%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP520-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 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 10:55:59 EDT 2022 % Result : Unsatisfiable 14.48s 14.60s % Output : Proof 14.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP520-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.11/0.12 % 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 : Tue Jun 14 12:37:24 EDT 2022 % 0.12/0.34 % CPUTime : % 14.48/14.60 % SZS status Unsatisfiable % 14.48/14.60 % SZS output start Proof % 14.48/14.60 The input problem is unsatisfiable because % 14.48/14.60 % 14.48/14.60 [1] the following set of Horn clauses is unsatisfiable: % 14.48/14.60 % 14.48/14.60 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C % 14.48/14.60 multiply(a, b) = multiply(b, a) ==> \bottom % 14.48/14.60 % 14.48/14.60 This holds because % 14.48/14.60 % 14.48/14.60 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 14.48/14.60 % 14.48/14.60 E: % 14.48/14.60 f1(multiply(a, b)) = true__ % 14.48/14.60 f1(multiply(b, a)) = false__ % 14.48/14.60 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C % 14.48/14.60 G: % 14.48/14.60 true__ = false__ % 14.48/14.60 % 14.48/14.60 This holds because % 14.48/14.60 % 14.48/14.60 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 14.48/14.60 % 14.48/14.60 multiply(X1, multiply(Y0, X2)) = multiply(multiply(inverse(Y2), multiply(X1, X2)), multiply(Y0, Y2)) % 14.48/14.60 multiply(X1, multiply(multiply(inverse(multiply(X1, X2)), Y1), multiply(Y2, X2))) = multiply(Y2, Y1) % 14.48/14.60 multiply(X2, multiply(X0, X1)) = multiply(X0, multiply(X2, X1)) % 14.48/14.60 multiply(Y0, X1) = multiply(multiply(inverse(Y2), X1), multiply(Y0, Y2)) % 14.48/14.60 multiply(Y0, Y1) = multiply(Y1, Y0) % 14.48/14.60 multiply(Y0, multiply(X2, X1)) = multiply(multiply(inverse(X0), X1), multiply(Y0, multiply(X2, X0))) % 14.48/14.60 multiply(Y0, multiply(X2, Y1)) = multiply(multiply(inverse(X1), X2), multiply(Y0, multiply(X1, Y1))) % 14.48/14.60 multiply(Y0, multiply(multiply(inverse(X2), Y2), multiply(Y1, X2))) = multiply(Y1, multiply(Y0, Y2)) % 14.48/14.60 multiply(multiply(X1, multiply(inverse(Y0), X2)), multiply(Y2, Y0)) = multiply(Y2, multiply(X1, X2)) % 14.48/14.60 multiply(multiply(inverse(X2), Y1), multiply(Y0, X2)) = multiply(multiply(inverse(Y2), Y1), multiply(Y0, Y2)) % 14.48/14.60 multiply(multiply(inverse(Y0), Y1), X1) = multiply(multiply(inverse(Y0), X1), Y1) % 14.48/14.60 multiply(multiply(inverse(Y0), Y1), multiply(multiply(inverse(X2), Y0), multiply(Y2, X2))) = multiply(Y2, Y1) % 14.48/14.60 multiply(multiply(multiply(inverse(X2), Y1), multiply(inverse(Y0), X2)), multiply(Y2, Y0)) = multiply(Y2, Y1) % 14.48/14.60 f1(multiply(a, b)) -> true__ % 14.48/14.60 f1(multiply(b, a)) -> false__ % 14.48/14.60 inverse(g1) -> g1 % 14.48/14.60 inverse(inverse(Y0)) -> Y0 % 14.48/14.60 multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) -> C % 14.48/14.60 multiply(Y0, g1) -> Y0 % 14.48/14.60 multiply(Y0, inverse(Y0)) -> g1 % 14.48/14.60 multiply(Y0, inverse(multiply(Y0, Y1))) -> inverse(Y1) % 14.48/14.60 multiply(Y0, inverse(multiply(Y1, Y0))) -> inverse(Y1) % 14.48/14.60 multiply(Y0, multiply(X1, multiply(multiply(inverse(multiply(X1, multiply(Y0, X2))), Y2), X2))) -> Y2 % 14.48/14.60 multiply(Y0, multiply(X1, multiply(multiply(inverse(multiply(Y0, multiply(X1, X2))), Y2), X2))) -> Y2 % 14.48/14.60 multiply(Y0, multiply(Y1, inverse(Y0))) -> Y1 % 14.48/14.60 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> g1 % 14.48/14.60 multiply(Y0, multiply(inverse(Y0), Y1)) -> Y1 % 14.48/14.60 multiply(Y0, multiply(multiply(X1, multiply(inverse(multiply(Y0, Y1)), X2)), Y1)) -> multiply(X1, X2) % 14.48/14.60 multiply(Y1, multiply(Y0, multiply(multiply(inverse(multiply(Y1, X1)), X2), X1))) -> multiply(Y0, X2) % 14.48/14.60 multiply(Y1, multiply(inverse(multiply(Y1, Y2)), Y2)) -> g1 % 14.48/14.60 multiply(g1, Y1) -> Y1 % 14.48/14.60 multiply(inverse(X1), multiply(multiply(inverse(Y1), X1), multiply(Y2, Y1))) -> Y2 % 14.48/14.60 multiply(inverse(Y1), Y1) -> g1 % 14.48/14.60 multiply(inverse(Y1), multiply(Y2, Y1)) -> Y2 % 14.48/14.60 multiply(inverse(multiply(X0, X1)), multiply(multiply(inverse(Y1), Y2), multiply(X0, multiply(Y1, X1)))) -> Y2 % 14.48/14.60 multiply(inverse(multiply(X1, X0)), X1) -> inverse(X0) % 14.48/14.60 multiply(inverse(multiply(Y0, Y1)), multiply(Y0, X1)) -> multiply(inverse(Y1), X1) % 14.48/14.60 multiply(inverse(multiply(multiply(inverse(multiply(Y2, Y1)), X1), Y1)), X1) -> Y2 % 14.48/14.60 multiply(multiply(X1, multiply(inverse(Y0), X2)), Y0) -> multiply(X1, X2) % 14.48/14.60 multiply(multiply(inverse(X2), multiply(Y2, Y0)), multiply(multiply(inverse(Y0), Y1), X2)) -> multiply(Y2, Y1) % 14.48/14.60 multiply(multiply(inverse(Y1), X1), multiply(multiply(inverse(X1), Y2), Y1)) -> Y2 % 14.48/14.60 multiply(multiply(inverse(Y1), Y2), Y1) -> Y2 % 14.48/14.60 multiply(multiply(inverse(Y2), Y1), multiply(inverse(Y1), Y2)) -> g1 % 14.48/14.60 multiply(multiply(inverse(Y3), Y1), multiply(multiply(inverse(multiply(Y1, Y2)), X1), multiply(Y3, Y2))) -> X1 % 14.48/14.60 multiply(multiply(inverse(multiply(inverse(Y0), X1)), X2), X1) -> multiply(X2, Y0) % 14.48/14.60 multiply(multiply(inverse(multiply(inverse(multiply(Y0, Y1)), X1)), X2), X1) -> multiply(Y0, multiply(X2, Y1)) % 14.48/14.60 true__ -> false__ % 14.48/14.60 with the LPO induced by % 14.48/14.60 a > b > f1 > multiply > inverse > g1 > true__ > false__ % 14.48/14.60 % 14.48/14.60 % SZS output end Proof % 14.48/14.60 %------------------------------------------------------------------------------