%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO006-4 : 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 23:46:16 EDT 2022 % Result : Unsatisfiable 0.90s 1.10s % Output : Proof 0.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : BOO006-4 : TPTP v8.1.0. Released v1.1.0. % 0.11/0.13 % 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 18:55:01 EDT 2022 % 0.13/0.32 % CPUTime : % 0.90/1.10 % SZS status Unsatisfiable % 0.90/1.10 % SZS output start Proof % 0.90/1.10 The input problem is unsatisfiable because % 0.90/1.10 % 0.90/1.10 [1] the following set of Horn clauses is unsatisfiable: % 0.90/1.10 % 0.90/1.10 add(X, Y) = add(Y, X) % 0.90/1.10 multiply(X, Y) = multiply(Y, X) % 0.90/1.10 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 0.90/1.10 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.90/1.10 add(X, additive_identity) = X % 0.90/1.10 multiply(X, multiplicative_identity) = X % 0.90/1.10 add(X, inverse(X)) = multiplicative_identity % 0.90/1.10 multiply(X, inverse(X)) = additive_identity % 0.90/1.10 multiply(a, additive_identity) = additive_identity ==> \bottom % 0.90/1.10 % 0.90/1.10 This holds because % 0.90/1.10 % 0.90/1.10 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.90/1.10 % 0.90/1.10 E: % 0.90/1.10 add(X, Y) = add(Y, X) % 0.90/1.10 add(X, additive_identity) = X % 0.90/1.10 add(X, inverse(X)) = multiplicative_identity % 0.90/1.10 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)) % 0.90/1.10 f1(additive_identity) = false__ % 0.90/1.10 f1(multiply(a, additive_identity)) = true__ % 0.90/1.10 multiply(X, Y) = multiply(Y, X) % 0.90/1.10 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.90/1.10 multiply(X, inverse(X)) = additive_identity % 0.90/1.10 multiply(X, multiplicative_identity) = X % 0.90/1.10 G: % 0.90/1.10 true__ = false__ % 0.90/1.10 % 0.90/1.10 This holds because % 0.90/1.10 % 0.90/1.10 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.90/1.10 % 0.90/1.10 add(X, Y) = add(Y, X) % 0.90/1.10 add(multiply(Y0, Y0), multiply(Y0, Y2)) = add(Y0, multiply(inverse(multiplicative_identity), Y2)) % 0.90/1.10 multiply(X, Y) = multiply(Y, X) % 0.90/1.10 add(X, inverse(X)) -> multiplicative_identity % 0.90/1.10 add(Y0, inverse(inverse(Y0))) -> Y0 % 0.90/1.10 add(Y0, inverse(multiplicative_identity)) -> Y0 % 0.90/1.10 add(Y0, multiplicative_identity) -> multiplicative_identity % 0.90/1.10 add(Y0, multiply(Y0, Y0)) -> Y0 % 0.90/1.10 add(Y1, Y1) -> Y1 % 0.90/1.10 add(inverse(multiplicative_identity), Y0) -> Y0 % 0.90/1.10 add(multiplicative_identity, multiplicative_identity) -> multiplicative_identity % 0.90/1.10 add(multiply(Y0, Y0), multiply(Y0, inverse(additive_identity))) -> Y0 % 0.90/1.10 add(multiply(Y0, Y1), multiply(Y0, inverse(Y1))) -> Y0 % 0.90/1.10 additive_identity -> inverse(multiplicative_identity) % 0.90/1.10 f1(inverse(multiplicative_identity)) -> false__ % 0.90/1.10 f1(inverse(multiplicative_identity)) -> true__ % 0.90/1.10 f1(multiply(a, additive_identity)) -> true__ % 0.90/1.10 f1(multiply(inverse(multiplicative_identity), a)) -> true__ % 0.90/1.10 inverse(inverse(multiplicative_identity)) -> multiplicative_identity % 0.90/1.10 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z)) % 0.90/1.10 multiply(X, inverse(X)) -> inverse(multiplicative_identity) % 0.90/1.10 multiply(X, multiplicative_identity) -> X % 0.90/1.10 multiply(Y0, inverse(multiplicative_identity)) -> inverse(multiplicative_identity) % 0.90/1.10 multiply(add(X, Y), add(X, Z)) -> add(X, multiply(Y, Z)) % 0.90/1.10 multiply(add(Y0, Y0), add(Y0, Y1)) -> add(multiply(Y0, Y1), Y0) % 0.90/1.10 multiply(add(Y0, Y0), add(Y0, Y2)) -> add(Y0, multiply(Y0, Y2)) % 0.90/1.10 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0 % 0.90/1.10 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1) % 0.90/1.10 multiply(inverse(multiplicative_identity), Y0) -> inverse(multiplicative_identity) % 0.90/1.10 multiply(multiplicative_identity, Y0) -> Y0 % 0.90/1.10 true__ -> false__ % 0.90/1.10 with the LPO induced by % 0.90/1.10 a > f1 > multiply > additive_identity > inverse > multiplicative_identity > add > true__ > false__ % 0.90/1.10 % 0.90/1.10 % SZS output end Proof % 0.90/1.10 %------------------------------------------------------------------------------