TSTP Solution File: GRP579-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 10:56:24 EDT 2022
% Result : Unsatisfiable 57.86s 57.68s
% Output : Proof 57.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP579-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 12:26:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 57.86/57.68 % SZS status Unsatisfiable
% 57.86/57.68 % SZS output start Proof
% 57.86/57.68 The input problem is unsatisfiable because
% 57.86/57.68
% 57.86/57.68 [1] the following set of Horn clauses is unsatisfiable:
% 57.86/57.68
% 57.86/57.68 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C
% 57.86/57.68 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 57.86/57.68 inverse(A) = double_divide(A, identity)
% 57.86/57.68 identity = double_divide(A, inverse(A))
% 57.86/57.68 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom
% 57.86/57.68
% 57.86/57.68 This holds because
% 57.86/57.68
% 57.86/57.68 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 57.86/57.68
% 57.86/57.68 E:
% 57.86/57.68 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C
% 57.86/57.68 f1(multiply(a3, multiply(b3, c3))) = false__
% 57.86/57.68 f1(multiply(multiply(a3, b3), c3)) = true__
% 57.86/57.68 identity = double_divide(A, inverse(A))
% 57.86/57.68 inverse(A) = double_divide(A, identity)
% 57.86/57.68 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 57.86/57.68 G:
% 57.86/57.68 true__ = false__
% 57.86/57.68
% 57.86/57.68 This holds because
% 57.86/57.68
% 57.86/57.68 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 57.86/57.68
% 57.86/57.68 double_divide(X0, inverse(identity)) = inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0)))))
% 57.86/57.68 double_divide(X1, X0) = double_divide(X0, X1)
% 57.86/57.68 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(X1, double_divide(X0, Y0)))
% 57.86/57.68 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), inverse(Y0)))
% 57.86/57.68 double_divide(Y0, inverse(X1)) = inverse(double_divide(X1, inverse(Y0)))
% 57.86/57.68 double_divide(Y0, inverse(double_divide(X1, X0))) = inverse(double_divide(double_divide(X0, X1), inverse(Y0)))
% 57.86/57.68 double_divide(Y0, inverse(double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), Y0)
% 57.86/57.68 double_divide(double_divide(Y0, Y1), X0) = double_divide(X0, double_divide(Y1, Y0))
% 57.86/57.68 inverse(double_divide(Y0, double_divide(X1, inverse(X0)))) = double_divide(X1, double_divide(X0, Y0))
% 57.86/57.68 inverse(double_divide(Y0, double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), inverse(Y0))
% 57.86/57.68 inverse(double_divide(Y0, inverse(X0))) = inverse(double_divide(inverse(X0), Y0))
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(X1, X0)))) = double_divide(double_divide(X0, X1), inverse(Y0))
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(X1, inverse(X0))))) = inverse(double_divide(double_divide(X0, inverse(X1)), Y0))
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y2))))) = double_divide(Y2, double_divide(Y1, Y0))
% 57.86/57.68 inverse(double_divide(Y0, inverse(inverse(Y1)))) = inverse(double_divide(Y1, Y0))
% 57.86/57.68 inverse(double_divide(Y2, inverse(double_divide(Y1, inverse(Y0))))) = inverse(double_divide(Y1, inverse(double_divide(Y2, inverse(Y0)))))
% 57.86/57.68 inverse(double_divide(double_divide(Y0, Y1), X0)) = inverse(double_divide(X0, double_divide(Y1, Y0)))
% 57.86/57.68 double_divide(A, identity) -> inverse(A)
% 57.86/57.68 double_divide(A, inverse(A)) -> identity
% 57.86/57.68 double_divide(X0, double_divide(X0, Y1)) -> Y1
% 57.86/57.68 double_divide(X0, double_divide(X1, inverse(double_divide(Y1, inverse(double_divide(X0, inverse(X1))))))) -> Y1
% 57.86/57.68 double_divide(X0, double_divide(identity, X0)) -> identity
% 57.86/57.68 double_divide(X0, double_divide(identity, inverse(inverse(X0)))) -> identity
% 57.86/57.68 double_divide(X0, inverse(double_divide(X1, inverse(double_divide(X2, double_divide(X1, X0)))))) -> inverse(X2)
% 57.86/57.68 double_divide(X0, inverse(double_divide(X1, inverse(double_divide(double_divide(X0, X1), X2))))) -> inverse(X2)
% 57.86/57.68 double_divide(X0, inverse(double_divide(X1, inverse(double_divide(double_divide(X1, X0), X2))))) -> inverse(X2)
% 57.86/57.68 double_divide(X0, inverse(double_divide(inverse(X0), X1))) -> inverse(X1)
% 57.86/57.68 double_divide(X0, inverse(inverse(inverse(X0)))) -> identity
% 57.86/57.68 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X0, X1)))) -> identity
% 57.86/57.68 double_divide(X1, double_divide(inverse(X0), inverse(double_divide(X1, X0)))) -> identity
% 57.86/57.68 double_divide(X2, double_divide(X0, inverse(double_divide(X1, inverse(double_divide(X2, double_divide(X0, X1))))))) -> identity
% 57.86/57.68 double_divide(X2, double_divide(X0, inverse(double_divide(X1, inverse(double_divide(X2, double_divide(X1, X0))))))) -> identity
% 57.86/57.68 double_divide(X2, double_divide(X0, inverse(double_divide(X1, inverse(double_divide(double_divide(X1, X0), X2)))))) -> identity
% 57.86/57.68 double_divide(Y0, double_divide(Y1, Y0)) -> Y1
% 57.86/57.68 double_divide(Y0, inverse(double_divide(Y1, inverse(Y0)))) -> inverse(Y1)
% 57.86/57.68 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) -> C
% 57.86/57.68 double_divide(double_divide(X0, double_divide(X1, X2)), inverse(double_divide(double_divide(X2, X1), X0))) -> identity
% 57.86/57.68 double_divide(double_divide(X0, double_divide(X1, inverse(X2))), double_divide(double_divide(X2, inverse(X1)), inverse(X0))) -> identity
% 57.86/57.68 double_divide(double_divide(X0, double_divide(inverse(identity), X0)), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(X0, inverse(X1)), inverse(double_divide(inverse(X1), X0))) -> identity
% 57.86/57.68 double_divide(double_divide(X0, inverse(double_divide(X1, X2))), double_divide(double_divide(X2, X1), inverse(X0))) -> identity
% 57.86/57.68 double_divide(double_divide(X0, inverse(double_divide(inverse(X0), X1))), X1) -> identity
% 57.86/57.68 double_divide(double_divide(Y0, double_divide(Y2, Y1)), inverse(double_divide(double_divide(Y2, Y1), Y0))) -> identity
% 57.86/57.68 double_divide(double_divide(Y0, double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(Y1))), inverse(identity)) -> Y2
% 57.86/57.68 double_divide(double_divide(Y0, double_divide(identity, inverse(Y1))), inverse(identity)) -> inverse(double_divide(Y1, Y0))
% 57.86/57.68 double_divide(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(Y0, inverse(double_divide(identity, double_divide(identity, Y0)))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(Y0, inverse(inverse(double_divide(double_divide(identity, inverse(inverse(identity))), Y0)))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(Y1, Y0), X1) -> inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(X1)))))
% 57.86/57.68 double_divide(double_divide(double_divide(X0, X1), X2), inverse(double_divide(X2, double_divide(X1, X0)))) -> identity
% 57.86/57.68 double_divide(double_divide(double_divide(X0, inverse(X1)), inverse(Y1)), double_divide(Y1, double_divide(X1, inverse(X0)))) -> identity
% 57.86/57.68 double_divide(double_divide(double_divide(X2, X1), inverse(X0)), double_divide(X0, inverse(double_divide(X1, X2)))) -> identity
% 57.86/57.68 double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(double_divide(Y2, double_divide(Y1, Y0)))) -> identity
% 57.86/57.68 double_divide(double_divide(identity, X0), inverse(inverse(X0))) -> identity
% 57.86/57.68 double_divide(double_divide(identity, double_divide(double_divide(inverse(Y1), Y2), inverse(Y1))), inverse(identity)) -> Y2
% 57.86/57.68 double_divide(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0)))), double_divide(X0, inverse(identity))) -> identity
% 57.86/57.68 double_divide(double_divide(identity, double_divide(inverse(X0), X0)), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(identity, double_divide(inverse(double_divide(identity, Y0)), inverse(Y0))), inverse(identity)) -> inverse(identity)
% 57.86/57.68 double_divide(double_divide(identity, double_divide(inverse(inverse(Y1)), inverse(Y1))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(identity, inverse(double_divide(identity, X0))), X0) -> identity
% 57.86/57.68 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(inverse(X0), X1), inverse(double_divide(X1, inverse(X0)))) -> identity
% 57.86/57.68 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y2), inverse(Y1))), inverse(identity)) -> Y2
% 57.86/57.68 double_divide(double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(inverse(identity), double_divide(inverse(X1), inverse(double_divide(identity, double_divide(double_divide(inverse(X0), X1), inverse(X0)))))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(X0, double_divide(inverse(double_divide(X1, X0)), inverse(X1)))))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(identity, double_divide(inverse(inverse(Y1)), inverse(Y1)))))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1)))))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(double_divide(identity, X0))), inverse(inverse(X0)))), inverse(identity)) -> identity
% 57.86/57.68 double_divide(identity, X0) -> inverse(X0)
% 57.86/57.68 double_divide(identity, double_divide(X0, double_divide(identity, X0))) -> identity
% 57.86/57.68 double_divide(identity, inverse(inverse(X0))) -> inverse(inverse(inverse(X0)))
% 57.86/57.68 double_divide(identity, inverse(inverse(identity))) -> inverse(inverse(identity))
% 57.86/57.68 double_divide(inverse(X0), X0) -> identity
% 57.86/57.68 double_divide(inverse(X0), inverse(double_divide(X0, X1))) -> inverse(X1)
% 57.86/57.68 double_divide(inverse(X0), inverse(double_divide(X1, X0))) -> inverse(X1)
% 57.86/57.68 double_divide(inverse(Y0), X1) -> inverse(double_divide(Y0, inverse(X1)))
% 57.86/57.68 double_divide(inverse(Y0), double_divide(Y1, inverse(Y0))) -> Y1
% 57.86/57.68 double_divide(inverse(Y0), double_divide(inverse(Y0), Y1)) -> Y1
% 57.86/57.68 double_divide(inverse(Y0), inverse(X1)) -> inverse(double_divide(Y0, X1))
% 57.86/57.68 double_divide(inverse(Y0), inverse(identity)) -> inverse(double_divide(identity, Y0))
% 57.86/57.68 double_divide(inverse(double_divide(X1, inverse(X0))), double_divide(inverse(X0), X1)) -> identity
% 57.86/57.68 double_divide(inverse(double_divide(X1, inverse(identity))), inverse(X1)) -> double_divide(inverse(identity), inverse(identity))
% 57.86/57.68 double_divide(inverse(double_divide(inverse(X1), X0)), double_divide(X0, inverse(X1))) -> identity
% 57.86/57.68 double_divide(inverse(inverse(X0)), double_divide(identity, X0)) -> identity
% 57.86/57.68 double_divide(inverse(inverse(double_divide(identity, Y1))), inverse(identity)) -> Y1
% 57.86/57.68 double_divide(inverse(inverse(inverse(X0))), X0) -> identity
% 57.86/57.68 f1(double_divide(double_divide(a3, b3), inverse(c3))) -> true__
% 57.86/57.68 f1(inverse(double_divide(a3, inverse(double_divide(b3, c3))))) -> false__
% 57.86/57.68 f1(inverse(double_divide(c3, inverse(double_divide(b3, a3))))) -> true__
% 57.86/57.68 f1(inverse(double_divide(inverse(double_divide(a3, b3)), c3))) -> true__
% 57.86/57.68 f1(inverse(double_divide(inverse(double_divide(c3, b3)), a3))) -> false__
% 57.86/57.68 f1(multiply(a3, multiply(b3, c3))) -> false__
% 57.86/57.68 f1(multiply(multiply(a3, b3), c3)) -> true__
% 57.86/57.68 inverse(double_divide(X1, double_divide(X0, double_divide(Y1, double_divide(X1, inverse(X0)))))) -> Y1
% 57.86/57.68 inverse(double_divide(Y0, double_divide(identity, Y0))) -> identity
% 57.86/57.68 inverse(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1)))) -> identity
% 57.86/57.68 inverse(double_divide(Y0, double_divide(inverse(double_divide(inverse(inverse(inverse(X0))), Y0)), X0))) -> identity
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(Y0))))) -> Y1
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(double_divide(Y2, double_divide(Y0, Y1))))))) -> Y2
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(double_divide(Y2, double_divide(Y1, Y0))))))) -> Y2
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(double_divide(double_divide(Y0, Y1), Y2)))))) -> Y2
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(Y1, inverse(double_divide(double_divide(Y1, Y0), Y2)))))) -> Y2
% 57.86/57.68 inverse(double_divide(Y0, inverse(double_divide(inverse(Y0), Y2)))) -> Y2
% 57.86/57.68 inverse(double_divide(double_divide(X2, double_divide(X1, X0)), double_divide(double_divide(double_divide(X0, X1), X2), inverse(Y1)))) -> Y1
% 57.86/57.68 inverse(double_divide(double_divide(X2, double_divide(X1, X0)), inverse(double_divide(Y1, inverse(double_divide(double_divide(X0, X1), X2)))))) -> Y1
% 57.86/57.68 inverse(double_divide(double_divide(X2, double_divide(X1, X0)), inverse(double_divide(double_divide(X0, X1), X2)))) -> identity
% 57.86/57.68 inverse(double_divide(double_divide(Y1, X1), inverse(double_divide(Y1, inverse(double_divide(X1, Y2)))))) -> Y2
% 57.86/57.68 inverse(double_divide(double_divide(double_divide(X0, X1), X2), double_divide(double_divide(X2, double_divide(X1, X0)), inverse(Y1)))) -> Y1
% 57.86/57.68 inverse(double_divide(double_divide(double_divide(X0, X1), X2), inverse(double_divide(Y1, inverse(double_divide(X2, double_divide(X1, X0))))))) -> Y1
% 57.86/57.68 inverse(double_divide(double_divide(double_divide(X2, X1), X0), inverse(double_divide(X0, double_divide(X1, X2))))) -> identity
% 57.86/57.68 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0))
% 57.86/57.68 inverse(double_divide(identity, double_divide(identity, double_divide(identity, inverse(inverse(identity)))))) -> identity
% 57.86/57.68 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))) -> inverse(X0)
% 57.86/57.68 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(Y0, double_divide(identity, Y0))))))) -> identity
% 57.86/57.68 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(identity, double_divide(X0, double_divide(identity, inverse(double_divide(identity, X0)))))))))) -> identity
% 57.86/57.68 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(identity, double_divide(identity, double_divide(identity, inverse(inverse(identity)))))))))) -> identity
% 57.86/57.68 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, inverse(inverse(inverse(identity)))))))) -> identity
% 57.86/57.68 inverse(double_divide(identity, double_divide(identity, inverse(inverse(identity))))) -> identity
% 57.86/57.68 inverse(double_divide(identity, double_divide(inverse(Y0), Y0))) -> identity
% 57.86/57.68 inverse(double_divide(identity, double_divide(inverse(inverse(Y0)), inverse(Y0)))) -> identity
% 57.86/57.68 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0
% 57.86/57.68 inverse(double_divide(identity, inverse(inverse(identity)))) -> identity
% 57.86/57.68 inverse(double_divide(inverse(X0), double_divide(inverse(X0), X1))) -> inverse(X1)
% 57.86/57.68 inverse(double_divide(inverse(X0), inverse(double_divide(X0, Y1)))) -> Y1
% 57.86/57.68 inverse(double_divide(inverse(Y0), X1)) -> double_divide(Y0, inverse(X1))
% 57.86/57.68 inverse(double_divide(inverse(Y0), double_divide(inverse(Y1), inverse(Y0)))) -> Y1
% 57.86/57.68 inverse(double_divide(inverse(Y0), inverse(X1))) -> double_divide(Y0, X1)
% 57.86/57.68 inverse(double_divide(inverse(Y0), inverse(double_divide(Y1, Y0)))) -> Y1
% 57.86/57.68 inverse(identity) -> identity
% 57.86/57.68 inverse(inverse(Y1)) -> Y1
% 57.86/57.68 inverse(inverse(double_divide(X0, inverse(inverse(inverse(X0)))))) -> identity
% 57.86/57.68 inverse(inverse(double_divide(double_divide(inverse(Y0), Y1), inverse(Y0)))) -> Y1
% 57.86/57.68 inverse(inverse(double_divide(inverse(Y0), Y0))) -> identity
% 57.86/57.68 inverse(inverse(double_divide(inverse(inverse(X0)), double_divide(identity, X0)))) -> identity
% 57.86/57.68 inverse(inverse(inverse(double_divide(identity, Y0)))) -> Y0
% 57.86/57.68 inverse(inverse(inverse(inverse(Y0)))) -> Y0
% 57.86/57.68 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 57.86/57.68 true__ -> false__
% 57.86/57.68 with the LPO induced by
% 57.86/57.68 c3 > b3 > a3 > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 57.86/57.68
% 57.86/57.68 % SZS output end Proof
% 57.86/57.68
%------------------------------------------------------------------------------