TSTP Solution File: GRP569-1 by Moca---0.1
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% File : Moca---0.1
% Problem : GRP569-1 : 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 10:56:20 EDT 2022
% Result : Unsatisfiable 3.79s 3.87s
% Output : Proof 3.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP569-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : moca.sh %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 18:05:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.79/3.87 % SZS status Unsatisfiable
% 3.79/3.87 % SZS output start Proof
% 3.79/3.87 The input problem is unsatisfiable because
% 3.79/3.87
% 3.79/3.87 [1] the following set of Horn clauses is unsatisfiable:
% 3.79/3.87
% 3.79/3.87 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B
% 3.79/3.87 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 3.79/3.87 inverse(A) = double_divide(A, identity)
% 3.79/3.87 identity = double_divide(A, inverse(A))
% 3.79/3.87 multiply(inverse(a1), a1) = identity ==> \bottom
% 3.79/3.87
% 3.79/3.87 This holds because
% 3.79/3.87
% 3.79/3.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.79/3.87
% 3.79/3.87 E:
% 3.79/3.87 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) = B
% 3.79/3.87 f1(identity) = false__
% 3.79/3.87 f1(multiply(inverse(a1), a1)) = true__
% 3.79/3.87 identity = double_divide(A, inverse(A))
% 3.79/3.87 inverse(A) = double_divide(A, identity)
% 3.79/3.87 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 3.79/3.87 G:
% 3.79/3.87 true__ = false__
% 3.79/3.87
% 3.79/3.87 This holds because
% 3.79/3.87
% 3.79/3.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.79/3.87
% 3.79/3.87
% 3.79/3.87 double_divide(A, inverse(A)) -> identity
% 3.79/3.87 double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(C, identity))), double_divide(identity, identity)) -> B
% 3.79/3.87 double_divide(double_divide(Y0, double_divide(inverse(Y1), inverse(inverse(Y0)))), inverse(identity)) -> Y1
% 3.79/3.87 double_divide(double_divide(identity, double_divide(X0, double_divide(identity, identity))), double_divide(identity, identity)) -> double_divide(X0, identity)
% 3.79/3.87 double_divide(identity, identity) -> identity
% 3.79/3.87 double_divide(inverse(Y0), inverse(identity)) -> Y0
% 3.79/3.87 f1(identity) -> false__
% 3.79/3.87 f1(inverse(identity)) -> true__
% 3.79/3.87 f1(multiply(inverse(a1), a1)) -> true__
% 3.79/3.87 inverse(A) -> double_divide(A, identity)
% 3.79/3.87 inverse(identity) -> identity
% 3.79/3.87 inverse(inverse(X0)) -> double_divide(double_divide(identity, X0), double_divide(identity, identity))
% 3.79/3.87 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 3.79/3.87 true__ -> false__
% 3.79/3.87 with the LPO induced by
% 3.79/3.87 a1 > multiply > inverse > double_divide > f1 > identity > true__ > false__
% 3.79/3.87
% 3.79/3.87 % SZS output end Proof
% 3.79/3.87
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