%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : RNG008-7 : 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 20:36:10 EDT 2022 % Result : Unsatisfiable 29.76s 29.55s % Output : Proof 29.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n025.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon May 30 11:38:57 EDT 2022 % 0.14/0.35 % CPUTime : % 29.76/29.55 % SZS status Unsatisfiable % 29.76/29.55 % SZS output start Proof % 29.76/29.55 The input problem is unsatisfiable because % 29.76/29.55 % 29.76/29.55 [1] the following set of Horn clauses is unsatisfiable: % 29.76/29.55 % 29.76/29.55 add(additive_identity, X) = X % 29.76/29.55 add(X, additive_identity) = X % 29.76/29.55 add(additive_inverse(X), X) = additive_identity % 29.76/29.55 add(X, additive_inverse(X)) = additive_identity % 29.76/29.55 add(X, add(Y, Z)) = add(add(X, Y), Z) % 29.76/29.55 add(X, Y) = add(Y, X) % 29.76/29.55 multiply(X, multiply(Y, Z)) = multiply(multiply(X, Y), Z) % 29.76/29.55 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 29.76/29.55 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 29.76/29.55 multiply(X, X) = X % 29.76/29.55 multiply(a, b) = c % 29.76/29.55 multiply(b, a) = c ==> \bottom % 29.76/29.55 % 29.76/29.55 This holds because % 29.76/29.55 % 29.76/29.55 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 29.76/29.55 % 29.76/29.55 E: % 29.76/29.55 add(X, Y) = add(Y, X) % 29.76/29.55 add(X, add(Y, Z)) = add(add(X, Y), Z) % 29.76/29.55 add(X, additive_identity) = X % 29.76/29.55 add(X, additive_inverse(X)) = additive_identity % 29.76/29.55 add(additive_identity, X) = X % 29.76/29.55 add(additive_inverse(X), X) = additive_identity % 29.76/29.55 f1(c) = false__ % 29.76/29.55 f1(multiply(b, a)) = true__ % 29.76/29.55 multiply(X, X) = X % 29.76/29.55 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 29.76/29.55 multiply(X, multiply(Y, Z)) = multiply(multiply(X, Y), Z) % 29.76/29.55 multiply(a, b) = c % 29.76/29.55 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 29.76/29.55 G: % 29.76/29.55 true__ = false__ % 29.76/29.55 % 29.76/29.55 This holds because % 29.76/29.55 % 29.76/29.55 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 29.76/29.55 % 29.76/29.55 add(X, Y) = add(Y, X) % 29.76/29.55 add(X0, X0) = add(Y0, Y0) % 29.76/29.55 add(X0, X0) = multiply(Y0, add(Y1, Y1)) % 29.76/29.55 add(X1, X1) = multiply(add(Y0, Y0), Y1) % 29.76/29.55 add(X1, add(X2, add(Y1, add(X1, add(X2, Y1))))) = add(false__, false__) % 29.76/29.55 add(Y0, X1) = add(X0, add(X1, add(Y0, additive_inverse(X0)))) % 29.76/29.55 add(Y0, X1) = add(Y1, add(X1, add(Y1, Y0))) % 29.76/29.55 add(Y0, X1) = add(Y1, add(X1, add(additive_inverse(Y1), Y0))) % 29.76/29.55 add(Y0, Y0) = add(false__, false__) % 29.76/29.55 add(Y0, Y0) = multiply(additive_identity, Y0) % 29.76/29.55 add(Y0, add(X1, add(X2, Y1))) = add(Y1, add(X1, add(X2, Y0))) % 29.76/29.55 add(Y0, add(X1, add(X2, Y1))) = add(Y1, add(Y0, add(X1, X2))) % 29.76/29.55 add(Y0, add(X1, add(X2, add(X1, add(X2, Y0))))) = add(false__, false__) % 29.76/29.55 add(Y0, add(X1, add(Y1, X2))) = add(Y1, add(X1, add(X2, Y0))) % 29.76/29.55 add(Y0, add(X1, add(Y1, X2))) = add(Y1, add(Y0, add(X1, X2))) % 29.76/29.55 add(Y0, add(Y1, add(Y2, Y0))) = add(Y2, Y1) % 29.76/29.55 add(Y0, multiply(Y1, add(X1, Y1))) = add(Y1, add(Y0, multiply(Y1, X1))) % 29.76/29.55 add(Y0, multiply(Y1, add(X1, Y1))) = add(Y1, add(multiply(Y1, X1), Y0)) % 29.76/29.55 add(Y0, multiply(additive_identity, X1)) = multiply(Y0, add(multiply(additive_identity, X1), Y0)) % 29.76/29.55 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 29.76/29.55 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 29.76/29.55 add(Y2, multiply(Y2, Y1)) = multiply(Y2, add(Y1, Y2)) % 29.76/29.55 add(false__, false__) = multiply(Y1, multiply(X1, multiply(Y1, add(Y1, X1)))) % 29.76/29.55 additive_identity = add(Y0, Y0) % 29.76/29.55 additive_identity = add(Y1, add(Y2, add(Y1, Y2))) % 29.76/29.55 additive_identity = add(Y2, add(Y1, add(Y1, Y2))) % 29.76/29.55 multiply(X0, add(X1, X1)) = multiply(Y0, add(Y1, Y1)) % 29.76/29.55 multiply(X0, multiply(add(X1, X1), Y0)) = add(Y0, Y0) % 29.76/29.55 multiply(X0, multiply(add(X1, X1), Y0)) = add(false__, false__) % 29.76/29.55 multiply(X1, add(X2, X2)) = multiply(add(Y1, Y1), Y2) % 29.76/29.55 multiply(X1, multiply(add(X2, X2), Y1)) = add(Y2, Y2) % 29.76/29.55 multiply(X1, multiply(add(X2, X2), Y1)) = multiply(add(Y2, Y2), Y3) % 29.76/29.55 multiply(Y0, Y1) = multiply(Y1, Y0) % 29.76/29.55 multiply(Y0, add(X0, X0)) = add(false__, false__) % 29.76/29.55 multiply(Y0, add(Y1, Y1)) = additive_identity % 29.76/29.55 multiply(Y0, multiply(X0, add(X1, X1))) = add(false__, false__) % 29.76/29.55 multiply(Y0, multiply(X0, multiply(X1, add(X2, X2)))) = add(false__, false__) % 29.76/29.55 multiply(Y0, multiply(X0, multiply(add(X1, X1), Y1))) = add(false__, false__) % 29.76/29.55 multiply(Y0, multiply(X1, add(X2, X2))) = add(Y2, Y2) % 29.76/29.55 multiply(Y0, multiply(X1, add(X2, X2))) = multiply(Y2, add(Y3, Y3)) % 29.76/29.55 multiply(Y0, multiply(X1, add(X2, X2))) = multiply(add(Y2, Y2), Y3) % 29.76/29.55 multiply(Y0, multiply(X1, multiply(add(X2, X2), Y2))) = add(Y2, Y2) % 29.76/29.55 multiply(Y0, multiply(X1, multiply(add(X2, X2), Y2))) = add(Y3, Y3) % 29.76/29.55 multiply(Y0, multiply(Y1, multiply(X1, add(X2, X2)))) = add(Y3, Y3) % 29.76/29.55 multiply(Y0, multiply(add(X1, X1), X2)) = add(Y0, Y0) % 29.76/29.55 multiply(Y0, multiply(add(X1, X1), X2)) = multiply(Y2, add(Y3, Y3)) % 29.76/29.55 multiply(Y1, multiply(Y0, Y2)) = multiply(Y0, multiply(Y1, Y2)) % 29.76/29.55 multiply(Y2, multiply(Y0, Y1)) = multiply(Y0, multiply(Y1, Y2)) % 29.76/29.55 multiply(add(X0, X0), Y0) = add(Y0, Y0) % 29.76/29.55 multiply(add(X0, X0), Y0) = add(false__, false__) % 29.76/29.55 multiply(add(X1, X1), X2) = multiply(add(Y1, Y1), Y2) % 29.76/29.55 multiply(add(X1, X2), add(X1, add(X2, add(X1, X2)))) = add(X2, add(X1, add(X1, X2))) % 29.76/29.55 multiply(add(X1, add(X2, add(X1, X2))), add(X1, X2)) = add(X2, add(X1, add(X1, X2))) % 29.76/29.55 multiply(add(Y1, Y0), Y0) = multiply(Y0, add(Y0, Y1)) % 29.76/29.55 add(X, additive_identity) -> X % 29.76/29.55 add(X, additive_inverse(X)) -> additive_identity % 29.76/29.55 add(X0, add(X1, add(Y1, add(additive_inverse(X1), additive_inverse(X0))))) -> Y1 % 29.76/29.55 add(X0, add(additive_inverse(X1), add(Y1, add(X1, additive_inverse(X0))))) -> Y1 % 29.76/29.55 add(X0, multiply(add(additive_inverse(X0), Y1), additive_inverse(X0))) -> multiply(Y1, additive_inverse(X0)) % 29.76/29.55 add(X0, multiply(additive_inverse(X0), add(additive_inverse(X0), Y1))) -> multiply(additive_inverse(X0), Y1) % 29.76/29.55 add(X1, add(Y1, multiply(X1, add(X1, Y1)))) -> multiply(add(X1, Y1), Y1) % 29.76/29.55 add(X1, add(Y1, multiply(add(X1, Y1), X1))) -> multiply(add(X1, Y1), Y1) % 29.76/29.55 add(X1, additive_inverse(add(Y0, X1))) -> additive_inverse(Y0) % 29.76/29.55 add(X1, additive_inverse(add(additive_inverse(Y0), X1))) -> Y0 % 29.76/29.55 add(Y0, add(X0, X0)) -> Y0 % 29.76/29.55 add(Y0, add(X1, add(X2, Y0))) -> add(X1, X2) % 29.76/29.55 add(Y0, add(Y1, additive_inverse(Y0))) -> Y1 % 29.76/29.55 add(Y0, add(Y1, additive_inverse(add(Y0, Y1)))) -> additive_identity % 29.76/29.55 add(Y0, add(Y1, additive_inverse(add(Y1, Y0)))) -> additive_identity % 29.76/29.55 add(Y0, add(additive_inverse(Y0), Y2)) -> Y2 % 29.76/29.55 add(Y0, additive_inverse(add(Y0, Y1))) -> additive_inverse(Y1) % 29.76/29.55 add(Y0, additive_inverse(add(Y0, additive_inverse(Y1)))) -> Y1 % 29.76/29.55 add(Y0, additive_inverse(multiply(Y0, add(X1, Y0)))) -> additive_inverse(multiply(Y0, X1)) % 29.76/29.55 add(Y0, multiply(X0, add(X1, X1))) -> Y0 % 29.76/29.55 add(Y0, multiply(X1, multiply(add(X2, X2), Y2))) -> Y0 % 29.76/29.55 add(Y0, multiply(Y1, multiply(X1, add(X2, X2)))) -> Y0 % 29.76/29.55 add(Y0, multiply(Y1, multiply(Y2, multiply(X1, add(X2, X2))))) -> Y0 % 29.76/29.55 add(Y0, multiply(Y1, multiply(Y2, multiply(add(X1, X1), X2)))) -> Y0 % 29.76/29.55 add(Y0, multiply(additive_inverse(Y0), add(X1, additive_inverse(Y0)))) -> multiply(additive_inverse(Y0), X1) % 29.76/29.55 add(Y1, add(Y0, add(X1, additive_inverse(Y1)))) -> add(Y0, X1) % 29.76/29.55 add(Y1, add(Y0, add(Y1, X1))) -> add(Y0, X1) % 29.76/29.55 add(Y1, add(Y0, add(additive_inverse(Y1), X1))) -> add(Y0, X1) % 29.76/29.55 add(Y1, add(Y1, add(Y1, Y1))) -> multiply(add(Y1, Y1), add(Y1, add(Y1, Y1))) % 29.76/29.55 add(Y1, multiply(Y1, Y2)) -> multiply(Y1, add(Y1, Y2)) % 29.76/29.55 add(Y1, multiply(Y2, Y1)) -> multiply(add(Y1, Y2), Y1) % 29.76/29.55 add(Y1, multiply(add(X1, X1), X2)) -> Y1 % 29.76/29.55 add(Y2, add(Y0, Y2)) -> Y0 % 29.76/29.55 add(Y2, add(Y2, Y0)) -> Y0 % 29.76/29.55 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 29.76/29.55 add(additive_identity, X) -> X % 29.76/29.55 add(additive_inverse(X), X) -> additive_identity % 29.76/29.55 add(additive_inverse(Y0), multiply(Y0, add(X1, Y0))) -> multiply(Y0, X1) % 29.76/29.55 add(additive_inverse(Y0), multiply(Y0, add(Y0, X1))) -> multiply(Y0, X1) % 29.76/29.55 add(additive_inverse(Y0), multiply(add(Y0, X1), Y0)) -> multiply(X1, Y0) % 29.76/29.55 add(additive_inverse(Y1), add(Y1, Y2)) -> Y2 % 29.76/29.55 add(additive_inverse(Y1), additive_inverse(Y1)) -> multiply(additive_identity, additive_inverse(Y1)) % 29.76/29.55 add(additive_inverse(additive_inverse(X0)), X1) -> add(X0, X1) % 29.76/29.55 add(false__, add(Y0, add(additive_inverse(false__), add(additive_inverse(Y0), additive_inverse(X1))))) -> additive_inverse(X1) % 29.76/29.55 add(false__, add(additive_inverse(X1), add(additive_inverse(false__), add(X1, Y1)))) -> Y1 % 29.76/29.55 add(false__, add(additive_inverse(X1), add(additive_inverse(false__), add(Y1, X1)))) -> Y1 % 29.76/29.55 add(false__, add(additive_inverse(X1), add(additive_inverse(false__), add(additive_inverse(Y1), X1)))) -> additive_inverse(Y1) % 29.76/29.55 add(false__, add(additive_inverse(Y0), add(additive_inverse(false__), add(Y0, additive_inverse(X1))))) -> additive_inverse(X1) % 29.76/29.55 add(false__, multiply(add(X0, X0), X1)) -> false__ % 29.76/29.55 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z)) % 29.76/29.55 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z) % 29.76/29.55 add(multiply(X0, add(X1, X1)), Y0) -> Y0 % 29.76/29.55 add(multiply(Y0, multiply(X1, add(X2, X2))), Y2) -> Y2 % 29.76/29.55 add(multiply(Y0, multiply(Y1, multiply(X1, add(X2, X2)))), Y3) -> Y3 % 29.76/29.55 add(multiply(Y0, multiply(Y1, multiply(add(X1, X1), X2))), Y3) -> Y3 % 29.76/29.55 add(multiply(Y0, multiply(add(X1, X1), X2)), Y2) -> Y2 % 29.76/29.55 add(multiply(Y1, X1), additive_inverse(multiply(Y1, add(X1, Y1)))) -> additive_inverse(Y1) % 29.76/29.55 add(multiply(add(Y1, Y1), Y2), Y0) -> Y0 % 29.76/29.55 add(multiply(additive_inverse(Y1), X1), additive_inverse(multiply(additive_inverse(Y1), add(X1, additive_inverse(Y1))))) -> Y1 % 29.76/29.55 additive_inverse(Y1) -> Y1 % 29.76/29.55 additive_inverse(add(X1, Y0)) -> add(additive_inverse(Y0), additive_inverse(X1)) % 29.76/29.55 additive_inverse(add(X1, additive_inverse(Y0))) -> add(Y0, additive_inverse(X1)) % 29.76/29.55 additive_inverse(add(additive_inverse(X1), Y0)) -> add(additive_inverse(Y0), X1) % 29.76/29.55 additive_inverse(add(additive_inverse(X1), additive_inverse(Y0))) -> add(Y0, X1) % 29.76/29.55 additive_inverse(additive_identity) -> additive_identity % 29.76/29.55 additive_inverse(additive_inverse(Y1)) -> Y1 % 29.76/29.55 c -> multiply(a, b) % 29.76/29.55 f1(c) -> false__ % 29.76/29.55 f1(multiply(a, b)) -> false__ % 29.76/29.55 f1(multiply(b, a)) -> true__ % 29.76/29.55 multiply(X, X) -> X % 29.76/29.55 multiply(Y0, additive_identity) -> additive_identity % 29.76/29.55 multiply(Y0, additive_inverse(Y0)) -> additive_inverse(Y0) % 29.76/29.55 multiply(Y0, multiply(Y1, Y0)) -> multiply(Y0, Y1) % 29.76/29.55 multiply(Y0, multiply(Y1, additive_inverse(multiply(Y0, Y1)))) -> additive_inverse(multiply(Y0, Y1)) % 29.76/29.55 multiply(Y0, multiply(Y1, multiply(Y0, Y1))) -> multiply(Y0, Y1) % 29.76/29.55 multiply(Y0, multiply(Y1, multiply(Y0, multiply(Y1, X1)))) -> multiply(Y0, multiply(Y1, X1)) % 29.76/29.55 multiply(Y0, multiply(Y1, multiply(add(Y0, Y0), Y1))) -> multiply(add(Y0, Y0), Y1) % 29.76/29.55 multiply(Y0, multiply(add(Y0, Y0), Y2)) -> multiply(add(Y0, Y0), Y2) % 29.76/29.55 multiply(Y0, multiply(additive_identity, Y2)) -> multiply(additive_identity, Y2) % 29.76/29.55 multiply(Y0, multiply(additive_inverse(Y0), Y2)) -> multiply(additive_inverse(Y0), Y2) % 29.76/29.55 multiply(Y1, add(Y1, Y1)) -> add(Y1, Y1) % 29.76/29.55 multiply(Y1, multiply(Y1, Y2)) -> multiply(Y1, Y2) % 29.76/29.55 multiply(add(X0, X0), add(Y1, Y1)) -> multiply(add(X0, X0), Y1) % 29.76/29.55 multiply(add(X0, X1), add(additive_inverse(X1), additive_inverse(X0))) -> add(additive_inverse(X1), additive_inverse(X0)) % 29.76/29.55 multiply(add(X1, X0), multiply(add(X0, X1), Y1)) -> multiply(add(X0, X1), Y1) % 29.76/29.55 multiply(add(X1, X2), add(X2, add(X1, add(X1, X2)))) -> add(X2, add(X1, add(X1, X2))) % 29.76/29.55 multiply(add(X1, additive_inverse(X0)), add(X0, additive_inverse(X1))) -> add(X0, additive_inverse(X1)) % 29.76/29.55 multiply(add(X2, add(X1, add(X1, X2))), add(X1, X2)) -> add(X2, add(X1, add(X1, X2))) % 29.76/29.55 multiply(add(Y0, Y0), Y0) -> add(Y0, Y0) % 29.76/29.55 multiply(add(Y1, X1), Y1) -> multiply(Y1, add(Y1, X1)) % 29.76/29.55 multiply(add(additive_inverse(X1), X0), add(additive_inverse(X0), X1)) -> add(additive_inverse(X0), X1) % 29.76/29.55 multiply(add(additive_inverse(X1), additive_inverse(X0)), add(X0, X1)) -> add(X0, X1) % 29.76/29.55 multiply(additive_identity, Y0) -> additive_identity % 29.76/29.55 multiply(additive_inverse(Y0), add(Y0, Y0)) -> add(Y0, Y0) % 29.76/29.55 multiply(additive_inverse(Y1), Y1) -> Y1 % 29.76/29.55 multiply(additive_inverse(Y1), multiply(Y1, Y2)) -> multiply(Y1, Y2) % 29.76/29.55 multiply(multiply(X, Y), Z) -> multiply(X, multiply(Y, Z)) % 29.76/29.55 true__ -> false__ % 29.76/29.55 with the LPO induced by % 29.76/29.55 f1 > additive_inverse > additive_identity > add > c > a > multiply > b > true__ > false__ % 29.76/29.55 % 29.76/29.55 % SZS output end Proof % 29.76/29.55 %------------------------------------------------------------------------------