%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 20:36:08 EDT 2022 % Result : Unsatisfiable 25.76s 25.71s % Output : Proof 25.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n026.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 18:56:55 EDT 2022 % 0.13/0.34 % CPUTime : % 25.76/25.71 % SZS status Unsatisfiable % 25.76/25.71 % SZS output start Proof % 25.76/25.71 The input problem is unsatisfiable because % 25.76/25.71 % 25.76/25.71 [1] the following set of Horn clauses is unsatisfiable: % 25.76/25.71 % 25.76/25.71 add(additive_identity, X) = X % 25.76/25.71 add(additive_inverse(X), X) = additive_identity % 25.76/25.71 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 25.76/25.71 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 25.76/25.71 additive_inverse(additive_identity) = additive_identity % 25.76/25.71 additive_inverse(additive_inverse(X)) = X % 25.76/25.71 multiply(X, additive_identity) = additive_identity % 25.76/25.71 multiply(additive_identity, X) = additive_identity % 25.76/25.71 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y)) % 25.76/25.71 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 25.76/25.71 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 25.76/25.71 add(add(X, Y), Z) = add(X, add(Y, Z)) % 25.76/25.71 add(X, Y) = add(Y, X) % 25.76/25.71 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 25.76/25.71 add(X, additive_identity) = X % 25.76/25.71 add(X, additive_inverse(X)) = additive_identity % 25.76/25.71 multiply(X, X) = X % 25.76/25.71 multiply(a, b) = c % 25.76/25.71 multiply(b, a) = c ==> \bottom % 25.76/25.71 % 25.76/25.71 This holds because % 25.76/25.71 % 25.76/25.71 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 25.76/25.71 % 25.76/25.71 E: % 25.76/25.71 add(X, Y) = add(Y, X) % 25.76/25.71 add(X, additive_identity) = X % 25.76/25.71 add(X, additive_inverse(X)) = additive_identity % 25.76/25.71 add(add(X, Y), Z) = add(X, add(Y, Z)) % 25.76/25.71 add(additive_identity, X) = X % 25.76/25.71 add(additive_inverse(X), X) = additive_identity % 25.76/25.71 additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y)) % 25.76/25.71 additive_inverse(additive_identity) = additive_identity % 25.76/25.71 additive_inverse(additive_inverse(X)) = X % 25.76/25.71 f1(c) = false__ % 25.76/25.71 f1(multiply(b, a)) = true__ % 25.76/25.71 multiply(X, X) = X % 25.76/25.71 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 25.76/25.71 multiply(X, additive_identity) = additive_identity % 25.76/25.71 multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)) % 25.76/25.71 multiply(a, b) = c % 25.76/25.71 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 25.76/25.71 multiply(additive_identity, X) = additive_identity % 25.76/25.71 multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)) % 25.76/25.71 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)) % 25.76/25.71 G: % 25.76/25.71 true__ = false__ % 25.76/25.71 % 25.76/25.71 This holds because % 25.76/25.71 % 25.76/25.71 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 25.76/25.71 % 25.76/25.71 add(X, Y) = add(Y, X) % 25.76/25.71 add(Y0, multiply(Y1, add(Y1, X1))) = add(Y1, add(Y0, multiply(Y1, X1))) % 25.76/25.71 add(Y0, multiply(Y1, add(Y1, X1))) = add(Y1, add(multiply(Y1, X1), Y0)) % 25.76/25.71 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 25.76/25.71 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 25.76/25.71 multiply(X0, X1) = multiply(X1, X0) % 25.76/25.71 multiply(Y1, multiply(Y0, Y2)) = multiply(Y0, multiply(Y1, Y2)) % 25.76/25.71 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y1, Y2)) % 25.76/25.71 multiply(add(Y1, Y0), Y1) = multiply(add(Y0, Y1), Y1) % 25.76/25.71 add(X, additive_identity) -> X % 25.76/25.71 add(X, additive_inverse(X)) -> additive_identity % 25.76/25.71 add(X0, X0) -> g1 % 25.76/25.71 add(X0, add(X0, Y0)) -> Y0 % 25.76/25.71 add(Y0, add(X1, add(Y0, Y2))) -> add(X1, Y2) % 25.76/25.71 add(Y0, add(Y1, Y0)) -> Y1 % 25.76/25.71 add(Y0, add(Y1, add(X1, add(Y0, Y1)))) -> X1 % 25.76/25.71 add(Y0, g1) -> Y0 % 25.76/25.71 add(Y1, multiply(Y1, Y2)) -> multiply(Y1, add(Y1, Y2)) % 25.76/25.71 add(Y1, multiply(Y2, Y1)) -> multiply(add(Y1, Y2), Y1) % 25.76/25.71 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 25.76/25.71 add(additive_identity, X) -> X % 25.76/25.71 add(additive_inverse(X), X) -> additive_identity % 25.76/25.71 add(g1, Y0) -> Y0 % 25.76/25.71 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 25.76/25.71 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 25.76/25.71 add(multiply(X0, X1), add(Y0, multiply(X1, X0))) -> Y0 % 25.76/25.71 add(multiply(X0, X1), add(multiply(X1, X0), Y0)) -> Y0 % 25.76/25.71 add(multiply(X0, multiply(X1, Y1)), multiply(Y1, multiply(X0, X1))) -> g1 % 25.76/25.71 add(multiply(Y0, X1), multiply(X1, Y0)) -> g1 % 25.76/25.71 additive_inverse(X0) -> X0 % 25.76/25.71 c -> multiply(a, b) % 25.76/25.71 f1(multiply(a, b)) -> false__ % 25.76/25.71 f1(multiply(b, a)) -> true__ % 25.76/25.71 g1 -> additive_identity % 25.76/25.71 multiply(X, X) -> X % 25.76/25.71 multiply(X, additive_identity) -> additive_identity % 25.76/25.71 multiply(Y0, add(Y0, multiply(X1, multiply(Y0, add(Y0, X1))))) -> Y0 % 25.76/25.71 multiply(Y0, g1) -> g1 % 25.76/25.71 multiply(Y0, multiply(X0, multiply(X1, Y0))) -> multiply(Y0, multiply(X0, X1)) % 25.76/25.71 multiply(Y0, multiply(X1, add(X1, Y0))) -> g1 % 25.76/25.71 multiply(Y0, multiply(X1, add(Y0, X1))) -> g1 % 25.76/25.71 multiply(Y0, multiply(X1, multiply(Y0, Y2))) -> multiply(Y0, multiply(X1, Y2)) % 25.76/25.71 multiply(Y1, multiply(X1, Y1)) -> multiply(Y1, X1) % 25.76/25.71 multiply(Y1, multiply(Y1, Y2)) -> multiply(Y1, Y2) % 25.76/25.71 multiply(add(X1, Y0), X1) -> multiply(X1, add(X1, Y0)) % 25.76/25.71 multiply(additive_identity, X) -> additive_identity % 25.76/25.71 multiply(g1, Y0) -> g1 % 25.76/25.71 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 25.76/25.71 true__ -> false__ % 25.76/25.71 with the LPO induced by % 25.76/25.71 c > a > b > add > multiply > g1 > f1 > additive_identity > additive_inverse > true__ > false__ % 25.76/25.71 % 25.76/25.71 % SZS output end Proof % 25.76/25.71 %------------------------------------------------------------------------------