%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 23:46:15 EDT 2022 % Result : Unsatisfiable 0.87s 1.05s % Output : Proof 0.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.11/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n026.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 16:12:27 EDT 2022 % 0.13/0.34 % CPUTime : % 0.87/1.05 % SZS status Unsatisfiable % 0.87/1.05 % SZS output start Proof % 0.87/1.05 The input problem is unsatisfiable because % 0.87/1.05 % 0.87/1.05 [1] the following set of Horn clauses is unsatisfiable: % 0.87/1.05 % 0.87/1.05 add(X, Y) = add(Y, X) % 0.87/1.05 multiply(X, Y) = multiply(Y, X) % 0.87/1.05 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 0.87/1.05 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 0.87/1.05 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 0.87/1.05 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.87/1.05 add(X, inverse(X)) = multiplicative_identity % 0.87/1.05 add(inverse(X), X) = multiplicative_identity % 0.87/1.05 multiply(X, inverse(X)) = additive_identity % 0.87/1.05 multiply(inverse(X), X) = additive_identity % 0.87/1.05 multiply(X, multiplicative_identity) = X % 0.87/1.05 multiply(multiplicative_identity, X) = X % 0.87/1.05 add(X, additive_identity) = X % 0.87/1.05 add(additive_identity, X) = X % 0.87/1.05 add(a, multiplicative_identity) = multiplicative_identity ==> \bottom % 0.87/1.05 % 0.87/1.05 This holds because % 0.87/1.05 % 0.87/1.05 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.87/1.05 % 0.87/1.05 E: % 0.87/1.05 add(X, Y) = add(Y, X) % 0.87/1.05 add(X, additive_identity) = X % 0.87/1.05 add(X, inverse(X)) = multiplicative_identity % 0.87/1.05 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 0.87/1.05 add(additive_identity, X) = X % 0.87/1.05 add(inverse(X), X) = multiplicative_identity % 0.87/1.05 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 0.87/1.05 f1(add(a, multiplicative_identity)) = true__ % 0.87/1.05 f1(multiplicative_identity) = false__ % 0.87/1.05 multiply(X, Y) = multiply(Y, X) % 0.87/1.05 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.87/1.05 multiply(X, inverse(X)) = additive_identity % 0.87/1.05 multiply(X, multiplicative_identity) = X % 0.87/1.05 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 0.87/1.05 multiply(inverse(X), X) = additive_identity % 0.87/1.05 multiply(multiplicative_identity, X) = X % 0.87/1.05 G: % 0.87/1.05 true__ = false__ % 0.87/1.05 % 0.87/1.05 This holds because % 0.87/1.05 % 0.87/1.05 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.87/1.05 % 0.87/1.05 add(X, Y) = add(Y, X) % 0.87/1.05 multiply(X, Y) = multiply(Y, X) % 0.87/1.05 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2)) % 0.87/1.05 add(X, additive_identity) -> X % 0.87/1.05 add(X, inverse(X)) -> multiplicative_identity % 0.87/1.05 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z)) % 0.87/1.05 add(Y0, Y0) -> Y0 % 0.87/1.05 add(Y0, multiplicative_identity) -> multiplicative_identity % 0.87/1.05 add(additive_identity, X) -> X % 0.87/1.05 add(inverse(X), X) -> multiplicative_identity % 0.87/1.05 add(multiplicative_identity, Y1) -> multiplicative_identity % 0.87/1.05 add(multiplicative_identity, inverse(Y0)) -> multiplicative_identity % 0.87/1.05 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z)) % 0.87/1.05 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 0.87/1.05 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 0.87/1.05 f1(add(a, multiplicative_identity)) -> true__ % 0.87/1.05 f1(multiplicative_identity) -> false__ % 0.87/1.05 inverse(additive_identity) -> multiplicative_identity % 0.87/1.05 inverse(multiplicative_identity) -> additive_identity % 0.87/1.05 multiply(X, inverse(X)) -> additive_identity % 0.87/1.05 multiply(X, multiplicative_identity) -> X % 0.87/1.05 multiply(Y0, add(Y0, Y0)) -> Y0 % 0.87/1.05 multiply(Y0, add(Y0, multiplicative_identity)) -> Y0 % 0.87/1.05 multiply(Y1, add(multiplicative_identity, Y1)) -> Y1 % 0.87/1.05 multiply(add(Y0, Y0), add(Y0, Y2)) -> Y0 % 0.87/1.05 multiply(add(Y0, Y0), add(Y1, Y0)) -> Y0 % 0.87/1.05 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1) % 0.87/1.05 multiply(add(Y0, Y2), add(multiplicative_identity, Y2)) -> add(Y0, Y2) % 0.87/1.05 multiply(add(Y0, multiplicative_identity), add(Y0, Y2)) -> add(Y0, Y2) % 0.87/1.05 multiply(add(Y1, Y2), add(Y1, Y1)) -> Y1 % 0.87/1.05 multiply(add(multiplicative_identity, Y2), add(Y1, Y2)) -> add(Y1, Y2) % 0.87/1.05 multiply(additive_identity, Y0) -> additive_identity % 0.87/1.05 multiply(additive_identity, add(multiplicative_identity, Y1)) -> multiply(additive_identity, Y1) % 0.87/1.05 multiply(additive_identity, additive_identity) -> additive_identity % 0.87/1.05 multiply(inverse(X), X) -> additive_identity % 0.87/1.05 multiply(multiplicative_identity, X) -> X % 0.87/1.05 true__ -> false__ % 0.87/1.05 with the LPO induced by % 0.87/1.05 a > f1 > inverse > additive_identity > multiplicative_identity > add > multiply > true__ > false__ % 0.87/1.05 % 0.87/1.05 % SZS output end Proof % 0.87/1.05 %------------------------------------------------------------------------------