TSTP Solution File: GRP517-1 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n027.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 10:55:58 EDT 2022
% Result : Unsatisfiable 11.92s 12.10s
% Output : Proof 11.92s
% 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 : GRP517-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : moca.sh %s
% 0.14/0.35 % Computer : n027.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 21:37:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 11.92/12.10 % SZS status Unsatisfiable
% 11.92/12.10 % SZS output start Proof
% 11.92/12.10 The input problem is unsatisfiable because
% 11.92/12.10
% 11.92/12.10 [1] the following set of Horn clauses is unsatisfiable:
% 11.92/12.10
% 11.92/12.10 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C
% 11.92/12.10 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 11.92/12.10
% 11.92/12.10 This holds because
% 11.92/12.10
% 11.92/12.10 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 11.92/12.10
% 11.92/12.10 E:
% 11.92/12.10 f1(multiply(inverse(a1), a1)) = true__
% 11.92/12.10 f1(multiply(inverse(b1), b1)) = false__
% 11.92/12.10 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C
% 11.92/12.10 G:
% 11.92/12.10 true__ = false__
% 11.92/12.10
% 11.92/12.10 This holds because
% 11.92/12.10
% 11.92/12.10 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 11.92/12.10
% 11.92/12.10 multiply(X1, multiply(Y0, X2)) = multiply(multiply(inverse(Y2), multiply(X1, X2)), multiply(Y0, Y2))
% 11.92/12.10 multiply(X1, multiply(multiply(inverse(multiply(X1, X2)), Y1), multiply(Y2, X2))) = multiply(Y2, Y1)
% 11.92/12.10 multiply(X2, multiply(X0, X1)) = multiply(X0, multiply(X2, X1))
% 11.92/12.10 multiply(Y0, X1) = multiply(multiply(inverse(Y2), X1), multiply(Y0, Y2))
% 11.92/12.10 multiply(Y0, Y1) = multiply(Y1, Y0)
% 11.92/12.10 multiply(Y0, multiply(X2, X1)) = multiply(multiply(inverse(X0), X1), multiply(Y0, multiply(X2, X0)))
% 11.92/12.10 multiply(Y0, multiply(X2, Y1)) = multiply(multiply(inverse(X1), X2), multiply(Y0, multiply(X1, Y1)))
% 11.92/12.10 multiply(Y0, multiply(multiply(inverse(X2), Y2), multiply(Y1, X2))) = multiply(Y1, multiply(Y0, Y2))
% 11.92/12.10 multiply(multiply(X1, multiply(inverse(Y0), X2)), multiply(Y2, Y0)) = multiply(Y2, multiply(X1, X2))
% 11.92/12.10 multiply(multiply(inverse(X2), Y1), multiply(Y0, X2)) = multiply(multiply(inverse(Y2), Y1), multiply(Y0, Y2))
% 11.92/12.10 multiply(multiply(inverse(Y0), Y1), X1) = multiply(multiply(inverse(Y0), X1), Y1)
% 11.92/12.10 f1(g1) -> false__
% 11.92/12.10 f1(g1) -> true__
% 11.92/12.10 f1(multiply(inverse(a1), a1)) -> true__
% 11.92/12.10 f1(multiply(multiply(inverse(X2), a1), multiply(inverse(a1), X2))) -> true__
% 11.92/12.10 inverse(g1) -> g1
% 11.92/12.10 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) -> C
% 11.92/12.10 multiply(Y0, g1) -> Y0
% 11.92/12.10 multiply(Y0, inverse(Y0)) -> g1
% 11.92/12.10 multiply(Y0, multiply(X1, multiply(multiply(inverse(multiply(X1, multiply(Y0, X2))), Y2), X2))) -> Y2
% 11.92/12.10 multiply(Y0, multiply(X1, multiply(multiply(inverse(multiply(Y0, multiply(X1, X2))), Y2), X2))) -> Y2
% 11.92/12.10 multiply(Y0, multiply(multiply(X1, multiply(inverse(multiply(Y0, Y1)), X2)), Y1)) -> multiply(X1, X2)
% 11.92/12.10 multiply(Y1, multiply(Y0, multiply(multiply(inverse(multiply(Y1, X1)), X2), X1))) -> multiply(Y0, X2)
% 11.92/12.10 multiply(Y1, multiply(inverse(multiply(Y1, Y2)), Y2)) -> g1
% 11.92/12.10 multiply(g1, Y1) -> Y1
% 11.92/12.10 multiply(inverse(X1), multiply(multiply(inverse(Y1), X1), multiply(Y2, Y1))) -> Y2
% 11.92/12.10 multiply(inverse(Y1), Y1) -> g1
% 11.92/12.10 multiply(inverse(Y1), multiply(Y2, Y1)) -> Y2
% 11.92/12.10 multiply(inverse(g1), Y1) -> Y1
% 11.92/12.10 multiply(inverse(multiply(X0, X1)), multiply(multiply(inverse(Y1), Y2), multiply(X0, multiply(Y1, X1)))) -> Y2
% 11.92/12.10 multiply(inverse(multiply(X1, X0)), X1) -> inverse(X0)
% 11.92/12.10 multiply(inverse(multiply(Y0, Y1)), multiply(Y0, X1)) -> multiply(inverse(Y1), X1)
% 11.92/12.10 multiply(inverse(multiply(multiply(inverse(multiply(Y2, Y1)), X1), Y1)), X1) -> Y2
% 11.92/12.10 multiply(multiply(X1, multiply(inverse(Y0), X2)), Y0) -> multiply(X1, X2)
% 11.92/12.10 multiply(multiply(inverse(X2), multiply(Y2, Y0)), multiply(multiply(inverse(Y0), Y1), X2)) -> multiply(Y2, Y1)
% 11.92/12.10 multiply(multiply(inverse(Y1), X1), multiply(multiply(inverse(X1), Y2), Y1)) -> Y2
% 11.92/12.10 multiply(multiply(inverse(Y1), Y2), Y1) -> Y2
% 11.92/12.10 multiply(multiply(inverse(Y2), Y1), multiply(inverse(Y1), Y2)) -> g1
% 11.92/12.10 multiply(multiply(inverse(Y3), Y1), multiply(multiply(inverse(multiply(Y1, Y2)), X1), multiply(Y3, Y2))) -> X1
% 11.92/12.10 multiply(multiply(inverse(g1), Y1), inverse(Y1)) -> g1
% 11.92/12.10 multiply(multiply(inverse(multiply(inverse(Y0), X1)), X2), X1) -> multiply(X2, Y0)
% 11.92/12.10 multiply(multiply(inverse(multiply(inverse(multiply(Y0, Y1)), X1)), X2), X1) -> multiply(Y0, multiply(X2, Y1))
% 11.92/12.10 true__ -> false__
% 11.92/12.10 with the LPO induced by
% 11.92/12.10 a1 > b1 > inverse > g1 > multiply > f1 > true__ > false__
% 11.92/12.10
% 11.92/12.10 % SZS output end Proof
% 11.92/12.10
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