TSTP Solution File: GRP481-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP481-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n011.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 10:55:44 EDT 2022
% Result : Unsatisfiable 3.91s 3.95s
% Output : Proof 3.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP481-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jun 13 09:42:33 EDT 2022
% 0.12/0.32 % CPUTime :
% 3.91/3.95 % SZS status Unsatisfiable
% 3.91/3.95 % SZS output start Proof
% 3.91/3.95 The input problem is unsatisfiable because
% 3.91/3.95
% 3.91/3.95 [1] the following set of Horn clauses is unsatisfiable:
% 3.91/3.95
% 3.91/3.95 double_divide(double_divide(double_divide(A, double_divide(B, identity)), double_divide(double_divide(C, double_divide(D, double_divide(D, identity))), double_divide(A, identity))), B) = C
% 3.91/3.95 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 3.91/3.95 inverse(A) = double_divide(A, identity)
% 3.91/3.95 identity = double_divide(A, inverse(A))
% 3.91/3.95 multiply(inverse(a1), a1) = identity ==> \bottom
% 3.91/3.95
% 3.91/3.95 This holds because
% 3.91/3.95
% 3.91/3.95 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.91/3.95
% 3.91/3.95 E:
% 3.91/3.95 double_divide(double_divide(double_divide(A, double_divide(B, identity)), double_divide(double_divide(C, double_divide(D, double_divide(D, identity))), double_divide(A, identity))), B) = C
% 3.91/3.95 f1(identity) = false__
% 3.91/3.95 f1(multiply(inverse(a1), a1)) = true__
% 3.91/3.95 identity = double_divide(A, inverse(A))
% 3.91/3.95 inverse(A) = double_divide(A, identity)
% 3.91/3.95 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 3.91/3.95 G:
% 3.91/3.95 true__ = false__
% 3.91/3.95
% 3.91/3.95 This holds because
% 3.91/3.95
% 3.91/3.95 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.91/3.95
% 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), X2), Y1) = double_divide(double_divide(X2, identity), Y0)
% 3.91/3.95 double_divide(double_divide(double_divide(Y0, identity), Y2), identity) = double_divide(double_divide(Y2, identity), Y0)
% 3.91/3.95 double_divide(identity, Y1) = double_divide(Y1, identity)
% 3.91/3.95 double_divide(Y0, double_divide(Y0, identity)) -> identity
% 3.91/3.95 double_divide(Y0, double_divide(identity, Y0)) -> identity
% 3.91/3.95 double_divide(double_divide(X0, identity), X0) -> identity
% 3.91/3.95 double_divide(double_divide(Y0, identity), identity) -> Y0
% 3.91/3.95 double_divide(double_divide(double_divide(X0, inverse(identity)), double_divide(inverse(X1), inverse(X0))), X1) -> identity
% 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), double_divide(double_divide(Y2, identity), double_divide(Y0, identity))), Y1) -> Y2
% 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(Y1, identity)), identity), Y1) -> double_divide(identity, Y0)
% 3.91/3.95 double_divide(double_divide(double_divide(Y0, double_divide(identity, identity)), double_divide(double_divide(Y1, identity), double_divide(Y0, identity))), Y1) -> identity
% 3.91/3.95 double_divide(double_divide(double_divide(double_divide(Y0, identity), double_divide(identity, identity)), identity), Y0) -> identity
% 3.91/3.95 double_divide(double_divide(identity, double_divide(double_divide(Y0, identity), double_divide(Y1, identity))), Y1) -> Y0
% 3.91/3.95 double_divide(double_divide(identity, double_divide(identity, double_divide(Y1, identity))), Y1) -> identity
% 3.91/3.95 double_divide(double_divide(identity, identity), double_divide(Y0, identity)) -> Y0
% 3.91/3.95 double_divide(double_divide(identity, identity), multiply(identity, double_divide(Y0, identity))) -> Y0
% 3.91/3.95 double_divide(identity, double_divide(Y0, identity)) -> Y0
% 3.91/3.95 double_divide(identity, double_divide(identity, Y0)) -> Y0
% 3.91/3.95 double_divide(identity, double_divide(identity, double_divide(identity, double_divide(Y0, identity)))) -> Y0
% 3.91/3.95 double_divide(identity, identity) -> identity
% 3.91/3.95 double_divide(inverse(identity), inverse(inverse(inverse(Y2)))) -> Y2
% 3.91/3.95 f1(double_divide(identity, identity)) -> true__
% 3.91/3.95 f1(identity) -> false__
% 3.91/3.95 inverse(A) -> double_divide(A, identity)
% 3.91/3.95 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 3.91/3.95 true__ -> false__
% 3.91/3.95 with the LPO induced by
% 3.91/3.95 a1 > multiply > inverse > double_divide > identity > f1 > true__ > false__
% 3.91/3.95
% 3.91/3.95 % SZS output end Proof
% 3.91/3.95
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