TSTP Solution File: GRP493-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP493-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n016.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 10:55:49 EDT 2022
% Result : Unsatisfiable 0.94s 1.14s
% Output : Proof 0.94s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP493-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : moca.sh %s
% 0.13/0.35 % Computer : n016.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 : Tue Jun 14 13:40:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.94/1.14 % SZS status Unsatisfiable
% 0.94/1.14 % SZS output start Proof
% 0.94/1.14 The input problem is unsatisfiable because
% 0.94/1.14
% 0.94/1.14 [1] the following set of Horn clauses is unsatisfiable:
% 0.94/1.14
% 0.94/1.14 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B
% 0.94/1.14 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 0.94/1.14 inverse(A) = double_divide(A, identity)
% 0.94/1.14 identity = double_divide(A, inverse(A))
% 0.94/1.14 multiply(inverse(a1), a1) = identity ==> \bottom
% 0.94/1.14
% 0.94/1.14 This holds because
% 0.94/1.14
% 0.94/1.14 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.94/1.14
% 0.94/1.14 E:
% 0.94/1.14 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B
% 0.94/1.14 f1(identity) = false__
% 0.94/1.14 f1(multiply(inverse(a1), a1)) = true__
% 0.94/1.14 identity = double_divide(A, inverse(A))
% 0.94/1.14 inverse(A) = double_divide(A, identity)
% 0.94/1.14 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 0.94/1.14 G:
% 0.94/1.14 true__ = false__
% 0.94/1.14
% 0.94/1.14 This holds because
% 0.94/1.14
% 0.94/1.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.94/1.14
% 0.94/1.14 double_divide(X0, inverse(identity)) = double_divide(identity, double_divide(inverse(identity), inverse(X0)))
% 0.94/1.14 double_divide(inverse(identity), double_divide(identity, double_divide(identity, X0))) = double_divide(identity, double_divide(inverse(X0), inverse(identity)))
% 0.94/1.14 double_divide(A, identity) -> inverse(A)
% 0.94/1.14 double_divide(A, inverse(A)) -> identity
% 0.94/1.14 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) -> B
% 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(Y0, Y2))) -> Y1
% 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(Y0))) -> Y1
% 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1
% 0.94/1.14 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(Y0))) -> identity
% 0.94/1.14 double_divide(double_divide(identity, Y0), inverse(double_divide(double_divide(Y1, inverse(Y0)), inverse(identity)))) -> Y1
% 0.94/1.14 double_divide(double_divide(identity, Y1), inverse(identity)) -> Y1
% 0.94/1.14 double_divide(double_divide(identity, double_divide(identity, X0)), double_divide(identity, X0)) -> identity
% 0.94/1.14 double_divide(double_divide(identity, double_divide(inverse(X0), inverse(identity))), X0) -> identity
% 0.94/1.14 double_divide(double_divide(identity, inverse(inverse(Y0))), Y0) -> identity
% 0.94/1.14 double_divide(identity, double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(inverse(identity), Y2))) -> Y1
% 0.94/1.14 double_divide(identity, double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(inverse(identity)))) -> Y1
% 0.94/1.14 double_divide(identity, double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0
% 0.94/1.14 double_divide(identity, double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1
% 0.94/1.14 double_divide(identity, double_divide(identity, inverse(Y0))) -> inverse(Y0)
% 0.94/1.14 double_divide(identity, double_divide(inverse(X0), inverse(identity))) -> inverse(double_divide(identity, double_divide(X0, inverse(identity))))
% 0.94/1.14 double_divide(inverse(identity), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(identity, Y2))) -> Y1
% 0.94/1.14 double_divide(inverse(identity), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(identity))) -> Y1
% 0.94/1.14 double_divide(inverse(identity), double_divide(identity, double_divide(identity, inverse(Y1)))) -> Y1
% 0.94/1.14 double_divide(inverse(identity), inverse(double_divide(double_divide(Y1, inverse(identity)), inverse(identity)))) -> Y1
% 0.94/1.14 double_divide(inverse(identity), inverse(identity)) -> identity
% 0.94/1.14 f1(identity) -> false__
% 0.94/1.14 f1(inverse(identity)) -> true__
% 0.94/1.14 f1(multiply(inverse(a1), a1)) -> true__
% 0.94/1.14 inverse(double_divide(identity, Y0)) -> Y0
% 0.94/1.14 inverse(double_divide(identity, double_divide(inverse(Y1), inverse(identity)))) -> Y1
% 0.94/1.14 inverse(double_divide(identity, inverse(inverse(Y0)))) -> Y0
% 0.94/1.14 inverse(identity) -> identity
% 0.94/1.14 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 0.94/1.14 true__ -> false__
% 0.94/1.14 with the LPO induced by
% 0.94/1.14 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 0.94/1.14
% 0.94/1.14 % SZS output end Proof
% 0.94/1.14
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