TSTP Solution File: GRP494-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP494-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n022.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 4.06s 4.13s
% Output : Proof 4.06s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP494-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 04:46:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 4.06/4.13 % SZS status Unsatisfiable
% 4.06/4.13 % SZS output start Proof
% 4.06/4.13 The input problem is unsatisfiable because
% 4.06/4.13
% 4.06/4.13 [1] the following set of Horn clauses is unsatisfiable:
% 4.06/4.13
% 4.06/4.13 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B
% 4.06/4.13 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 4.06/4.13 inverse(A) = double_divide(A, identity)
% 4.06/4.13 identity = double_divide(A, inverse(A))
% 4.06/4.13 multiply(identity, a2) = a2 ==> \bottom
% 4.06/4.13
% 4.06/4.13 This holds because
% 4.06/4.13
% 4.06/4.13 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 4.06/4.13
% 4.06/4.13 E:
% 4.06/4.13 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B
% 4.06/4.13 f1(a2) = false__
% 4.06/4.13 f1(multiply(identity, a2)) = true__
% 4.06/4.13 identity = double_divide(A, inverse(A))
% 4.06/4.13 inverse(A) = double_divide(A, identity)
% 4.06/4.13 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 4.06/4.13 G:
% 4.06/4.13 true__ = false__
% 4.06/4.13
% 4.06/4.13 This holds because
% 4.06/4.13
% 4.06/4.13 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 4.06/4.13
% 4.06/4.13 double_divide(X0, identity) = double_divide(identity, X0)
% 4.06/4.13 double_divide(X0, double_divide(identity, X0)) -> identity
% 4.06/4.13 double_divide(Y0, double_divide(Y0, identity)) -> identity
% 4.06/4.13 double_divide(double_divide(X0, identity), X0) -> identity
% 4.06/4.13 double_divide(double_divide(Y0, identity), identity) -> Y0
% 4.06/4.13 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) -> B
% 4.06/4.13 double_divide(double_divide(identity, X0), X0) -> identity
% 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(Y0))) -> Y1
% 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, double_divide(Y1, identity)))) -> Y1
% 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, identity))) -> identity
% 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1
% 4.06/4.13 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(Y0))) -> identity
% 4.06/4.13 double_divide(double_divide(identity, Y0), identity) -> Y0
% 4.06/4.13 double_divide(double_divide(identity, Y0), inverse(double_divide(double_divide(Y1, inverse(Y0)), inverse(identity)))) -> Y1
% 4.06/4.13 double_divide(identity, double_divide(Y0, identity)) -> Y0
% 4.06/4.13 double_divide(identity, double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(inverse(identity), Y2))) -> Y1
% 4.06/4.13 double_divide(identity, double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(inverse(identity)))) -> Y1
% 4.06/4.13 double_divide(identity, double_divide(identity, X0)) -> X0
% 4.06/4.13 double_divide(identity, double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1
% 4.06/4.13 double_divide(identity, identity) -> identity
% 4.06/4.13 double_divide(identity, inverse(inverse(inverse(Y0)))) -> Y0
% 4.06/4.13 f1(a2) -> false__
% 4.06/4.13 f1(double_divide(double_divide(a2, identity), identity)) -> true__
% 4.06/4.13 inverse(A) -> double_divide(A, identity)
% 4.06/4.13 inverse(double_divide(identity, double_divide(X0, inverse(identity)))) -> double_divide(identity, X0)
% 4.06/4.13 inverse(inverse(X0)) -> double_divide(identity, double_divide(X0, identity))
% 4.06/4.13 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 4.06/4.13 true__ -> false__
% 4.06/4.13 with the LPO induced by
% 4.06/4.13 a2 > f1 > multiply > inverse > double_divide > identity > true__ > false__
% 4.06/4.13
% 4.06/4.13 % SZS output end Proof
% 4.06/4.13
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