%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n004.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 10:51:39 EDT 2022 % Result : Unsatisfiable 0.88s 1.06s % Output : Proof 0.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : GRP001-2 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.14 % Command : moca.sh %s % 0.13/0.35 % Computer : n004.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon Jun 13 18:33:09 EDT 2022 % 0.13/0.35 % CPUTime : % 0.88/1.06 % SZS status Unsatisfiable % 0.88/1.06 % SZS output start Proof % 0.88/1.06 The input problem is unsatisfiable because % 0.88/1.06 % 0.88/1.06 [1] the following set of Horn clauses is unsatisfiable: % 0.88/1.06 % 0.88/1.06 multiply(identity, X) = X % 0.88/1.06 multiply(inverse(X), X) = identity % 0.88/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.88/1.06 multiply(X, identity) = X % 0.88/1.06 multiply(X, inverse(X)) = identity % 0.88/1.06 multiply(X, X) = identity % 0.88/1.06 multiply(a, b) = c % 0.88/1.06 multiply(b, a) = c ==> \bottom % 0.88/1.06 % 0.88/1.06 This holds because % 0.88/1.06 % 0.88/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.88/1.06 % 0.88/1.06 E: % 0.88/1.06 f1(c) = false__ % 0.88/1.06 f1(multiply(b, a)) = true__ % 0.88/1.06 multiply(X, X) = identity % 0.88/1.06 multiply(X, identity) = X % 0.88/1.06 multiply(X, inverse(X)) = identity % 0.88/1.06 multiply(a, b) = c % 0.88/1.06 multiply(identity, X) = X % 0.88/1.06 multiply(inverse(X), X) = identity % 0.88/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.88/1.06 G: % 0.88/1.06 true__ = false__ % 0.88/1.06 % 0.88/1.06 This holds because % 0.88/1.06 % 0.88/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.88/1.06 % 0.88/1.06 multiply(Y0, X1) = multiply(X1, Y0) % 0.88/1.06 multiply(Y1, multiply(Y0, Y2)) = multiply(Y0, multiply(Y1, Y2)) % 0.88/1.06 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y1, Y2)) % 0.88/1.06 c -> multiply(a, b) % 0.88/1.06 f1(c) -> false__ % 0.88/1.06 f1(multiply(a, b)) -> false__ % 0.88/1.06 f1(multiply(b, a)) -> true__ % 0.88/1.06 inverse(Y1) -> Y1 % 0.88/1.06 inverse(identity) -> identity % 0.88/1.06 inverse(inverse(Y1)) -> Y1 % 0.88/1.06 multiply(X, X) -> identity % 0.88/1.06 multiply(X, identity) -> X % 0.88/1.06 multiply(X, inverse(X)) -> identity % 0.88/1.06 multiply(X1, inverse(multiply(Y0, X1))) -> Y0 % 0.88/1.06 multiply(X1, multiply(Y0, X1)) -> Y0 % 0.88/1.06 multiply(X1, multiply(Y0, X1)) -> inverse(Y0) % 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, Y0))) -> multiply(X0, X1) % 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, multiply(X0, X1))))) -> identity % 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, multiply(Y0, multiply(X0, multiply(X1, Y2)))))) -> Y2 % 0.88/1.06 multiply(Y0, multiply(X0, multiply(X1, multiply(Y2, multiply(Y0, multiply(X0, X1)))))) -> Y2 % 0.88/1.06 multiply(Y0, multiply(X1, multiply(X2, multiply(Y0, multiply(X1, Y2))))) -> multiply(X2, Y2) % 0.88/1.06 multiply(Y0, multiply(X1, multiply(Y0, Y2))) -> multiply(X1, Y2) % 0.88/1.06 multiply(Y0, multiply(Y1, inverse(multiply(Y0, Y1)))) -> identity % 0.88/1.06 multiply(Y0, multiply(Y1, multiply(X0, multiply(X1, multiply(Y0, Y1))))) -> multiply(X0, X1) % 0.88/1.06 multiply(Y0, multiply(Y1, multiply(X1, multiply(Y0, Y1)))) -> X1 % 0.88/1.06 multiply(Y0, multiply(Y1, multiply(Y0, Y1))) -> identity % 0.88/1.06 multiply(Y0, multiply(Y1, multiply(Y0, multiply(Y1, X1)))) -> X1 % 0.88/1.06 multiply(Y0, multiply(inverse(Y0), Y2)) -> Y2 % 0.88/1.06 multiply(Y1, multiply(Y1, Y2)) -> Y2 % 0.88/1.06 multiply(identity, X) -> X % 0.88/1.06 multiply(inverse(X), X) -> identity % 0.88/1.06 multiply(inverse(Y0), X1) -> multiply(Y0, X1) % 0.88/1.06 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 0.88/1.06 multiply(inverse(inverse(X0)), X1) -> multiply(X0, X1) % 0.88/1.06 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 0.88/1.06 true__ -> false__ % 0.88/1.06 with the LPO induced by % 0.88/1.06 f1 > c > a > b > multiply > identity > inverse > true__ > false__ % 0.88/1.06 % 0.88/1.06 % SZS output end Proof % 0.88/1.06 %------------------------------------------------------------------------------