%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP022-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n028.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 10:51:54 EDT 2022 % Result : Unsatisfiable 0.37s 0.62s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP022-2 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n028.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 14:08:09 EDT 2022 % 0.12/0.33 % CPUTime : % 0.37/0.62 % SZS status Unsatisfiable % 0.37/0.62 % SZS output start Proof % 0.37/0.62 The input problem is unsatisfiable because % 0.37/0.62 % 0.37/0.62 [1] the following set of Horn clauses is unsatisfiable: % 0.37/0.62 % 0.37/0.62 multiply(identity, X) = X % 0.37/0.62 multiply(inverse(X), X) = identity % 0.37/0.62 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.37/0.62 multiply(X, identity) = X % 0.37/0.62 multiply(X, inverse(X)) = identity % 0.37/0.62 inverse(inverse(a)) = a ==> \bottom % 0.37/0.62 % 0.37/0.62 This holds because % 0.37/0.62 % 0.37/0.62 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.37/0.62 % 0.37/0.62 E: % 0.37/0.62 f1(a) = false__ % 0.37/0.62 f1(inverse(inverse(a))) = true__ % 0.37/0.62 multiply(X, identity) = X % 0.37/0.62 multiply(X, inverse(X)) = identity % 0.37/0.62 multiply(identity, X) = X % 0.37/0.62 multiply(inverse(X), X) = identity % 0.37/0.62 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.37/0.62 G: % 0.37/0.62 true__ = false__ % 0.37/0.62 % 0.37/0.62 This holds because % 0.37/0.62 % 0.37/0.62 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.37/0.62 % 0.37/0.62 % 0.37/0.62 f1(a) -> false__ % 0.37/0.62 f1(inverse(inverse(a))) -> true__ % 0.37/0.62 inverse(identity) -> identity % 0.37/0.62 inverse(inverse(Y1)) -> Y1 % 0.37/0.62 inverse(multiply(X1, Y0)) -> multiply(inverse(Y0), inverse(X1)) % 0.37/0.62 inverse(multiply(X1, inverse(Y0))) -> multiply(Y0, inverse(X1)) % 0.37/0.62 inverse(multiply(inverse(X1), Y0)) -> multiply(inverse(Y0), X1) % 0.37/0.62 inverse(multiply(inverse(multiply(Y1, Y2)), Y1)) -> Y2 % 0.37/0.62 multiply(X, identity) -> X % 0.37/0.62 multiply(X, inverse(X)) -> identity % 0.37/0.62 multiply(X1, inverse(multiply(Y0, X1))) -> inverse(Y0) % 0.37/0.62 multiply(X1, inverse(multiply(inverse(Y0), X1))) -> Y0 % 0.37/0.62 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity % 0.37/0.62 multiply(Y0, multiply(Y1, multiply(X1, inverse(multiply(Y0, multiply(Y1, X1)))))) -> identity % 0.37/0.62 multiply(Y0, multiply(Y1, multiply(inverse(multiply(Y0, Y1)), X1))) -> X1 % 0.37/0.62 multiply(Y0, multiply(inverse(Y0), Y2)) -> Y2 % 0.37/0.62 multiply(identity, X) -> X % 0.37/0.62 multiply(inverse(X), X) -> identity % 0.37/0.62 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 0.37/0.62 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1) % 0.37/0.62 multiply(inverse(multiply(X0, X1)), multiply(X0, multiply(X1, Y1))) -> Y1 % 0.37/0.62 multiply(inverse(multiply(Y0, Y1)), Y0) -> inverse(Y1) % 0.37/0.62 multiply(inverse(multiply(Y0, inverse(Y2))), Y0) -> Y2 % 0.37/0.62 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 0.37/0.62 true__ -> false__ % 0.37/0.62 with the LPO induced by % 0.37/0.62 a > f1 > inverse > identity > multiply > true__ > false__ % 0.37/0.62 % 0.37/0.62 % SZS output end Proof % 0.37/0.62 %------------------------------------------------------------------------------