%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n016.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 10:51:47 EDT 2022 % Result : Unsatisfiable 0.46s 0.65s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP010-4 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n016.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 06:54:59 EDT 2022 % 0.12/0.33 % CPUTime : % 0.46/0.65 % SZS status Unsatisfiable % 0.46/0.65 % SZS output start Proof % 0.46/0.65 The input problem is unsatisfiable because % 0.46/0.65 % 0.46/0.65 [1] the following set of Horn clauses is unsatisfiable: % 0.46/0.65 % 0.46/0.65 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.46/0.65 multiply(identity, X) = X % 0.46/0.65 multiply(inverse(X), X) = identity % 0.46/0.65 multiply(c, b) = identity % 0.46/0.65 multiply(b, c) = identity ==> \bottom % 0.46/0.65 % 0.46/0.65 This holds because % 0.46/0.65 % 0.46/0.65 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.46/0.65 % 0.46/0.65 E: % 0.46/0.65 f1(identity) = false__ % 0.46/0.65 f1(multiply(b, c)) = true__ % 0.46/0.65 multiply(c, b) = identity % 0.46/0.65 multiply(identity, X) = X % 0.46/0.65 multiply(inverse(X), X) = identity % 0.46/0.65 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.46/0.65 G: % 0.46/0.65 true__ = false__ % 0.46/0.65 % 0.46/0.65 This holds because % 0.46/0.65 % 0.46/0.65 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.46/0.65 % 0.46/0.65 % 0.46/0.65 f1(identity) -> false__ % 0.46/0.65 f1(multiply(b, c)) -> true__ % 0.46/0.65 f1(multiply(c, b)) -> false__ % 0.46/0.65 identity -> multiply(c, b) % 0.46/0.65 inverse(b) -> c % 0.46/0.65 inverse(c) -> b % 0.46/0.65 inverse(inverse(Y1)) -> Y1 % 0.46/0.65 inverse(multiply(b, c)) -> multiply(b, c) % 0.46/0.65 multiply(Y0, inverse(Y0)) -> multiply(c, b) % 0.46/0.65 multiply(Y0, multiply(b, c)) -> Y0 % 0.46/0.65 multiply(Y1, multiply(c, b)) -> Y1 % 0.46/0.65 multiply(c, b) -> multiply(b, c) % 0.46/0.65 multiply(c, multiply(b, Y0)) -> Y0 % 0.46/0.65 multiply(identity, X) -> X % 0.46/0.65 multiply(inverse(X), X) -> identity % 0.46/0.65 multiply(inverse(Y1), multiply(Y1, Y2)) -> multiply(c, multiply(b, Y2)) % 0.46/0.65 multiply(inverse(c), X0) -> multiply(b, X0) % 0.46/0.65 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1) % 0.46/0.65 multiply(inverse(inverse(Y1)), multiply(c, b)) -> Y1 % 0.46/0.65 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1 % 0.46/0.65 multiply(inverse(multiply(Y0, c)), multiply(Y0, X0)) -> multiply(b, X0) % 0.46/0.65 multiply(inverse(multiply(Y0, inverse(Y2))), multiply(Y0, multiply(c, b))) -> Y2 % 0.46/0.65 multiply(inverse(multiply(Y0, multiply(c, b))), multiply(Y0, Y2)) -> Y2 % 0.46/0.65 multiply(inverse(multiply(b, c)), Y0) -> Y0 % 0.46/0.65 multiply(inverse(multiply(c, b)), Y1) -> Y1 % 0.46/0.65 multiply(inverse(multiply(inverse(multiply(Y1, Y2)), Y1)), multiply(c, b)) -> Y2 % 0.46/0.65 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 0.46/0.65 true__ -> false__ % 0.46/0.65 with the LPO induced by % 0.46/0.65 f1 > inverse > identity > c > b > multiply > true__ > false__ % 0.46/0.65 % 0.46/0.65 % SZS output end Proof % 0.46/0.65 %------------------------------------------------------------------------------