%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP182-2 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 10:53:50 EDT 2022 % Result : Unsatisfiable 0.21s 0.41s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP182-2 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.04/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n003.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Tue Jun 14 08:07:25 EDT 2022 % 0.14/0.34 % CPUTime : % 0.21/0.41 % SZS status Unsatisfiable % 0.21/0.41 % SZS output start Proof % 0.21/0.41 The input problem is unsatisfiable because % 0.21/0.41 % 0.21/0.41 [1] the following set of Horn clauses is unsatisfiable: % 0.21/0.41 % 0.21/0.41 multiply(identity, X) = X % 0.21/0.41 multiply(inverse(X), X) = identity % 0.21/0.41 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.21/0.41 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 0.21/0.41 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 0.21/0.41 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 0.21/0.41 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 0.21/0.41 least_upper_bound(X, X) = X % 0.21/0.41 greatest_lower_bound(X, X) = X % 0.21/0.41 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 0.21/0.41 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 0.21/0.41 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 0.21/0.41 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 0.21/0.41 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 0.21/0.41 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 0.21/0.41 inverse(identity) = identity % 0.21/0.41 inverse(inverse(X)) = X % 0.21/0.41 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)) % 0.21/0.41 least_upper_bound(identity, greatest_lower_bound(a, identity)) = identity ==> \bottom % 0.21/0.41 % 0.21/0.41 This holds because % 0.21/0.41 % 0.21/0.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.21/0.41 % 0.21/0.41 E: % 0.21/0.41 f1(identity) = false__ % 0.21/0.41 f1(least_upper_bound(identity, greatest_lower_bound(a, identity))) = true__ % 0.21/0.41 greatest_lower_bound(X, X) = X % 0.21/0.41 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 0.21/0.41 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z) % 0.21/0.41 greatest_lower_bound(X, least_upper_bound(X, Y)) = X % 0.21/0.41 inverse(identity) = identity % 0.21/0.41 inverse(inverse(X)) = X % 0.21/0.41 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)) % 0.21/0.41 least_upper_bound(X, X) = X % 0.21/0.41 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 0.21/0.41 least_upper_bound(X, greatest_lower_bound(X, Y)) = X % 0.21/0.41 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z) % 0.21/0.41 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)) % 0.21/0.41 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)) % 0.21/0.41 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X)) % 0.21/0.41 multiply(identity, X) = X % 0.21/0.41 multiply(inverse(X), X) = identity % 0.21/0.41 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X)) % 0.21/0.41 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.21/0.41 G: % 0.21/0.41 true__ = false__ % 0.21/0.41 % 0.21/0.41 This holds because % 0.21/0.41 % 0.21/0.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.21/0.41 % 0.21/0.41 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X) % 0.21/0.41 least_upper_bound(X, Y) = least_upper_bound(Y, X) % 0.21/0.41 f1(identity) -> false__ % 0.21/0.41 f1(least_upper_bound(identity, greatest_lower_bound(a, identity))) -> true__ % 0.21/0.41 greatest_lower_bound(X, X) -> X % 0.21/0.41 greatest_lower_bound(X, least_upper_bound(X, Y)) -> X % 0.21/0.41 greatest_lower_bound(Y0, greatest_lower_bound(Y1, Y0)) -> greatest_lower_bound(Y0, Y1) % 0.21/0.41 greatest_lower_bound(Y0, greatest_lower_bound(Y1, greatest_lower_bound(Y0, Y1))) -> greatest_lower_bound(Y0, Y1) % 0.21/0.41 greatest_lower_bound(Y0, least_upper_bound(Y1, Y0)) -> Y0 % 0.21/0.41 greatest_lower_bound(Y1, greatest_lower_bound(Y1, Y2)) -> greatest_lower_bound(Y1, Y2) % 0.21/0.41 greatest_lower_bound(greatest_lower_bound(X, Y), Z) -> greatest_lower_bound(X, greatest_lower_bound(Y, Z)) % 0.21/0.41 greatest_lower_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, greatest_lower_bound(Y, Z)) % 0.21/0.41 greatest_lower_bound(multiply(Y, X), multiply(Z, X)) -> multiply(greatest_lower_bound(Y, Z), X) % 0.21/0.41 inverse(identity) -> identity % 0.21/0.41 inverse(inverse(X)) -> X % 0.21/0.41 inverse(multiply(X, Y)) -> multiply(inverse(Y), inverse(X)) % 0.21/0.41 least_upper_bound(X, X) -> X % 0.21/0.41 least_upper_bound(X, greatest_lower_bound(X, Y)) -> X % 0.21/0.41 least_upper_bound(Y0, greatest_lower_bound(Y1, Y0)) -> Y0 % 0.21/0.41 least_upper_bound(Y0, least_upper_bound(Y1, Y0)) -> least_upper_bound(Y0, Y1) % 0.21/0.41 least_upper_bound(Y0, least_upper_bound(Y1, least_upper_bound(Y0, Y1))) -> least_upper_bound(Y0, Y1) % 0.21/0.41 least_upper_bound(Y1, least_upper_bound(Y1, Y2)) -> least_upper_bound(Y1, Y2) % 0.21/0.41 least_upper_bound(least_upper_bound(X, Y), Z) -> least_upper_bound(X, least_upper_bound(Y, Z)) % 0.21/0.41 least_upper_bound(multiply(X, Y), multiply(X, Z)) -> multiply(X, least_upper_bound(Y, Z)) % 0.21/0.41 least_upper_bound(multiply(Y, X), multiply(Z, X)) -> multiply(least_upper_bound(Y, Z), X) % 0.21/0.41 multiply(X0, identity) -> X0 % 0.21/0.41 multiply(X0, inverse(X0)) -> identity % 0.21/0.41 multiply(identity, X) -> X % 0.21/0.41 multiply(inverse(X), X) -> identity % 0.21/0.41 multiply(inverse(X1), multiply(inverse(X0), multiply(X0, X1))) -> identity % 0.21/0.41 multiply(inverse(Y1), identity) -> inverse(Y1) % 0.21/0.41 multiply(inverse(Y1), multiply(Y1, Y2)) -> Y2 % 0.21/0.41 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 0.21/0.41 true__ -> false__ % 0.21/0.41 with the LPO induced by % 0.21/0.41 a > f1 > inverse > greatest_lower_bound > least_upper_bound > multiply > identity > true__ > false__ % 0.21/0.41 % 0.21/0.41 % SZS output end Proof % 0.21/0.41 %------------------------------------------------------------------------------