%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO003-4 : TPTP v8.1.0. Released v1.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 3.22s 3.39s % Output : Proof 3.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : BOO003-4 : TPTP v8.1.0. Released v1.1.0. % 0.07/0.12 % Command : moca.sh %s % 0.13/0.32 % Computer : n021.cluster.edu % 0.13/0.32 % Model : x86_64 x86_64 % 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.32 % Memory : 8042.1875MB % 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.32 % CPULimit : 300 % 0.13/0.32 % WCLimit : 600 % 0.13/0.32 % DateTime : Wed Jun 1 18:30:46 EDT 2022 % 0.13/0.32 % CPUTime : % 3.22/3.39 % SZS status Unsatisfiable % 3.22/3.39 % SZS output start Proof % 3.22/3.39 The input problem is unsatisfiable because % 3.22/3.39 % 3.22/3.39 [1] the following set of Horn clauses is unsatisfiable: % 3.22/3.39 % 3.22/3.39 add(X, Y) = add(Y, X) % 3.22/3.39 multiply(X, Y) = multiply(Y, X) % 3.22/3.39 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 3.22/3.39 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 3.22/3.39 add(X, additive_identity) = X % 3.22/3.39 multiply(X, multiplicative_identity) = X % 3.22/3.39 add(X, inverse(X)) = multiplicative_identity % 3.22/3.39 multiply(X, inverse(X)) = additive_identity % 3.22/3.39 multiply(a, a) = a ==> \bottom % 3.22/3.39 % 3.22/3.39 This holds because % 3.22/3.39 % 3.22/3.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.22/3.39 % 3.22/3.39 E: % 3.22/3.39 add(X, Y) = add(Y, X) % 3.22/3.39 add(X, additive_identity) = X % 3.22/3.39 add(X, inverse(X)) = multiplicative_identity % 3.22/3.39 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 3.22/3.39 f1(a) = false__ % 3.22/3.39 f1(multiply(a, a)) = true__ % 3.22/3.39 multiply(X, Y) = multiply(Y, X) % 3.22/3.39 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 3.22/3.39 multiply(X, inverse(X)) = additive_identity % 3.22/3.39 multiply(X, multiplicative_identity) = X % 3.22/3.39 G: % 3.22/3.39 true__ = false__ % 3.22/3.39 % 3.22/3.39 This holds because % 3.22/3.39 % 3.22/3.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.22/3.39 % 3.22/3.39 add(X, Y) = add(Y, X) % 3.22/3.39 multiply(X, Y) = multiply(Y, X) % 3.22/3.39 add(X, inverse(X)) -> multiplicative_identity % 3.22/3.39 add(Y0, add(Y1, Y0)) -> add(Y0, Y1) % 3.22/3.39 add(Y0, inverse(inverse(Y0))) -> Y0 % 3.22/3.39 add(Y0, inverse(multiplicative_identity)) -> Y0 % 3.22/3.39 add(Y0, multiplicative_identity) -> multiplicative_identity % 3.22/3.39 add(Y0, multiply(Y0, Y1)) -> Y0 % 3.22/3.39 add(Y0, multiply(Y1, inverse(Y0))) -> add(Y0, Y1) % 3.22/3.39 add(Y0, multiply(inverse(Y0), Y2)) -> add(Y0, Y2) % 3.22/3.39 add(Y0, multiply(inverse(Y1), Y0)) -> Y0 % 3.22/3.39 add(Y1, Y1) -> Y1 % 3.22/3.39 add(Y2, multiply(Y1, Y2)) -> Y2 % 3.22/3.39 add(inverse(multiplicative_identity), Y0) -> Y0 % 3.22/3.39 add(multiplicative_identity, Y1) -> multiplicative_identity % 3.22/3.39 add(multiply(Y0, Y0), multiply(Y0, Y2)) -> Y0 % 3.22/3.39 add(multiply(Y0, Y1), multiply(Y0, Y0)) -> Y0 % 3.22/3.39 add(multiply(Y0, Y1), multiply(Y0, inverse(Y1))) -> Y0 % 3.22/3.39 additive_identity -> inverse(multiplicative_identity) % 3.22/3.39 f1(a) -> false__ % 3.22/3.39 f1(multiply(a, a)) -> true__ % 3.22/3.39 inverse(inverse(multiplicative_identity)) -> multiplicative_identity % 3.22/3.39 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z)) % 3.22/3.39 multiply(X, inverse(X)) -> inverse(multiplicative_identity) % 3.22/3.39 multiply(X, multiplicative_identity) -> X % 3.22/3.39 multiply(Y0, Y0) -> Y0 % 3.22/3.39 multiply(Y0, inverse(inverse(Y0))) -> Y0 % 3.22/3.39 multiply(Y0, inverse(multiplicative_identity)) -> inverse(multiplicative_identity) % 3.22/3.39 multiply(add(X, Y), add(X, Z)) -> add(X, multiply(Y, Z)) % 3.22/3.39 multiply(add(Y0, Y0), add(Y0, Y1)) -> add(multiply(Y0, Y1), Y0) % 3.22/3.39 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0 % 3.22/3.39 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1) % 3.22/3.39 multiply(inverse(multiplicative_identity), Y0) -> inverse(multiplicative_identity) % 3.22/3.39 multiply(multiplicative_identity, Y0) -> Y0 % 3.22/3.39 true__ -> false__ % 3.22/3.39 with the LPO induced by % 3.22/3.39 multiply > add > additive_identity > multiplicative_identity > inverse > f1 > a > true__ > false__ % 3.22/3.39 % 3.22/3.39 % SZS output end Proof % 3.22/3.39 %------------------------------------------------------------------------------