%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 20:36:14 EDT 2022 % Result : Unsatisfiable 2.13s 2.25s % Output : Proof 2.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Mon May 30 20:01:57 EDT 2022 % 0.14/0.35 % CPUTime : % 2.13/2.25 % SZS status Unsatisfiable % 2.13/2.25 % SZS output start Proof % 2.13/2.25 The input problem is unsatisfiable because % 2.13/2.25 % 2.13/2.25 [1] the following set of Horn clauses is unsatisfiable: % 2.13/2.25 % 2.13/2.25 add(X, Y) = add(Y, X) % 2.13/2.25 add(add(X, Y), Z) = add(X, add(Y, Z)) % 2.13/2.25 add(X, additive_identity) = X % 2.13/2.25 add(additive_identity, X) = X % 2.13/2.25 add(X, additive_inverse(X)) = additive_identity % 2.13/2.25 add(additive_inverse(X), X) = additive_identity % 2.13/2.25 additive_inverse(additive_identity) = additive_identity % 2.13/2.25 add(X, add(additive_inverse(X), Y)) = Y % 2.13/2.25 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y)) % 2.13/2.25 additive_inverse(additive_inverse(X)) = X % 2.13/2.25 multiply(X, additive_identity) = additive_identity % 2.13/2.25 multiply(additive_identity, X) = additive_identity % 2.13/2.25 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y) % 2.13/2.25 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 2.13/2.25 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 2.13/2.25 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 2.13/2.25 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 2.13/2.25 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 2.13/2.25 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 2.13/2.25 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 2.13/2.25 multiply(multiply(associator(X, X, Y), X), associator(X, X, Y)) = additive_identity % 2.13/2.25 multiply(multiply(associator(a, a, b), a), associator(a, a, b)) = additive_identity ==> \bottom % 2.13/2.25 % 2.13/2.25 This holds because % 2.13/2.25 % 2.13/2.25 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.13/2.25 % 2.13/2.25 E: % 2.13/2.25 add(X, Y) = add(Y, X) % 2.13/2.25 add(X, add(additive_inverse(X), Y)) = Y % 2.13/2.25 add(X, additive_identity) = X % 2.13/2.25 add(X, additive_inverse(X)) = additive_identity % 2.13/2.25 add(add(X, Y), Z) = add(X, add(Y, Z)) % 2.13/2.25 add(additive_identity, X) = X % 2.13/2.25 add(additive_inverse(X), X) = additive_identity % 2.13/2.25 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y)) % 2.13/2.25 additive_inverse(additive_identity) = additive_identity % 2.13/2.25 additive_inverse(additive_inverse(X)) = X % 2.13/2.25 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 2.13/2.25 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 2.13/2.25 f1(additive_identity) = false__ % 2.13/2.25 f1(multiply(multiply(associator(a, a, b), a), associator(a, a, b))) = true__ % 2.13/2.25 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 2.13/2.25 multiply(X, additive_identity) = additive_identity % 2.13/2.25 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 2.13/2.25 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 2.13/2.25 multiply(additive_identity, X) = additive_identity % 2.13/2.25 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 2.13/2.25 multiply(additive_inverse(X), additive_inverse(Y)) = multiply(X, Y) % 2.13/2.25 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 2.13/2.25 multiply(multiply(associator(X, X, Y), X), associator(X, X, Y)) = additive_identity % 2.13/2.25 G: % 2.13/2.25 true__ = false__ % 2.13/2.25 % 2.13/2.25 This holds because % 2.13/2.25 % 2.13/2.25 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.13/2.25 % 2.13/2.25 add(X, Y) = add(Y, X) % 2.13/2.25 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 2.13/2.25 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 2.13/2.25 add(multiply(X0, X1), multiply(Y2, additive_inverse(X1))) = multiply(add(additive_inverse(X0), Y2), additive_inverse(X1)) % 2.13/2.25 add(multiply(X0, X1), multiply(additive_inverse(X0), Y2)) = multiply(additive_inverse(X0), add(additive_inverse(X1), Y2)) % 2.13/2.25 add(multiply(X0, multiply(Y2, Y2)), multiply(multiply(X0, Y2), Y1)) = multiply(multiply(X0, Y2), add(Y1, Y2)) % 2.13/2.25 multiply(X0, additive_inverse(Y1)) = multiply(additive_inverse(X0), Y1) % 2.13/2.25 multiply(Y2, add(Y1, Y1)) = multiply(add(Y2, Y2), Y1) % 2.13/2.25 multiply(multiply(X0, X1), additive_inverse(X1)) = multiply(additive_inverse(X0), multiply(X1, X1)) % 2.13/2.25 add(X, add(additive_inverse(X), Y)) -> Y % 2.13/2.25 add(X, additive_identity) -> X % 2.13/2.25 add(X, additive_inverse(X)) -> additive_identity % 2.13/2.25 add(Y0, add(Y1, add(additive_inverse(add(Y0, Y1)), X1))) -> X1 % 2.13/2.25 add(Y0, add(Y1, additive_inverse(Y0))) -> Y1 % 2.13/2.25 add(Y0, add(Y1, additive_inverse(add(Y0, Y1)))) -> additive_identity % 2.13/2.25 add(Y0, additive_inverse(add(Y0, X1))) -> additive_inverse(X1) % 2.13/2.25 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 2.13/2.25 add(additive_identity, X) -> X % 2.13/2.25 add(additive_inverse(X), X) -> additive_identity % 2.13/2.25 add(additive_inverse(X), additive_inverse(Y)) -> additive_inverse(add(X, Y)) % 2.13/2.25 add(additive_inverse(X0), add(X0, Y1)) -> Y1 % 2.13/2.25 add(additive_inverse(Y0), X0) -> additive_inverse(add(Y0, additive_inverse(X0))) % 2.13/2.25 add(additive_inverse(Y0), multiply(X0, additive_inverse(X1))) -> additive_inverse(add(Y0, multiply(X0, X1))) % 2.13/2.25 add(additive_inverse(Y0), multiply(additive_inverse(X0), X1)) -> additive_inverse(add(Y0, multiply(X0, X1))) % 2.13/2.25 add(additive_inverse(add(X0, X1)), Y2) -> add(additive_inverse(X0), add(additive_inverse(X1), Y2)) % 2.13/2.25 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 2.13/2.25 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 2.13/2.25 add(multiply(X0, X1), add(multiply(X0, additive_inverse(X1)), Y1)) -> Y1 % 2.13/2.25 add(multiply(X0, X1), add(multiply(additive_inverse(X0), X1), Y1)) -> Y1 % 2.13/2.25 add(multiply(X0, add(X1, X2)), Y2) -> add(multiply(X0, X1), add(multiply(X0, X2), Y2)) % 2.13/2.25 add(multiply(X0, additive_inverse(X1)), additive_inverse(Y1)) -> additive_inverse(add(multiply(X0, X1), Y1)) % 2.13/2.25 add(multiply(X0, multiply(Y1, Y1)), multiply(Y2, Y1)) -> multiply(add(multiply(X0, Y1), Y2), Y1) % 2.13/2.25 add(multiply(X0, multiply(Y1, Y1)), multiply(multiply(X0, Y1), Y2)) -> multiply(multiply(X0, Y1), add(Y1, Y2)) % 2.13/2.25 add(multiply(Y0, Y1), multiply(X0, multiply(Y1, Y1))) -> multiply(add(Y0, multiply(X0, Y1)), Y1) % 2.13/2.25 add(multiply(Y0, additive_inverse(X1)), multiply(X0, X1)) -> multiply(add(Y0, additive_inverse(X0)), additive_inverse(X1)) % 2.13/2.25 add(multiply(add(X0, X2), X1), Y2) -> add(multiply(X0, X1), add(multiply(X2, X1), Y2)) % 2.13/2.25 add(multiply(additive_inverse(X0), X1), additive_inverse(Y1)) -> additive_inverse(add(multiply(X0, X1), Y1)) % 2.13/2.25 add(multiply(additive_inverse(X0), Y1), multiply(X0, X1)) -> multiply(additive_inverse(X0), add(Y1, additive_inverse(X1))) % 2.13/2.25 additive_inverse(add(additive_inverse(X0), Y1)) -> add(X0, additive_inverse(Y1)) % 2.13/2.25 additive_inverse(additive_identity) -> additive_identity % 2.13/2.25 additive_inverse(additive_inverse(X)) -> X % 2.13/2.25 additive_inverse(multiply(X, Y)) -> multiply(X, additive_inverse(Y)) % 2.13/2.25 additive_inverse(multiply(X, Y)) -> multiply(additive_inverse(X), Y) % 2.13/2.25 associator(X, Y, Z) -> add(multiply(multiply(X, Y), Z), multiply(X, multiply(Y, additive_inverse(Z)))) % 2.13/2.25 commutator(X, Y) -> add(multiply(Y, X), multiply(X, additive_inverse(Y))) % 2.13/2.25 f1(additive_identity) -> false__ % 2.13/2.25 f1(multiply(multiply(add(multiply(multiply(a, a), b), multiply(a, multiply(a, additive_inverse(b)))), a), add(multiply(multiply(a, a), b), multiply(a, multiply(a, additive_inverse(b)))))) -> true__ % 2.13/2.25 f1(multiply(multiply(associator(a, a, b), a), associator(a, a, b))) -> true__ % 2.13/2.25 multiply(X, additive_identity) -> additive_identity % 2.13/2.25 multiply(add(Y0, multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0)), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) -> multiply(Y0, add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) % 2.13/2.25 multiply(add(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), Y2), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) -> multiply(Y2, add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) % 2.13/2.25 multiply(additive_identity, X) -> additive_identity % 2.13/2.25 multiply(additive_inverse(X), additive_inverse(Y)) -> multiply(X, Y) % 2.13/2.25 multiply(additive_inverse(Y0), multiply(X0, additive_inverse(X1))) -> multiply(Y0, multiply(X0, X1)) % 2.13/2.25 multiply(additive_inverse(Y0), multiply(additive_inverse(X0), X1)) -> multiply(Y0, multiply(X0, X1)) % 2.13/2.25 multiply(multiply(X, Y), Y) -> multiply(X, multiply(Y, Y)) % 2.13/2.25 multiply(multiply(X0, additive_inverse(X1)), additive_inverse(Y1)) -> multiply(multiply(X0, X1), Y1) % 2.13/2.25 multiply(multiply(X0, multiply(Y1, Y1)), Y1) -> multiply(multiply(X0, Y1), multiply(Y1, Y1)) % 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), add(Y1, add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))) -> multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), Y1) % 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), add(multiply(multiply(X0, X0), X1), add(multiply(X0, multiply(X0, additive_inverse(X1))), Y2))) -> multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), Y2) % 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), additive_inverse(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))) -> additive_identity % 2.13/2.25 multiply(multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), X0), multiply(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1)))))) -> additive_identity % 2.13/2.25 multiply(multiply(add(multiply(multiply(Y0, Y0), Y1), multiply(Y0, multiply(Y0, additive_inverse(Y1)))), Y0), add(multiply(multiply(Y0, Y0), Y1), multiply(Y0, multiply(Y0, additive_inverse(Y1))))) -> additive_identity % 2.13/2.25 multiply(multiply(additive_inverse(X0), X1), additive_inverse(Y1)) -> multiply(multiply(X0, X1), Y1) % 2.13/2.25 multiply(multiply(additive_inverse(add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))), X0), add(multiply(multiply(X0, X0), X1), multiply(X0, multiply(X0, additive_inverse(X1))))) -> additive_identity % 2.13/2.25 multiply(multiply(associator(X, X, Y), X), associator(X, X, Y)) -> additive_identity % 2.13/2.25 true__ -> false__ % 2.13/2.25 with the LPO induced by % 2.13/2.25 b > commutator > a > associator > add > additive_identity > additive_inverse > multiply > f1 > true__ > false__ % 2.13/2.25 % 2.13/2.25 % SZS output end Proof % 2.13/2.25 %------------------------------------------------------------------------------