%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO003-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 23:46:12 EDT 2022 % Result : Unsatisfiable 5.55s 5.60s % Output : Proof 5.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : BOO003-2 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n022.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Wed Jun 1 21:35:52 EDT 2022 % 0.14/0.36 % CPUTime : % 5.55/5.60 % SZS status Unsatisfiable % 5.55/5.60 % SZS output start Proof % 5.55/5.60 The input problem is unsatisfiable because % 5.55/5.60 % 5.55/5.60 [1] the following set of Horn clauses is unsatisfiable: % 5.55/5.60 % 5.55/5.60 add(X, Y) = add(Y, X) % 5.55/5.60 multiply(X, Y) = multiply(Y, X) % 5.55/5.60 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 5.55/5.60 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 5.55/5.60 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 5.55/5.60 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 5.55/5.60 add(X, inverse(X)) = multiplicative_identity % 5.55/5.60 add(inverse(X), X) = multiplicative_identity % 5.55/5.60 multiply(X, inverse(X)) = additive_identity % 5.55/5.60 multiply(inverse(X), X) = additive_identity % 5.55/5.60 multiply(X, multiplicative_identity) = X % 5.55/5.60 multiply(multiplicative_identity, X) = X % 5.55/5.60 add(X, additive_identity) = X % 5.55/5.60 add(additive_identity, X) = X % 5.55/5.60 multiply(a, a) = a ==> \bottom % 5.55/5.60 % 5.55/5.60 This holds because % 5.55/5.60 % 5.55/5.60 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.55/5.60 % 5.55/5.60 E: % 5.55/5.60 add(X, Y) = add(Y, X) % 5.55/5.60 add(X, additive_identity) = X % 5.55/5.60 add(X, inverse(X)) = multiplicative_identity % 5.55/5.60 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 5.55/5.60 add(additive_identity, X) = X % 5.55/5.60 add(inverse(X), X) = multiplicative_identity % 5.55/5.60 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)) % 5.55/5.60 f1(a) = false__ % 5.55/5.60 f1(multiply(a, a)) = true__ % 5.55/5.60 multiply(X, Y) = multiply(Y, X) % 5.55/5.60 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 5.55/5.60 multiply(X, inverse(X)) = additive_identity % 5.55/5.60 multiply(X, multiplicative_identity) = X % 5.55/5.60 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 5.55/5.60 multiply(inverse(X), X) = additive_identity % 5.55/5.60 multiply(multiplicative_identity, X) = X % 5.55/5.60 G: % 5.55/5.60 true__ = false__ % 5.55/5.60 % 5.55/5.60 This holds because % 5.55/5.60 % 5.55/5.60 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.55/5.60 % 5.55/5.60 add(X, Y) = add(Y, X) % 5.55/5.60 multiply(X, Y) = multiply(Y, X) % 5.55/5.60 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2)) % 5.55/5.60 add(X, additive_identity) -> X % 5.55/5.60 add(X, inverse(X)) -> multiplicative_identity % 5.55/5.60 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z)) % 5.55/5.60 add(Y0, Y0) -> Y0 % 5.55/5.60 add(Y0, inverse(inverse(Y0))) -> Y0 % 5.55/5.60 add(Y0, inverse(inverse(Y0))) -> inverse(inverse(Y0)) % 5.55/5.60 add(Y0, multiplicative_identity) -> multiplicative_identity % 5.55/5.60 add(additive_identity, X) -> X % 5.55/5.60 add(inverse(X), X) -> multiplicative_identity % 5.55/5.60 add(multiplicative_identity, Y1) -> multiplicative_identity % 5.55/5.60 add(multiplicative_identity, inverse(Y0)) -> multiplicative_identity % 5.55/5.60 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z)) % 5.55/5.60 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 5.55/5.60 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 5.55/5.60 f1(a) -> false__ % 5.55/5.60 f1(multiply(a, a)) -> true__ % 5.55/5.60 inverse(additive_identity) -> multiplicative_identity % 5.55/5.60 inverse(multiplicative_identity) -> additive_identity % 5.55/5.60 multiply(X, inverse(X)) -> additive_identity % 5.55/5.60 multiply(X, multiplicative_identity) -> X % 5.55/5.60 multiply(Y0, Y0) -> Y0 % 5.55/5.60 multiply(Y0, add(Y0, Y0)) -> Y0 % 5.55/5.60 multiply(Y0, add(Y0, Y1)) -> Y0 % 5.55/5.60 multiply(Y0, add(Y0, multiplicative_identity)) -> Y0 % 5.55/5.60 multiply(Y0, add(Y1, Y0)) -> Y0 % 5.55/5.60 multiply(Y0, add(inverse(Y0), Y2)) -> multiply(Y0, Y2) % 5.55/5.60 multiply(Y1, add(multiplicative_identity, Y1)) -> Y1 % 5.55/5.60 multiply(Y1, additive_identity) -> additive_identity % 5.55/5.60 multiply(add(Y0, Y0), add(Y0, Y2)) -> Y0 % 5.55/5.60 multiply(add(Y0, Y0), add(Y1, Y0)) -> Y0 % 5.55/5.60 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0 % 5.55/5.60 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1) % 5.55/5.60 multiply(add(Y0, Y1), add(Y1, Y1)) -> Y1 % 5.55/5.60 multiply(add(Y0, Y1), add(Y1, inverse(Y0))) -> Y1 % 5.55/5.60 multiply(add(Y0, Y2), add(inverse(Y0), Y2)) -> Y2 % 5.55/5.60 multiply(add(Y0, Y2), add(multiplicative_identity, Y2)) -> add(Y0, Y2) % 5.55/5.60 multiply(add(Y0, Y2), inverse(Y0)) -> multiply(Y2, inverse(Y0)) % 5.55/5.60 multiply(add(Y0, Y2), inverse(Y2)) -> multiply(Y0, inverse(Y2)) % 5.55/5.60 multiply(add(Y0, inverse(multiply(Y0, Y1))), add(Y1, inverse(multiply(Y0, Y1)))) -> multiplicative_identity % 5.55/5.60 multiply(add(Y0, multiplicative_identity), add(Y0, Y2)) -> add(Y0, Y2) % 5.55/5.60 multiply(add(Y1, Y2), add(Y1, Y1)) -> Y1 % 5.55/5.60 multiply(add(multiplicative_identity, Y2), add(Y1, Y2)) -> add(Y1, Y2) % 5.55/5.60 multiply(additive_identity, Y0) -> additive_identity % 5.55/5.60 multiply(additive_identity, add(multiplicative_identity, Y1)) -> multiply(additive_identity, Y1) % 5.55/5.60 multiply(additive_identity, additive_identity) -> additive_identity % 5.55/5.60 multiply(inverse(X), X) -> additive_identity % 5.55/5.60 multiply(multiplicative_identity, X) -> X % 5.55/5.60 true__ -> false__ % 5.55/5.60 with the LPO induced by % 5.55/5.60 a > f1 > inverse > additive_identity > multiplicative_identity > add > multiply > true__ > false__ % 5.55/5.60 % 5.55/5.60 % SZS output end Proof % 5.55/5.60 %------------------------------------------------------------------------------