%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : RNG012-6 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n023.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 37.88s 37.86s % Output : Proof 37.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : RNG012-6 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n023.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon May 30 06:01:27 EDT 2022 % 0.20/0.34 % CPUTime : % 37.88/37.86 % SZS status Unsatisfiable % 37.88/37.86 % SZS output start Proof % 37.88/37.86 The input problem is unsatisfiable because % 37.88/37.86 % 37.88/37.86 [1] the following set of Horn clauses is unsatisfiable: % 37.88/37.86 % 37.88/37.86 add(additive_identity, X) = X % 37.88/37.86 add(X, additive_identity) = X % 37.88/37.86 multiply(additive_identity, X) = additive_identity % 37.88/37.86 multiply(X, additive_identity) = additive_identity % 37.88/37.86 add(additive_inverse(X), X) = additive_identity % 37.88/37.86 add(X, additive_inverse(X)) = additive_identity % 37.88/37.86 additive_inverse(additive_inverse(X)) = X % 37.88/37.86 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 37.88/37.86 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 37.88/37.86 add(X, Y) = add(Y, X) % 37.88/37.86 add(X, add(Y, Z)) = add(add(X, Y), Z) % 37.88/37.86 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 37.88/37.86 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)) % 37.88/37.86 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 37.88/37.86 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 37.88/37.86 multiply(additive_inverse(a), additive_inverse(b)) = multiply(a, b) ==> \bottom % 37.88/37.86 % 37.88/37.86 This holds because % 37.88/37.86 % 37.88/37.86 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 37.88/37.86 % 37.88/37.86 E: % 37.88/37.86 add(X, Y) = add(Y, X) % 37.88/37.86 add(X, add(Y, Z)) = add(add(X, Y), Z) % 37.88/37.86 add(X, additive_identity) = X % 37.88/37.86 add(X, additive_inverse(X)) = additive_identity % 37.88/37.86 add(additive_identity, X) = X % 37.88/37.86 add(additive_inverse(X), X) = additive_identity % 37.88/37.86 additive_inverse(additive_inverse(X)) = X % 37.88/37.86 associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))) % 37.88/37.86 commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))) % 37.88/37.86 f1(multiply(a, b)) = false__ % 37.88/37.86 f1(multiply(additive_inverse(a), additive_inverse(b))) = true__ % 37.88/37.86 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)) % 37.88/37.86 multiply(X, additive_identity) = additive_identity % 37.88/37.86 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)) % 37.88/37.86 multiply(additive_identity, X) = additive_identity % 37.88/37.86 multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)) % 37.88/37.86 multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)) % 37.88/37.86 G: % 37.88/37.86 true__ = false__ % 37.88/37.86 % 37.88/37.86 This holds because % 37.88/37.86 % 37.88/37.86 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 37.88/37.86 % 37.88/37.86 add(X, Y) = add(Y, X) % 37.88/37.86 add(Y0, add(X1, X2)) = add(Y1, add(X1, add(X2, add(additive_inverse(Y1), Y0)))) % 37.88/37.86 add(Y0, add(Y2, additive_inverse(X0))) = add(additive_inverse(X0), add(Y2, Y0)) % 37.88/37.86 add(Y0, add(additive_inverse(X1), Y1)) = add(Y1, add(additive_inverse(X1), Y0)) % 37.88/37.86 add(Y0, additive_inverse(X1)) = add(additive_inverse(X1), Y0) % 37.88/37.86 add(Y0, multiply(X0, additive_inverse(X1))) = add(multiply(additive_inverse(X0), X1), Y0) % 37.88/37.86 add(Y1, add(Y0, Y2)) = add(Y0, add(Y1, Y2)) % 37.88/37.86 add(Y2, add(Y0, Y1)) = add(Y0, add(Y1, Y2)) % 37.88/37.86 add(additive_inverse(Y0), add(X2, add(additive_inverse(X1), Y0))) = add(additive_inverse(X1), X2) % 37.88/37.86 add(additive_inverse(Y0), add(additive_inverse(X2), add(X1, Y0))) = add(X1, additive_inverse(X2)) % 37.88/37.86 add(multiply(X0, additive_inverse(X1)), Y1) = add(Y1, multiply(additive_inverse(X0), X1)) % 37.88/37.86 multiply(X0, additive_inverse(Y1)) = multiply(additive_inverse(X0), Y1) % 37.88/37.86 add(X, additive_identity) -> X % 37.88/37.86 add(X, additive_inverse(X)) -> additive_identity % 37.88/37.86 add(X0, add(X1, add(Y1, add(Y2, add(additive_inverse(X1), additive_inverse(X0)))))) -> add(Y1, Y2) % 37.88/37.86 add(Y0, add(X1, add(X2, additive_inverse(Y0)))) -> add(X1, X2) % 37.88/37.86 add(Y0, add(Y1, additive_inverse(Y0))) -> Y1 % 37.88/37.86 add(Y0, add(additive_inverse(Y0), Y2)) -> Y2 % 37.88/37.86 add(Y1, add(Y0, add(additive_inverse(Y1), X1))) -> add(Y0, X1) % 37.88/37.86 add(add(X, Y), Z) -> add(X, add(Y, Z)) % 37.88/37.86 add(additive_identity, X) -> X % 37.88/37.86 add(additive_inverse(X), X) -> additive_identity % 37.88/37.86 add(additive_inverse(Y1), add(Y1, Y2)) -> Y2 % 37.88/37.86 add(additive_inverse(multiply(X0, X1)), multiply(X0, add(X1, X2))) -> multiply(X0, X2) % 37.88/37.86 add(additive_inverse(multiply(X0, X1)), multiply(add(X0, X2), X1)) -> multiply(X2, X1) % 37.88/37.86 add(multiply(X0, X1), add(Y1, multiply(X0, additive_inverse(X1)))) -> Y1 % 37.88/37.86 add(multiply(X0, X1), add(Y1, multiply(additive_inverse(X0), X1))) -> Y1 % 37.88/37.86 add(multiply(X0, X1), add(multiply(X0, additive_inverse(X1)), Y1)) -> Y1 % 37.88/37.86 add(multiply(X0, X1), add(multiply(additive_inverse(X0), X1), Y1)) -> Y1 % 37.88/37.86 add(multiply(X0, X1), multiply(X0, additive_inverse(X1))) -> additive_identity % 37.88/37.86 add(multiply(X0, X1), multiply(additive_inverse(X0), X1)) -> additive_identity % 37.88/37.86 add(multiply(multiply(X0, X1), Y1), multiply(multiply(X0, additive_inverse(X1)), Y1)) -> additive_identity % 37.88/37.86 additive_inverse(add(X1, Y0)) -> add(additive_inverse(Y0), additive_inverse(X1)) % 37.88/37.86 additive_inverse(additive_identity) -> additive_identity % 37.88/37.86 additive_inverse(additive_inverse(X)) -> X % 37.88/37.86 additive_inverse(multiply(Y0, Y1)) -> multiply(Y0, additive_inverse(Y1)) % 37.88/37.86 additive_inverse(multiply(Y0, Y1)) -> multiply(additive_inverse(Y0), Y1) % 37.88/37.86 associator(X, Y, Z) -> add(multiply(multiply(X, Y), Z), multiply(X, multiply(Y, additive_inverse(Z)))) % 37.88/37.86 commutator(X, Y) -> add(multiply(Y, X), multiply(X, additive_inverse(Y))) % 37.88/37.86 f1(multiply(a, b)) -> false__ % 37.88/37.86 f1(multiply(additive_inverse(a), additive_inverse(b))) -> true__ % 37.88/37.86 multiply(X, add(Y, Z)) -> add(multiply(X, Y), multiply(X, Z)) % 37.88/37.86 multiply(X, additive_identity) -> additive_identity % 37.88/37.86 multiply(add(X, Y), Z) -> add(multiply(X, Z), multiply(Y, Z)) % 37.88/37.86 multiply(additive_identity, X) -> additive_identity % 37.88/37.86 multiply(additive_inverse(X0), additive_inverse(X1)) -> multiply(X0, X1) % 37.88/37.86 multiply(additive_inverse(Y0), multiply(X0, additive_inverse(X1))) -> multiply(Y0, multiply(X0, X1)) % 37.88/37.86 multiply(multiply(X, X), Y) -> multiply(X, multiply(X, Y)) % 37.88/37.86 multiply(multiply(X, Y), Y) -> multiply(X, multiply(Y, Y)) % 37.88/37.86 multiply(multiply(X0, additive_inverse(X1)), additive_inverse(Y1)) -> multiply(multiply(X0, X1), Y1) % 37.88/37.86 multiply(multiply(X0, multiply(X0, Y1)), Y1) -> multiply(X0, multiply(X0, multiply(Y1, Y1))) % 37.88/37.86 multiply(multiply(X0, multiply(Y1, Y1)), Y1) -> multiply(multiply(X0, Y1), multiply(Y1, Y1)) % 37.88/37.86 true__ -> false__ % 37.88/37.86 with the LPO induced by % 37.88/37.86 associator > commutator > additive_inverse > multiply > additive_identity > b > f1 > a > add > true__ > false__ % 37.88/37.86 % 37.88/37.86 % SZS output end Proof % 37.88/37.86 %------------------------------------------------------------------------------