TSTP Solution File: GRP577-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP577-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 11.74s 11.74s
% Output : Proof 11.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP577-1 : TPTP v8.1.0. Released v2.6.0.
% 0.15/0.14 % Command : moca.sh %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 06:21:05 EDT 2022
% 0.15/0.35 % CPUTime :
% 11.74/11.74 % SZS status Unsatisfiable
% 11.74/11.74 % SZS output start Proof
% 11.74/11.74 The input problem is unsatisfiable because
% 11.74/11.74
% 11.74/11.74 [1] the following set of Horn clauses is unsatisfiable:
% 11.74/11.74
% 11.74/11.74 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C
% 11.74/11.74 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 11.74/11.74 inverse(A) = double_divide(A, identity)
% 11.74/11.74 identity = double_divide(A, inverse(A))
% 11.74/11.74 multiply(inverse(a1), a1) = identity ==> \bottom
% 11.74/11.74
% 11.74/11.74 This holds because
% 11.74/11.74
% 11.74/11.74 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 11.74/11.74
% 11.74/11.74 E:
% 11.74/11.74 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C
% 11.74/11.74 f1(identity) = false__
% 11.74/11.74 f1(multiply(inverse(a1), a1)) = true__
% 11.74/11.74 identity = double_divide(A, inverse(A))
% 11.74/11.74 inverse(A) = double_divide(A, identity)
% 11.74/11.74 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 11.74/11.74 G:
% 11.74/11.74 true__ = false__
% 11.74/11.74
% 11.74/11.74 This holds because
% 11.74/11.74
% 11.74/11.74 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 11.74/11.74
% 11.74/11.74 double_divide(X0, inverse(identity)) = inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0)))))
% 11.74/11.74 double_divide(A, identity) -> inverse(A)
% 11.74/11.74 double_divide(A, inverse(A)) -> identity
% 11.74/11.74 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) -> C
% 11.74/11.74 double_divide(double_divide(X0, double_divide(inverse(identity), X0)), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(Y0, double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(Y1))), inverse(identity)) -> Y2
% 11.74/11.74 double_divide(double_divide(Y0, double_divide(identity, inverse(Y1))), inverse(identity)) -> inverse(double_divide(Y1, Y0))
% 11.74/11.74 double_divide(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1))), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(Y0, inverse(double_divide(identity, double_divide(identity, Y0)))), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(Y0, inverse(inverse(double_divide(double_divide(identity, inverse(inverse(identity))), Y0)))), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(double_divide(X1, double_divide(identity, Y0)), X2), inverse(X1)) -> double_divide(double_divide(Y0, X2), inverse(identity))
% 11.74/11.74 double_divide(double_divide(identity, double_divide(X0, inverse(inverse(double_divide(identity, X0))))), inverse(identity)) -> inverse(identity)
% 11.74/11.74 double_divide(double_divide(identity, double_divide(double_divide(inverse(Y1), Y2), inverse(Y1))), inverse(identity)) -> Y2
% 11.74/11.74 double_divide(double_divide(identity, double_divide(inverse(X0), X0)), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(identity, double_divide(inverse(double_divide(identity, Y0)), inverse(Y0))), inverse(identity)) -> inverse(identity)
% 11.74/11.74 double_divide(double_divide(identity, double_divide(inverse(inverse(Y1)), inverse(Y1))), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(identity, inverse(double_divide(identity, X0))), X0) -> identity
% 11.74/11.74 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y2), inverse(Y1))), inverse(identity)) -> Y2
% 11.74/11.74 double_divide(double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> identity
% 11.74/11.74 double_divide(double_divide(inverse(identity), double_divide(inverse(X0), inverse(inverse(inverse(double_divide(identity, X0)))))), inverse(identity)) -> identity
% 11.74/11.74 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
% 11.74/11.74 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
% 11.74/11.74 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(double_divide(identity, X0))), inverse(inverse(X0)))), inverse(identity)) -> identity
% 11.74/11.74 double_divide(identity, inverse(inverse(identity))) -> inverse(inverse(identity))
% 11.74/11.74 double_divide(inverse(Y0), inverse(identity)) -> inverse(double_divide(identity, Y0))
% 11.74/11.74 double_divide(inverse(double_divide(X1, inverse(identity))), inverse(X1)) -> double_divide(inverse(identity), inverse(identity))
% 11.74/11.74 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity)))) -> identity
% 11.74/11.74 double_divide(inverse(inverse(double_divide(identity, Y1))), inverse(identity)) -> Y1
% 11.74/11.74 f1(identity) -> false__
% 11.74/11.74 f1(inverse(identity)) -> true__
% 11.74/11.74 f1(multiply(inverse(a1), a1)) -> true__
% 11.74/11.74 inverse(double_divide(Y0, double_divide(identity, Y0))) -> identity
% 11.74/11.74 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0))
% 11.74/11.74 inverse(double_divide(identity, double_divide(identity, double_divide(identity, inverse(inverse(identity)))))) -> identity
% 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))) -> inverse(X0)
% 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(Y0, double_divide(identity, Y0))))))) -> identity
% 11.74/11.74 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
% 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(identity, double_divide(identity, double_divide(identity, inverse(inverse(identity)))))))))) -> identity
% 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, inverse(inverse(inverse(identity)))))))) -> identity
% 11.74/11.74 inverse(double_divide(identity, double_divide(identity, inverse(inverse(identity))))) -> identity
% 11.74/11.74 inverse(double_divide(identity, double_divide(inverse(Y0), Y0))) -> identity
% 11.74/11.74 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0
% 11.74/11.74 inverse(double_divide(identity, inverse(inverse(identity)))) -> identity
% 11.74/11.74 inverse(identity) -> identity
% 11.74/11.74 inverse(inverse(inverse(double_divide(identity, Y0)))) -> Y0
% 11.74/11.74 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 11.74/11.74 true__ -> false__
% 11.74/11.74 with the LPO induced by
% 11.74/11.74 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 11.74/11.74
% 11.74/11.74 % SZS output end Proof
% 11.74/11.74
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