TSTP Solution File: GRP496-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP496-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n017.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 10:55:50 EDT 2022
% Result : Unsatisfiable 1.25s 1.36s
% Output : Proof 1.25s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP496-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.14 % Command : moca.sh %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 21:10:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.25/1.36 % SZS status Unsatisfiable
% 1.25/1.36 % SZS output start Proof
% 1.25/1.36 The input problem is unsatisfiable because
% 1.25/1.36
% 1.25/1.36 [1] the following set of Horn clauses is unsatisfiable:
% 1.25/1.36
% 1.25/1.36 double_divide(double_divide(identity, double_divide(A, double_divide(B, identity))), double_divide(double_divide(B, double_divide(C, A)), identity)) = C
% 1.25/1.36 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 1.25/1.36 inverse(A) = double_divide(A, identity)
% 1.25/1.36 identity = double_divide(A, inverse(A))
% 1.25/1.36 multiply(inverse(a1), a1) = identity ==> \bottom
% 1.25/1.36
% 1.25/1.36 This holds because
% 1.25/1.36
% 1.25/1.36 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.25/1.36
% 1.25/1.36 E:
% 1.25/1.36 double_divide(double_divide(identity, double_divide(A, double_divide(B, identity))), double_divide(double_divide(B, double_divide(C, A)), identity)) = C
% 1.25/1.36 f1(identity) = false__
% 1.25/1.36 f1(multiply(inverse(a1), a1)) = true__
% 1.25/1.36 identity = double_divide(A, inverse(A))
% 1.25/1.36 inverse(A) = double_divide(A, identity)
% 1.25/1.36 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 1.25/1.36 G:
% 1.25/1.36 true__ = false__
% 1.25/1.36
% 1.25/1.36 This holds because
% 1.25/1.36
% 1.25/1.36 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.25/1.36
% 1.25/1.36 double_divide(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(X0, inverse(X1)))))), inverse(X2)) = double_divide(X1, double_divide(X2, X0))
% 1.25/1.36 double_divide(A, identity) -> inverse(A)
% 1.25/1.36 double_divide(A, inverse(A)) -> identity
% 1.25/1.36 double_divide(Y1, double_divide(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(Y0, inverse(Y1)))))), Y0)) -> identity
% 1.25/1.36 double_divide(double_divide(identity, X2), inverse(double_divide(double_divide(X1, double_divide(X2, X0)), double_divide(Y2, double_divide(identity, double_divide(X0, inverse(X1))))))) -> Y2
% 1.25/1.36 double_divide(double_divide(identity, double_divide(A, double_divide(B, identity))), double_divide(double_divide(B, double_divide(C, A)), identity)) -> C
% 1.25/1.36 double_divide(double_divide(identity, double_divide(Y0, inverse(Y1))), inverse(double_divide(Y1, double_divide(Y2, Y0)))) -> Y2
% 1.25/1.36 double_divide(double_divide(identity, double_divide(identity, inverse(Y1))), inverse(double_divide(Y1, inverse(Y2)))) -> Y2
% 1.25/1.36 double_divide(double_divide(identity, double_divide(identity, inverse(Y1))), inverse(identity)) -> Y1
% 1.25/1.36 double_divide(double_divide(identity, double_divide(identity, inverse(Y1))), inverse(inverse(Y1))) -> identity
% 1.25/1.36 double_divide(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(identity, inverse(Y0)))))), inverse(Y1)) -> double_divide(Y0, inverse(Y1))
% 1.25/1.36 double_divide(double_divide(identity, double_divide(inverse(Y2), inverse(Y1))), inverse(inverse(Y1))) -> Y2
% 1.25/1.36 double_divide(double_divide(identity, double_divide(inverse(double_divide(X1, double_divide(X2, X0))), inverse(Y1))), inverse(double_divide(Y1, X2))) -> double_divide(identity, double_divide(X0, inverse(X1)))
% 1.25/1.36 double_divide(identity, inverse(double_divide(Y0, double_divide(Y1, Y0)))) -> Y1
% 1.25/1.36 double_divide(identity, inverse(double_divide(identity, inverse(Y0)))) -> Y0
% 1.25/1.36 double_divide(identity, inverse(inverse(inverse(Y0)))) -> Y0
% 1.25/1.36 double_divide(inverse(identity), inverse(double_divide(Y1, double_divide(Y2, Y1)))) -> Y2
% 1.25/1.36 double_divide(inverse(identity), inverse(double_divide(identity, inverse(Y1)))) -> Y1
% 1.25/1.36 double_divide(inverse(identity), inverse(inverse(inverse(Y0)))) -> Y0
% 1.25/1.36 f1(identity) -> false__
% 1.25/1.36 f1(inverse(identity)) -> true__
% 1.25/1.36 f1(multiply(inverse(a1), a1)) -> true__
% 1.25/1.36 inverse(double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0
% 1.25/1.36 inverse(double_divide(identity, inverse(inverse(Y0)))) -> Y0
% 1.25/1.36 inverse(identity) -> identity
% 1.25/1.36 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 1.25/1.36 true__ -> false__
% 1.25/1.36 with the LPO induced by
% 1.25/1.36 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 1.25/1.36
% 1.25/1.36 % SZS output end Proof
% 1.25/1.36
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