%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0. % 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 : Mon Jul 18 20:36:17 EDT 2022 % Result : Unsatisfiable 31.09s 31.06s % Output : Proof 31.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon May 30 13:20:44 EDT 2022 % 0.13/0.34 % CPUTime : % 31.09/31.06 % SZS status Unsatisfiable % 31.09/31.06 % SZS output start Proof % 31.09/31.06 The input problem is unsatisfiable because % 31.09/31.06 % 31.09/31.06 [1] the following set of Horn clauses is unsatisfiable: % 31.09/31.06 % 31.09/31.06 add(additive_identity, X) = X % 31.09/31.06 add(X, additive_identity) = X % 31.09/31.06 multiply(additive_identity, X) = additive_identity % 31.09/31.06 multiply(X, additive_identity) = additive_identity % 31.09/31.06 add(additive_inverse(X), X) = additive_identity % 31.09/31.06 add(X, additive_inverse(X)) = additive_identity % 31.09/31.06 additive_inverse(additive_inverse(X)) = X % 31.09/31.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 31.09/31.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 31.09/31.06 add(X, Y) = add(Y, X) % 31.09/31.06 add(X, add(Y, Z)) = add(add(X, Y), Z) % 31.09/31.06 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 31.09/31.06 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)) % 31.09/31.06 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 31.09/31.06 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 31.09/31.06 multiply(add(x, y), additive_inverse(z)) = add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))) ==> \bottom % 31.09/31.06 % 31.09/31.06 This holds because % 31.09/31.06 % 31.09/31.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 31.09/31.06 % 31.09/31.06 E: % 31.09/31.06 add(X, Y) = add(Y, X) % 31.09/31.06 add(X, add(Y, Z)) = add(add(X, Y), Z) % 31.09/31.06 add(X, additive_identity) = X % 31.09/31.06 add(X, additive_inverse(X)) = additive_identity % 31.09/31.06 add(additive_identity, X) = X % 31.09/31.06 add(additive_inverse(X), X) = additive_identity % 31.09/31.06 additive_inverse(additive_inverse(X)) = X % 31.09/31.06 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 31.09/31.06 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 31.09/31.06 f1(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z)))) = false__ % 31.09/31.06 f1(multiply(add(x, y), additive_inverse(z))) = true__ % 31.09/31.06 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 31.09/31.06 multiply(X, additive_identity) = additive_identity % 31.09/31.06 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 31.09/31.06 multiply(additive_identity, X) = additive_identity % 31.09/31.06 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)) % 31.09/31.06 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 31.09/31.06 G: % 31.09/31.06 true__ = false__ % 31.09/31.06 % 31.09/31.06 This holds because % 31.09/31.06 % 31.09/31.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 31.09/31.06 % 31.09/31.06 add(X, Y) = add(Y, X) % 31.09/31.06 add(Y0, add(Y2, additive_inverse(X0))) = add(additive_inverse(X0), add(Y2, Y0)) % 31.09/31.06 add(Y0, add(additive_inverse(X1), Y1)) = add(Y1, add(additive_inverse(X1), Y0)) % 31.09/31.06 add(Y0, additive_inverse(X1)) = add(additive_inverse(X1), Y0) % 31.09/31.06 add(Y0, additive_inverse(multiply(X0, X1))) = add(additive_inverse(multiply(X0, X1)), Y0) % 31.09/31.06 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 31.09/31.06 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 31.09/31.06 add(additive_inverse(Y0), add(X2, add(additive_inverse(X1), Y0))) = add(additive_inverse(X1), X2) % 31.09/31.06 add(additive_inverse(Y0), add(Y1, add(Y0, additive_inverse(Y2)))) = add(additive_inverse(Y2), Y1) % 31.09/31.06 add(additive_inverse(Y0), add(additive_inverse(X2), add(X1, Y0))) = add(X1, additive_inverse(X2)) % 31.09/31.06 add(additive_inverse(Y0), add(additive_inverse(Y1), add(Y0, Y2))) = add(Y2, additive_inverse(Y1)) % 31.09/31.06 add(X, additive_identity) -> X % 31.09/31.06 add(X, additive_inverse(X)) -> additive_identity % 31.09/31.06 add(X0, add(X1, add(Y1, add(Y2, add(additive_inverse(X1), additive_inverse(X0)))))) -> add(Y1, Y2) % 31.09/31.06 add(Y0, add(X1, add(X2, additive_inverse(Y0)))) -> add(X1, X2) % 31.09/31.06 add(Y0, add(Y1, additive_inverse(Y0))) -> Y1 % 31.09/31.06 add(Y0, add(additive_inverse(Y0), Y2)) -> Y2 % 31.09/31.06 add(Y1, add(Y0, add(additive_inverse(Y1), X1))) -> add(Y0, X1) % 31.09/31.06 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 31.09/31.06 add(additive_identity, X) -> X % 31.09/31.06 add(additive_inverse(X), X) -> additive_identity % 31.09/31.06 add(additive_inverse(Y0), add(Y2, add(Y0, additive_inverse(Y1)))) -> add(Y2, additive_inverse(Y1)) % 31.09/31.06 add(additive_inverse(Y0), add(additive_inverse(Y2), add(Y0, Y1))) -> add(additive_inverse(Y2), Y1) % 31.09/31.06 add(additive_inverse(Y1), add(Y1, Y2)) -> Y2 % 31.09/31.06 add(additive_inverse(Y2), add(Y1, add(additive_inverse(Y0), Y2))) -> add(Y1, additive_inverse(Y0)) % 31.09/31.06 additive_inverse(add(X1, Y0)) -> add(additive_inverse(Y0), additive_inverse(X1)) % 31.09/31.06 additive_inverse(additive_identity) -> additive_identity % 31.09/31.06 additive_inverse(additive_inverse(X)) -> X % 31.09/31.06 associator(X, Y, Z) -> add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 31.09/31.06 commutator(X, Y) -> add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 31.09/31.06 f1(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z)))) -> false__ % 31.09/31.06 f1(add(additive_inverse(multiply(y, z)), additive_inverse(multiply(x, z)))) -> false__ % 31.09/31.06 f1(multiply(add(x, y), additive_inverse(z))) -> true__ % 31.09/31.06 f1(multiply(add(y, x), additive_inverse(z))) -> true__ % 31.09/31.06 false__ -> true__ % 31.09/31.06 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z)) % 31.09/31.06 multiply(X, additive_identity) -> additive_identity % 31.09/31.06 multiply(X0, additive_inverse(X1)) -> additive_inverse(multiply(X0, X1)) % 31.09/31.06 multiply(add(X, Y), Z) -> add(multiply(X, Z), multiply(Y, Z)) % 31.09/31.06 multiply(additive_identity, X) -> additive_identity % 31.09/31.06 multiply(additive_inverse(X0), X1) -> additive_inverse(multiply(X0, X1)) % 31.09/31.06 multiply(multiply(X, X), Y) -> multiply(X, multiply(X, Y)) % 31.09/31.06 multiply(multiply(X, Y), Y) -> multiply(X, multiply(Y, Y)) % 31.09/31.06 multiply(multiply(X0, multiply(X0, Y1)), Y1) -> multiply(X0, multiply(X0, multiply(Y1, Y1))) % 31.09/31.06 multiply(multiply(X0, multiply(X0, multiply(X0, X0))), Y1) -> multiply(X0, multiply(X0, multiply(X0, multiply(X0, Y1)))) % 31.09/31.06 multiply(multiply(X0, multiply(Y1, Y1)), Y1) -> multiply(multiply(X0, Y1), multiply(Y1, Y1)) % 31.09/31.06 with the LPO induced by % 31.09/31.06 commutator > associator > multiply > additive_inverse > add > additive_identity > z > y > x > f1 > false__ > true__ % 31.09/31.06 % 31.09/31.06 % SZS output end Proof % 31.09/31.06 %------------------------------------------------------------------------------