TSTP Solution File: GRP491-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP491-1 : 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 10:55:48 EDT 2022
% Result : Unsatisfiable 6.13s 6.13s
% Output : Proof 6.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP491-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 14:17:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.13/6.13 % SZS status Unsatisfiable
% 6.13/6.13 % SZS output start Proof
% 6.13/6.13 The input problem is unsatisfiable because
% 6.13/6.13
% 6.13/6.13 [1] the following set of Horn clauses is unsatisfiable:
% 6.13/6.13
% 6.13/6.13 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) = C
% 6.13/6.13 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 6.13/6.13 inverse(A) = double_divide(A, identity)
% 6.13/6.13 identity = double_divide(A, inverse(A))
% 6.13/6.13 multiply(identity, a2) = a2 ==> \bottom
% 6.13/6.13
% 6.13/6.13 This holds because
% 6.13/6.13
% 6.13/6.13 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 6.13/6.13
% 6.13/6.13 E:
% 6.13/6.13 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) = C
% 6.13/6.13 f1(a2) = false__
% 6.13/6.13 f1(multiply(identity, a2)) = true__
% 6.13/6.13 identity = double_divide(A, inverse(A))
% 6.13/6.13 inverse(A) = double_divide(A, identity)
% 6.13/6.13 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 6.13/6.13 G:
% 6.13/6.13 true__ = false__
% 6.13/6.13
% 6.13/6.13 This holds because
% 6.13/6.13
% 6.13/6.13 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 6.13/6.13
% 6.13/6.13 double_divide(X0, double_divide(identity, inverse(inverse(identity)))) = double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(X0)))
% 6.13/6.13 double_divide(X0, inverse(identity)) = inverse(inverse(double_divide(identity, double_divide(identity, inverse(X0)))))
% 6.13/6.13 double_divide(X0, inverse(identity)) = inverse(inverse(double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(X0)))))
% 6.13/6.13 double_divide(X0, inverse(identity)) = inverse(inverse(double_divide(identity, inverse(inverse(double_divide(inverse(identity), inverse(X0)))))))
% 6.13/6.13 double_divide(A, identity) -> inverse(A)
% 6.13/6.13 double_divide(A, inverse(A)) -> identity
% 6.13/6.13 double_divide(X0, double_divide(identity, X0)) -> identity
% 6.13/6.13 double_divide(X0, double_divide(identity, double_divide(inverse(X0), inverse(Y1)))) -> Y1
% 6.13/6.13 double_divide(double_divide(identity, A), double_divide(identity, double_divide(double_divide(double_divide(A, B), identity), double_divide(C, B)))) -> C
% 6.13/6.13 double_divide(double_divide(identity, X0), X0) -> identity
% 6.13/6.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, X0))) -> inverse(X0)
% 6.13/6.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1
% 6.13/6.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(double_divide(Y0, Y1)), double_divide(Y2, Y1)))) -> Y2
% 6.13/6.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(identity), double_divide(Y2, inverse(Y0))))) -> Y2
% 6.13/6.13 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(inverse(inverse(Y0)), inverse(Y2)))) -> Y2
% 6.13/6.13 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(inverse(double_divide(Y0, inverse(Y2)))))) -> Y2
% 6.13/6.13 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(inverse(inverse(Y0))))) -> inverse(inverse(identity))
% 6.13/6.13 double_divide(double_divide(identity, Y0), inverse(identity)) -> inverse(inverse(Y0))
% 6.13/6.13 double_divide(double_divide(identity, Y1), double_divide(identity, inverse(inverse(identity)))) -> Y1
% 6.13/6.13 double_divide(double_divide(identity, inverse(X0)), inverse(X0)) -> identity
% 6.13/6.13 double_divide(double_divide(identity, inverse(inverse(identity))), double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1
% 6.13/6.13 double_divide(identity, X0) -> inverse(X0)
% 6.13/6.13 double_divide(identity, double_divide(identity, X0)) -> X0
% 6.13/6.13 double_divide(identity, double_divide(identity, double_divide(identity, X0))) -> double_divide(identity, X0)
% 6.13/6.13 double_divide(identity, double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0
% 6.13/6.13 double_divide(identity, double_divide(identity, double_divide(inverse(double_divide(inverse(identity), Y1)), double_divide(Y2, Y1)))) -> Y2
% 6.13/6.13 double_divide(identity, double_divide(identity, double_divide(inverse(identity), double_divide(Y0, inverse(identity))))) -> Y0
% 6.13/6.13 double_divide(identity, double_divide(identity, double_divide(inverse(identity), double_divide(Y1, inverse(inverse(identity)))))) -> Y1
% 6.13/6.13 double_divide(identity, double_divide(identity, double_divide(inverse(identity), inverse(Y0)))) -> Y0
% 6.13/6.13 double_divide(identity, double_divide(identity, double_divide(inverse(inverse(inverse(identity))), inverse(Y1)))) -> Y1
% 6.13/6.13 double_divide(identity, double_divide(identity, inverse(X0))) -> inverse(X0)
% 6.13/6.13 double_divide(identity, double_divide(identity, inverse(inverse(double_divide(inverse(identity), inverse(Y1)))))) -> Y1
% 6.13/6.13 double_divide(identity, double_divide(identity, inverse(inverse(identity)))) -> inverse(identity)
% 6.13/6.13 double_divide(identity, inverse(X0)) -> inverse(inverse(X0))
% 6.13/6.13 double_divide(identity, inverse(Y0)) -> Y0
% 6.13/6.13 double_divide(identity, inverse(inverse(identity))) -> identity
% 6.13/6.13 double_divide(inverse(X0), X0) -> identity
% 6.13/6.13 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(double_divide(identity, Y1)), double_divide(Y2, Y1)))) -> Y2
% 6.13/6.13 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(identity), double_divide(Y1, inverse(identity))))) -> Y1
% 6.13/6.13 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(identity), inverse(Y0)))) -> Y0
% 6.13/6.13 double_divide(inverse(identity), double_divide(identity, double_divide(inverse(inverse(identity)), inverse(Y1)))) -> Y1
% 6.13/6.13 double_divide(inverse(identity), double_divide(identity, inverse(inverse(double_divide(identity, inverse(Y1)))))) -> Y1
% 6.13/6.13 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity)))) -> identity
% 6.13/6.13 double_divide(inverse(identity), inverse(identity)) -> inverse(inverse(identity))
% 6.13/6.13 f1(a2) -> false__
% 6.13/6.13 f1(inverse(inverse(a2))) -> true__
% 6.13/6.13 f1(multiply(identity, a2)) -> true__
% 6.13/6.13 inverse(double_divide(identity, Y0)) -> Y0
% 6.13/6.13 inverse(identity) -> identity
% 6.13/6.13 inverse(inverse(Y0)) -> Y0
% 6.13/6.13 inverse(inverse(double_divide(identity, inverse(inverse(identity))))) -> inverse(inverse(identity))
% 6.13/6.13 inverse(inverse(identity)) -> inverse(identity)
% 6.13/6.13 inverse(inverse(inverse(identity))) -> identity
% 6.13/6.13 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 6.13/6.13 true__ -> false__
% 6.13/6.13 with the LPO induced by
% 6.13/6.13 a2 > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 6.13/6.13
% 6.13/6.13 % SZS output end Proof
% 6.13/6.13
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