1)) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(X2))), inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, X3), inverse(X2))), X3), inverse(Y2))), Y1))) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(double_divide(X0, inverse(X2))))), inverse(double_divide(inverse(double_divide(X2, inverse(Y2))), Y1))) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(X0, inverse(X0)), double_divide(X1, inverse(X1)))), inverse(Y1)) -> Y1
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(X2, Y2), inverse(double_divide(X2, inverse(Y3))))), Y2) -> Y3
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(Y0, X1), inverse(X2))), X1) -> double_divide(inverse(X2), inverse(Y0))
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(Y0, Y3), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), X1), inverse(X2))), X1)))), Y3) -> double_divide(inverse(X2), Y1)
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), Y1), inverse(X3))), inverse(double_divide(inverse(double_divide(double_divide(X0, inverse(double_divide(inverse(X3), X1))), inverse(Y2))), Y1))) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), Y1), inverse(double_divide(double_divide(X0, X1), inverse(X3))))), inverse(double_divide(inverse(double_divide(X3, inverse(Y2))), Y1))) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), Y2), inverse(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))), X3)))), Y2) -> double_divide(inverse(X1), X2)
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(double_divide(double_divide(X0, Y2), inverse(double_divide(X0, inverse(X2))))))), Y3) -> double_divide(Y0, inverse(X2))
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(double_divide(double_divide(Y0, Y2), inverse(X2))))), Y3) -> X2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y2), Y3), inverse(double_divide(double_divide(double_divide(X0, X1), Y2), inverse(double_divide(double_divide(X0, X1), inverse(X3))))))), Y3) -> double_divide(Y0, inverse(X3))
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), Y2), inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), inverse(Y3))))), Y2) -> Y3
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), false__), inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), inverse(Y2))))), false__) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), Y2), inverse(double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), X2))), inverse(Y3))))), Y2) -> Y3
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(inverse(double_divide(X0, inverse(X0))), Y1), inverse(Y2))), Y1) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, X3), inverse(X2))), X3), inverse(double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(X2))), inverse(Y2))))), Y1) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, Y1), inverse(double_divide(X0, inverse(X2))))), Y3), inverse(Y2))), Y3) -> double_divide(inverse(double_divide(X2, inverse(Y2))), Y1)
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X0, inverse(Y2)), inverse(X2))), Y1), inverse(double_divide(inverse(double_divide(double_divide(X0, X3), inverse(X2))), X3)))), Y1) -> Y2
% 117.69/117.86 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
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), inverse(Y2)), inverse(double_divide(double_divide(X0, X1), inverse(X3))))), Y1), inverse(X3))), Y1) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(Y0, X2), X3), inverse(X1))), X3), inverse(double_divide(Y0, inverse(Y2))))), inverse(double_divide(inverse(X1), X2))) -> Y2
% 117.69/117.86 double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))), X3), inverse(double_divide(double_divide(Y0, Y1), inverse(Y3))))), inverse(double_divide(inverse(X1), X2))) -> Y3
% 117.69/117.86 double_divide(inverse(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(double_divide(Y0, Y1), false__), X3), false__), inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))))), false__)), false__) -> double_divide(inverse(X1), X2)
% 117.69/117.86 double_divide(inverse(double_divide(inverse(double_divide(double_divide(double_divide(false__, X3), false__), inverse(double_divide(double_divide(double_divide(double_divide(Y0, Y1), X2), X3), inverse(X1))))), false__)), inverse(double_divide(inverse(double_divide(double_divide(double_divide(Y0, Y1), false__), inverse(false__))), false__))) -> double_divide(inverse(X1), X2)
% 117.69/117.86 double_divide(inverse(inverse(double_divide(X0, inverse(X0)))), inverse(Y1)) -> Y1
% 117.69/117.86 double_divide(inverse(inverse(inverse(double_divide(X0, inverse(X0))))), inverse(Y1)) -> Y1
% 117.69/117.86 f1(a2) -> false__
% 117.69/117.86 f1(inverse(double_divide(a2, inverse(double_divide(b2, inverse(b2)))))) -> true__
% 117.69/117.86 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__
% 117.69/117.86 inverse(double_divide(Y1, inverse(double_divide(X0, inverse(X0))))) -> Y1
% 117.69/117.86 multiply(A, B) -> inverse(double_divide(B, A))
% 117.69/117.86 true__ -> false__
% 117.69/117.86 with the LPO induced by
% 117.69/117.86 b2 > a2 > f1 > multiply > inverse > double_divide > true__ > false__
% 117.69/117.86
% 117.69/117.86 % SZS output end Proof
% 117.69/117.86
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