%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 : Mon Jul 18 20:36:07 EDT 2022 % Result : Unsatisfiable 0.90s 1.06s % Output : Proof 0.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.09 % Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0. % 0.02/0.10 % Command : moca.sh %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 600 % 0.09/0.28 % DateTime : Mon May 30 04:56:27 EDT 2022 % 0.09/0.28 % CPUTime : % 0.90/1.06 % SZS status Unsatisfiable % 0.90/1.06 % SZS output start Proof % 0.90/1.06 The input problem is unsatisfiable because % 0.90/1.06 % 0.90/1.06 [1] the following set of Horn clauses is unsatisfiable: % 0.90/1.06 % 0.90/1.06 add(additive_identity, X) = X % 0.90/1.06 add(additive_inverse(X), X) = additive_identity % 0.90/1.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.90/1.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 0.90/1.06 additive_inverse(additive_identity) = additive_identity % 0.90/1.06 additive_inverse(additive_inverse(X)) = X % 0.90/1.06 multiply(X, additive_identity) = additive_identity % 0.90/1.06 multiply(additive_identity, X) = additive_identity % 0.90/1.06 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y)) % 0.90/1.06 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 0.90/1.06 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 0.90/1.06 add(add(X, Y), Z) = add(X, add(Y, Z)) % 0.90/1.06 add(X, Y) = add(Y, X) % 0.90/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.90/1.06 multiply(X, X) = X % 0.90/1.06 add(a, a) = additive_identity ==> \bottom % 0.90/1.06 % 0.90/1.06 This holds because % 0.90/1.06 % 0.90/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.90/1.06 % 0.90/1.06 E: % 0.90/1.06 add(X, Y) = add(Y, X) % 0.90/1.06 add(add(X, Y), Z) = add(X, add(Y, Z)) % 0.90/1.06 add(additive_identity, X) = X % 0.90/1.06 add(additive_inverse(X), X) = additive_identity % 0.90/1.06 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y)) % 0.90/1.06 additive_inverse(additive_identity) = additive_identity % 0.90/1.06 additive_inverse(additive_inverse(X)) = X % 0.90/1.06 f1(add(a, a)) = true__ % 0.90/1.06 f1(additive_identity) = false__ % 0.90/1.06 multiply(X, X) = X % 0.90/1.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 0.90/1.06 multiply(X, additive_identity) = additive_identity % 0.90/1.06 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 0.90/1.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 0.90/1.06 multiply(additive_identity, X) = additive_identity % 0.90/1.06 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 0.90/1.06 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 0.90/1.06 G: % 0.90/1.06 true__ = false__ % 0.90/1.06 % 0.90/1.06 This holds because % 0.90/1.06 % 0.90/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.90/1.06 % 0.90/1.06 add(X, Y) = add(Y, X) % 0.90/1.06 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 0.90/1.06 add(Y1, multiply(Y0, Y1)) = multiply(add(Y0, Y1), Y1) % 0.90/1.06 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 0.90/1.06 add(Y2, multiply(Y2, Y1)) = multiply(Y2, add(Y1, Y2)) % 0.90/1.06 multiply(X0, additive_inverse(Y1)) = multiply(additive_inverse(X0), Y1) % 0.90/1.06 add(X0, additive_inverse(X0)) -> additive_identity % 0.90/1.06 add(X0, additive_inverse(add(X1, add(X0, additive_inverse(X1))))) -> additive_identity % 0.90/1.06 add(Y0, Y0) -> additive_identity % 0.90/1.06 add(Y0, add(Y1, Y0)) -> Y1 % 0.90/1.06 add(Y0, add(Y1, add(Y0, Y1))) -> additive_identity % 0.90/1.06 add(Y0, add(Y1, add(Y0, add(Y1, X1)))) -> X1 % 0.90/1.06 add(Y1, add(Y1, Y2)) -> Y2 % 0.90/1.06 add(Y1, additive_identity) -> Y1 % 0.90/1.06 add(Y1, multiply(Y1, Y2)) -> multiply(Y1, add(Y1, Y2)) % 0.90/1.06 add(Y1, multiply(Y2, Y1)) -> multiply(add(Y1, Y2), Y1) % 0.90/1.06 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 0.90/1.06 add(additive_identity, X) -> X % 0.90/1.06 add(additive_inverse(X), X) -> additive_identity % 0.90/1.06 add(additive_inverse(X), additive_inverse(Y)) -> additive_inverse(add(X, Y)) % 0.90/1.06 add(additive_inverse(Y0), X0) -> additive_inverse(add(Y0, additive_inverse(X0))) % 0.90/1.06 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 0.90/1.06 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 0.90/1.06 additive_inverse(Y1) -> Y1 % 0.90/1.06 additive_inverse(add(Y0, additive_identity)) -> additive_inverse(Y0) % 0.90/1.06 additive_inverse(add(additive_inverse(X0), Y1)) -> add(X0, additive_inverse(Y1)) % 0.90/1.06 additive_inverse(additive_identity) -> additive_identity % 0.90/1.06 additive_inverse(additive_inverse(X)) -> X % 0.90/1.06 additive_inverse(multiply(X, Y)) -> multiply(X, additive_inverse(Y)) % 0.90/1.06 additive_inverse(multiply(X, Y)) -> multiply(additive_inverse(X), Y) % 0.90/1.06 f1(add(a, a)) -> true__ % 0.90/1.06 f1(additive_identity) -> false__ % 0.90/1.06 multiply(X, X) -> X % 0.90/1.06 multiply(X, additive_identity) -> additive_identity % 0.90/1.06 multiply(Y0, add(Y0, add(X1, Y0))) -> multiply(Y0, X1) % 0.90/1.06 multiply(Y0, multiply(Y1, multiply(Y0, Y1))) -> multiply(Y0, Y1) % 0.90/1.06 multiply(Y1, additive_inverse(Y1)) -> additive_inverse(Y1) % 0.90/1.06 multiply(Y1, multiply(Y1, Y2)) -> multiply(Y1, Y2) % 0.90/1.06 multiply(add(Y0, add(X1, Y0)), Y0) -> multiply(X1, Y0) % 0.90/1.06 multiply(additive_identity, X) -> additive_identity % 0.90/1.06 multiply(additive_inverse(X0), X0) -> X0 % 0.90/1.06 multiply(additive_inverse(X0), additive_inverse(X1)) -> multiply(X0, X1) % 0.90/1.06 multiply(additive_inverse(Y1), Y1) -> additive_inverse(Y1) % 0.90/1.06 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 0.90/1.06 true__ -> false__ % 0.90/1.06 with the LPO induced by % 0.90/1.06 a > f1 > add > additive_inverse > multiply > additive_identity > true__ > false__ % 0.90/1.06 % 0.90/1.06 % SZS output end Proof % 0.90/1.06 %------------------------------------------------------------------------------