%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 0.74s 0.90s % Output : Proof 0.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.35 % Computer : n019.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 : Wed Jun 1 21:57:40 EDT 2022 % 0.13/0.35 % CPUTime : % 0.74/0.90 % SZS status Unsatisfiable % 0.74/0.90 % SZS output start Proof % 0.74/0.90 The input problem is unsatisfiable because % 0.74/0.90 % 0.74/0.90 [1] the following set of Horn clauses is unsatisfiable: % 0.74/0.90 % 0.74/0.90 add(X, Y) = add(Y, X) % 0.74/0.90 multiply(X, Y) = multiply(Y, X) % 0.74/0.90 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 0.74/0.90 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.74/0.90 add(X, additive_identity) = X % 0.74/0.90 multiply(X, multiplicative_identity) = X % 0.74/0.90 add(X, inverse(X)) = multiplicative_identity % 0.74/0.90 multiply(X, inverse(X)) = additive_identity % 0.74/0.90 add(a, multiplicative_identity) = multiplicative_identity ==> \bottom % 0.74/0.90 % 0.74/0.90 This holds because % 0.74/0.90 % 0.74/0.90 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.74/0.90 % 0.74/0.90 E: % 0.74/0.90 add(X, Y) = add(Y, X) % 0.74/0.90 add(X, additive_identity) = X % 0.74/0.90 add(X, inverse(X)) = multiplicative_identity % 0.74/0.90 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 0.74/0.90 f1(add(a, multiplicative_identity)) = true__ % 0.74/0.90 f1(multiplicative_identity) = false__ % 0.74/0.90 multiply(X, Y) = multiply(Y, X) % 0.74/0.90 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.74/0.90 multiply(X, inverse(X)) = additive_identity % 0.74/0.91 multiply(X, multiplicative_identity) = X % 0.74/0.91 G: % 0.74/0.91 true__ = false__ % 0.74/0.91 % 0.74/0.91 This holds because % 0.74/0.91 % 0.74/0.91 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.74/0.91 % 0.74/0.91 add(X, Y) = add(Y, X) % 0.74/0.91 multiply(X, Y) = multiply(Y, X) % 0.74/0.91 multiply(Y0, add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2)) % 0.74/0.91 multiply(add(Y0, Y0), add(Y0, Y1)) = multiply(Y0, add(Y1, multiplicative_identity)) % 0.74/0.91 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2)) % 0.74/0.91 multiply(add(multiplicative_identity, Y0), additive_identity) = multiply(additive_identity, Y0) % 0.74/0.91 add(X, additive_identity) -> X % 0.74/0.91 add(X, inverse(X)) -> multiplicative_identity % 0.74/0.91 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z)) % 0.74/0.91 add(Y0, inverse(inverse(Y0))) -> Y0 % 0.74/0.91 add(Y0, multiplicative_identity) -> multiplicative_identity % 0.74/0.91 add(Y1, Y1) -> Y1 % 0.74/0.91 add(additive_identity, Y0) -> Y0 % 0.74/0.91 add(multiplicative_identity, Y0) -> multiplicative_identity % 0.74/0.91 add(multiplicative_identity, multiplicative_identity) -> multiplicative_identity % 0.74/0.91 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 0.74/0.91 f1(add(a, multiplicative_identity)) -> true__ % 0.74/0.91 f1(add(multiplicative_identity, a)) -> true__ % 0.74/0.91 f1(multiplicative_identity) -> false__ % 0.74/0.91 inverse(additive_identity) -> multiplicative_identity % 0.74/0.91 inverse(multiplicative_identity) -> additive_identity % 0.74/0.91 multiply(X, inverse(X)) -> additive_identity % 0.74/0.91 multiply(X, multiplicative_identity) -> X % 0.74/0.91 multiply(Y0, Y0) -> Y0 % 0.74/0.91 multiply(Y0, add(Y0, Y0)) -> Y0 % 0.74/0.91 multiply(Y0, add(Y0, Y1)) -> Y0 % 0.74/0.91 multiply(Y0, add(Y0, inverse(additive_identity))) -> Y0 % 0.74/0.91 multiply(Y0, add(Y0, multiplicative_identity)) -> Y0 % 0.74/0.91 multiply(Y0, add(multiplicative_identity, Y0)) -> Y0 % 0.74/0.91 multiply(Y0, add(multiplicative_identity, inverse(Y0))) -> add(Y0, Y0) % 0.74/0.91 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0 % 0.74/0.91 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1) % 0.74/0.91 multiply(additive_identity, Y0) -> additive_identity % 0.74/0.91 multiply(additive_identity, add(Y1, multiplicative_identity)) -> multiply(additive_identity, Y1) % 0.74/0.91 multiply(additive_identity, add(multiplicative_identity, Y1)) -> multiply(additive_identity, Y1) % 0.74/0.91 multiply(additive_identity, additive_identity) -> additive_identity % 0.74/0.91 multiply(multiplicative_identity, Y0) -> Y0 % 0.74/0.91 true__ -> false__ % 0.74/0.91 with the LPO induced by % 0.74/0.91 a > f1 > inverse > additive_identity > add > multiply > multiplicative_identity > true__ > false__ % 0.74/0.91 % 0.74/0.91 % SZS output end Proof % 0.74/0.91 %------------------------------------------------------------------------------