%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : RNG023-7 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 20:36:19 EDT 2022 % Result : Unsatisfiable 18.65s 18.63s % Output : Proof 18.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : RNG023-7 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon May 30 22:32:44 EDT 2022 % 0.12/0.33 % CPUTime : % 18.65/18.63 % SZS status Unsatisfiable % 18.65/18.63 % SZS output start Proof % 18.65/18.63 The input problem is unsatisfiable because % 18.65/18.63 % 18.65/18.63 [1] the following set of Horn clauses is unsatisfiable: % 18.65/18.63 % 18.65/18.63 add(additive_identity, X) = X % 18.65/18.63 add(X, additive_identity) = X % 18.65/18.63 multiply(additive_identity, X) = additive_identity % 18.65/18.63 multiply(X, additive_identity) = additive_identity % 18.65/18.63 add(additive_inverse(X), X) = additive_identity % 18.65/18.63 add(X, additive_inverse(X)) = additive_identity % 18.65/18.63 additive_inverse(additive_inverse(X)) = X % 18.65/18.63 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 18.65/18.63 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 18.65/18.63 add(X, Y) = add(Y, X) % 18.65/18.63 add(X, add(Y, Z)) = add(add(X, Y), Z) % 18.65/18.63 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 18.65/18.63 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)) % 18.65/18.63 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 18.65/18.63 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 18.65/18.63 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y) % 18.65/18.63 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 18.65/18.63 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 18.65/18.63 multiply(X, add(Y, additive_inverse(Z))) = add(multiply(X, Y), additive_inverse(multiply(X, Z))) % 18.65/18.63 multiply(add(X, additive_inverse(Y)), Z) = add(multiply(X, Z), additive_inverse(multiply(Y, Z))) % 18.65/18.63 multiply(additive_inverse(X), add(Y, Z)) = add(additive_inverse(multiply(X, Y)), additive_inverse(multiply(X, Z))) % 18.65/18.63 multiply(add(X, Y), additive_inverse(Z)) = add(additive_inverse(multiply(X, Z)), additive_inverse(multiply(Y, Z))) % 18.65/18.63 associator(x, x, y) = additive_identity ==> \bottom % 18.65/18.63 % 18.65/18.63 This holds because % 18.65/18.63 % 18.65/18.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 18.65/18.63 % 18.65/18.63 E: % 18.65/18.63 add(X, Y) = add(Y, X) % 18.65/18.63 add(X, add(Y, Z)) = add(add(X, Y), Z) % 18.65/18.63 add(X, additive_identity) = X % 18.65/18.63 add(X, additive_inverse(X)) = additive_identity % 18.65/18.63 add(additive_identity, X) = X % 18.65/18.63 add(additive_inverse(X), X) = additive_identity % 18.65/18.63 additive_inverse(additive_inverse(X)) = X % 18.65/18.63 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 18.65/18.63 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 18.65/18.63 f1(additive_identity) = false__ % 18.65/18.63 f1(associator(x, x, y)) = true__ % 18.65/18.63 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 18.65/18.63 multiply(X, add(Y, additive_inverse(Z))) = add(multiply(X, Y), additive_inverse(multiply(X, Z))) % 18.65/18.63 multiply(X, additive_identity) = additive_identity % 18.65/18.63 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 18.65/18.63 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 18.65/18.63 multiply(add(X, Y), additive_inverse(Z)) = add(additive_inverse(multiply(X, Z)), additive_inverse(multiply(Y, Z))) % 18.65/18.63 multiply(add(X, additive_inverse(Y)), Z) = add(multiply(X, Z), additive_inverse(multiply(Y, Z))) % 18.65/18.63 multiply(additive_identity, X) = additive_identity % 18.65/18.63 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 18.65/18.63 multiply(additive_inverse(X), add(Y, Z)) = add(additive_inverse(multiply(X, Y)), additive_inverse(multiply(X, Z))) % 18.65/18.63 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y) % 18.65/18.63 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)) % 18.65/18.63 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 18.65/18.63 G: % 18.65/18.63 true__ = false__ % 18.65/18.63 % 18.65/18.63 This holds because % 18.65/18.63 % 18.65/18.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 18.65/18.63 % 18.65/18.63 add(X, Y) = add(Y, X) % 18.65/18.63 add(Y0, add(Y2, additive_inverse(X0))) = add(additive_inverse(X0), add(Y2, Y0)) % 18.65/18.63 add(Y0, add(additive_inverse(X1), Y1)) = add(Y1, add(additive_inverse(X1), Y0)) % 18.65/18.63 add(Y0, add(additive_inverse(X1), additive_inverse(X0))) = add(additive_inverse(X0), add(additive_inverse(X1), Y0)) % 18.65/18.63 add(Y0, additive_inverse(X1)) = add(additive_inverse(X1), Y0) % 18.65/18.63 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 18.65/18.63 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 18.65/18.63 add(X, additive_identity) -> X % 18.65/18.63 add(X, additive_inverse(X)) -> additive_identity % 18.65/18.63 add(X0, add(X1, add(Y1, add(Y2, add(additive_inverse(X0), additive_inverse(X1)))))) -> add(Y1, Y2) % 18.65/18.63 add(X0, add(X1, add(Y1, add(Y2, add(additive_inverse(X1), additive_inverse(X0)))))) -> add(Y1, Y2) % 18.65/18.63 add(X0, add(additive_inverse(X0), Y1)) -> Y1 % 18.65/18.63 add(Y0, add(X1, add(X2, additive_inverse(Y0)))) -> add(X1, X2) % 18.65/18.63 add(Y0, add(X1, add(additive_inverse(Y0), Y2))) -> add(X1, Y2) % 18.65/18.63 add(Y0, add(Y1, additive_inverse(Y0))) -> Y1 % 18.65/18.63 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 18.65/18.63 add(additive_identity, X) -> X % 18.65/18.63 add(additive_inverse(X), X) -> additive_identity % 18.65/18.63 add(additive_inverse(X0), add(Y1, X0)) -> Y1 % 18.65/18.63 add(additive_inverse(Y1), add(Y1, Y2)) -> Y2 % 18.65/18.63 additive_inverse(add(X0, X1)) -> add(additive_inverse(X0), additive_inverse(X1)) % 18.65/18.63 additive_inverse(add(X1, X0)) -> add(additive_inverse(X0), additive_inverse(X1)) % 18.65/18.63 additive_inverse(add(additive_inverse(Y0), X1)) -> add(Y0, additive_inverse(X1)) % 18.65/18.63 additive_inverse(additive_identity) -> additive_identity % 18.65/18.63 additive_inverse(additive_inverse(X)) -> X % 18.65/18.63 associator(X, Y, Z) -> add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 18.65/18.63 commutator(X, Y) -> add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 18.65/18.63 f1(additive_identity) -> false__ % 18.65/18.63 f1(associator(x, x, y)) -> true__ % 18.65/18.63 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z)) % 18.65/18.63 multiply(X, additive_identity) -> additive_identity % 18.65/18.63 multiply(X, additive_inverse(Y)) -> additive_inverse(multiply(X, Y)) % 18.65/18.63 multiply(add(X, Y), Z) -> add(multiply(X, Z), multiply(Y, Z)) % 18.65/18.63 multiply(add(X, Y), additive_inverse(Z)) -> add(additive_inverse(multiply(X, Z)), additive_inverse(multiply(Y, Z))) % 18.65/18.63 multiply(additive_identity, X) -> additive_identity % 18.65/18.63 multiply(additive_inverse(X), Y) -> additive_inverse(multiply(X, Y)) % 18.65/18.63 multiply(additive_inverse(X), add(Y, Z)) -> add(additive_inverse(multiply(X, Y)), additive_inverse(multiply(X, Z))) % 18.65/18.63 multiply(multiply(X, X), Y) -> multiply(X, multiply(X, Y)) % 18.65/18.63 multiply(multiply(X, Y), Y) -> multiply(X, multiply(Y, Y)) % 18.65/18.63 multiply(multiply(X0, multiply(Y1, Y1)), Y1) -> multiply(multiply(X0, Y1), multiply(Y1, Y1)) % 18.65/18.63 true__ -> false__ % 18.65/18.63 with the LPO induced by % 18.65/18.63 associator > commutator > multiply > additive_inverse > add > y > x > additive_identity > f1 > true__ > false__ % 18.65/18.63 % 18.65/18.63 % SZS output end Proof % 18.65/18.63 %------------------------------------------------------------------------------