%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 : Thu Jul 14 23:46:10 EDT 2022 % Result : Unsatisfiable 3.79s 3.89s % Output : Proof 3.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 1 20:09:53 EDT 2022 % 0.13/0.34 % CPUTime : % 3.79/3.89 % SZS status Unsatisfiable % 3.79/3.89 % SZS output start Proof % 3.79/3.89 The input problem is unsatisfiable because % 3.79/3.89 % 3.79/3.89 [1] the following set of Horn clauses is unsatisfiable: % 3.79/3.89 % 3.79/3.89 multiply(multiply(V, W, X), Y, multiply(V, W, Z)) = multiply(V, W, multiply(X, Y, Z)) % 3.79/3.89 multiply(Y, X, X) = X % 3.79/3.89 multiply(X, X, Y) = X % 3.79/3.89 multiply(inverse(Y), Y, X) = X % 3.79/3.89 multiply(X, Y, inverse(Y)) = X % 3.79/3.89 inverse(inverse(a)) = a ==> \bottom % 3.79/3.89 % 3.79/3.89 This holds because % 3.79/3.89 % 3.79/3.89 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.79/3.89 % 3.79/3.89 E: % 3.79/3.89 f1(a) = false__ % 3.79/3.89 f1(inverse(inverse(a))) = true__ % 3.79/3.89 multiply(X, X, Y) = X % 3.79/3.89 multiply(X, Y, inverse(Y)) = X % 3.79/3.89 multiply(Y, X, X) = X % 3.79/3.89 multiply(inverse(Y), Y, X) = X % 3.79/3.89 multiply(multiply(V, W, X), Y, multiply(V, W, Z)) = multiply(V, W, multiply(X, Y, Z)) % 3.79/3.89 G: % 3.79/3.89 true__ = false__ % 3.79/3.89 % 3.79/3.89 This holds because % 3.79/3.89 % 3.79/3.89 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.79/3.89 % 3.79/3.89 multiply(Y0, Y1, Y2) = multiply(Y2, Y0, Y1) % 3.79/3.89 multiply(Y0, Y1, Y3) = multiply(Y0, Y3, Y1) % 3.79/3.89 multiply(Y0, Y1, multiply(Y1, Y0, Y2)) = multiply(Y1, Y2, Y0) % 3.79/3.89 multiply(Y0, Y3, multiply(Y0, Y1, Y4)) = multiply(Y0, Y1, multiply(inverse(Y1), Y3, Y4)) % 3.79/3.89 multiply(Y0, inverse(X0), multiply(X0, Y2, Y3)) = multiply(Y0, Y2, multiply(Y0, inverse(X0), Y3)) % 3.79/3.89 multiply(Y2, Y3, multiply(Y0, Y2, Y4)) = multiply(Y0, Y2, multiply(Y2, Y3, Y4)) % 3.79/3.89 f1(a) -> false__ % 3.79/3.89 f1(inverse(inverse(a))) -> true__ % 3.79/3.89 inverse(inverse(Y0)) -> Y0 % 3.79/3.89 multiply(X, X, Y) -> X % 3.79/3.89 multiply(X, Y, inverse(Y)) -> X % 3.79/3.89 multiply(Y, X, X) -> X % 3.79/3.89 multiply(Y0, Y1, multiply(Y0, Y1, Y2)) -> multiply(Y0, Y1, Y2) % 3.79/3.89 multiply(Y0, Y1, multiply(Y0, Y2, multiply(inverse(Y2), Y1, Y2))) -> multiply(Y0, Y1, Y2) % 3.79/3.89 multiply(Y0, Y1, multiply(Y2, Y1, inverse(multiply(Y0, Y1, Y2)))) -> Y1 % 3.79/3.89 multiply(Y0, Y1, multiply(Y2, multiply(Y0, Y1, Y2), Y4)) -> multiply(Y0, Y1, Y2) % 3.79/3.89 multiply(Y0, Y1, multiply(Y2, multiply(Y0, Y1, Y4), Y4)) -> multiply(Y0, Y1, Y4) % 3.79/3.89 multiply(Y0, Y2, inverse(Y0)) -> Y2 % 3.79/3.89 multiply(Y0, inverse(Y0), Y2) -> Y2 % 3.79/3.89 multiply(Y0, inverse(Y1), Y1) -> Y0 % 3.79/3.89 multiply(Y1, Y2, multiply(Y0, Y1, inverse(Y2))) -> Y1 % 3.79/3.89 multiply(Y1, Y2, multiply(Y0, Y2, Y1)) -> multiply(Y0, Y2, Y1) % 3.79/3.89 multiply(Y1, Y2, multiply(Y1, Y3, inverse(multiply(Y1, Y2, Y3)))) -> Y1 % 3.79/3.89 multiply(Y1, Y2, multiply(inverse(Y2), Y1, Y3)) -> Y1 % 3.79/3.89 multiply(Y1, Y2, multiply(multiply(Y1, Y2, Y3), Y1, Y3)) -> multiply(Y1, Y2, Y3) % 3.79/3.89 multiply(Y1, Y3, Y1) -> Y1 % 3.79/3.89 multiply(Y1, Y3, multiply(Y0, Y1, Y3)) -> multiply(Y0, Y1, Y3) % 3.79/3.89 multiply(Y2, Y1, multiply(Y2, Y3, Y1)) -> multiply(Y2, Y3, Y1) % 3.79/3.89 multiply(Y3, Y0, multiply(Y0, Y1, Y3)) -> multiply(Y0, Y1, Y3) % 3.79/3.89 multiply(inverse(Y), Y, X) -> X % 3.79/3.89 multiply(inverse(Y2), Y1, Y2) -> Y1 % 3.79/3.89 multiply(inverse(Y3), Y0, multiply(Y0, Y1, Y3)) -> Y0 % 3.79/3.89 multiply(multiply(V, W, X), Y, multiply(V, W, Z)) -> multiply(V, W, multiply(X, Y, Z)) % 3.79/3.89 multiply(multiply(X2, Y1, Y2), Y1, multiply(X2, Y2, Y1)) -> multiply(X2, Y1, Y2) % 3.79/3.89 multiply(multiply(Y0, Y1, Y2), Y3, Y0) -> multiply(Y0, Y1, multiply(Y2, Y3, inverse(Y1))) % 3.79/3.89 multiply(multiply(Y0, Y4, Y2), Y3, Y4) -> multiply(Y0, Y4, multiply(Y2, Y3, Y4)) % 3.79/3.89 true__ -> false__ % 3.79/3.89 with the LPO induced by % 3.79/3.89 multiply > inverse > a > f1 > true__ > false__ % 3.79/3.89 % 3.79/3.89 % SZS output end Proof % 3.79/3.89 %------------------------------------------------------------------------------