%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP028-3 : TPTP v8.1.0. Released v1.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 : Sat Jul 16 10:51:59 EDT 2022 % Result : Unsatisfiable 8.23s 8.16s % Output : Proof 8.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : GRP028-3 : TPTP v8.1.0. Released v1.1.0. % 0.04/0.14 % Command : moca.sh %s % 0.16/0.36 % Computer : n024.cluster.edu % 0.16/0.36 % Model : x86_64 x86_64 % 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.36 % Memory : 8042.1875MB % 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.36 % CPULimit : 300 % 0.16/0.36 % WCLimit : 600 % 0.16/0.36 % DateTime : Mon Jun 13 04:48:33 EDT 2022 % 0.16/0.36 % CPUTime : % 8.23/8.16 % SZS status Unsatisfiable % 8.23/8.16 % SZS output start Proof % 8.23/8.16 The input problem is unsatisfiable because % 8.23/8.16 % 8.23/8.16 [1] the following set of Horn clauses is unsatisfiable: % 8.23/8.16 % 8.23/8.16 product(X, Y, multiply(X, Y)) % 8.23/8.16 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 8.23/8.16 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 8.23/8.16 product(left_solution(X, Y), X, Y) % 8.23/8.16 product(X, right_solution(X, Y), Y) % 8.23/8.16 product(not_identity(X), X, not_identity(X)) ==> \bottom % 8.23/8.16 % 8.23/8.16 This holds because % 8.23/8.16 % 8.23/8.16 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.23/8.16 % 8.23/8.16 E: % 8.23/8.16 f1(true__, X, V, W) = product(X, V, W) % 8.23/8.16 f2(true__, X, Y, U, V, W) = f1(product(X, Y, U), X, V, W) % 8.23/8.16 f3(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 8.23/8.16 f3(true__, Y, Z, V, X, U, W) = f2(product(Y, Z, V), X, Y, U, V, W) % 8.23/8.16 f4(true__, U, Z, W) = product(U, Z, W) % 8.23/8.16 f5(true__, X, Y, U, Z, W) = f4(product(X, Y, U), U, Z, W) % 8.23/8.16 f6(product(X, V, W), Y, Z, V, X, U, W) = true__ % 8.23/8.16 f6(true__, Y, Z, V, X, U, W) = f5(product(Y, Z, V), X, Y, U, Z, W) % 8.23/8.16 f7(product(not_identity(X), X, not_identity(X))) = true__ % 8.23/8.16 f7(true__) = false__ % 8.23/8.16 product(X, Y, multiply(X, Y)) = true__ % 8.23/8.16 product(X, right_solution(X, Y), Y) = true__ % 8.23/8.16 product(left_solution(X, Y), X, Y) = true__ % 8.23/8.16 G: % 8.23/8.16 true__ = false__ % 8.23/8.16 % 8.23/8.16 This holds because % 8.23/8.16 % 8.23/8.16 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.23/8.16 % 8.23/8.16 % 8.23/8.16 f1(f1(true__, Y3, Y0, Y4), Y3, Y2, multiply(Y4, right_solution(Y0, Y2))) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, Y4), Y3, multiply(X1, X2), multiply(Y4, multiply(right_solution(Y0, X1), X2))) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, Y4), Y3, multiply(X2, multiply(right_solution(X2, Y0), Y1)), multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, Y4), Y3, multiply(Y0, Y1), multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, Y4), Y3, multiply(left_solution(X2, Y0), multiply(X2, Y1)), multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, Y4), Y3, multiply(multiply(Y0, X1), X2), multiply(Y4, multiply(X1, X2))) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, Y4), Y3, multiply(multiply(Y0, left_solution(X2, Y1)), X2), multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, left_solution(Y1, Y4)), Y3, multiply(X2, multiply(right_solution(X2, Y0), Y1)), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, left_solution(Y1, Y4)), Y3, multiply(Y0, Y1), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, left_solution(Y1, Y4)), Y3, multiply(left_solution(X2, Y0), multiply(X2, Y1)), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, left_solution(Y1, Y4)), Y3, multiply(multiply(Y0, left_solution(X2, Y1)), X2), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, left_solution(multiply(X1, X2), Y4)), Y3, multiply(multiply(Y0, X1), X2), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, left_solution(multiply(right_solution(Y0, X1), X2), Y4)), Y3, multiply(X1, X2), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y0, left_solution(right_solution(Y0, Y2), Y4)), Y3, Y2, Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, Y2, Y4), Y3, Y2, multiply(Y4, right_solution(X1, X1))) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(X0, X0), Y4), Y3, Y2, multiply(Y4, Y2)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(X0, X0), left_solution(Y2, Y4)), Y3, Y2, Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(X0, X1), Y4), Y3, multiply(X1, X2), multiply(Y4, multiply(X0, X2))) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(X0, X1), left_solution(multiply(X0, X2), Y4)), Y3, multiply(X1, X2), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(Y1, Y2), Y4), Y3, Y2, multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(Y1, Y2), left_solution(Y1, Y4)), Y3, Y2, Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(left_solution(X0, Y1), X2), Y4), Y3, multiply(X2, X0), multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(left_solution(X0, Y1), X2), left_solution(Y1, Y4)), Y3, multiply(X2, X0), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, left_solution(left_solution(X0, multiply(X1, X0)), X1), Y4), Y3, Y2, multiply(Y4, Y2)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, multiply(X0, X1), Y4), Y3, multiply(X0, multiply(X1, Y1)), multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y3, multiply(X0, X1), left_solution(Y1, Y4)), Y3, multiply(X0, multiply(X1, Y1)), Y4) -> true__ % 8.23/8.16 f1(f1(true__, Y3, multiply(X0, left_solution(Y1, X2)), Y4), Y3, multiply(X0, X2), multiply(Y4, Y1)) -> true__ % 8.23/8.16 f1(f1(true__, Y4, Y0, Y1), Y4, multiply(Y0, right_solution(Y1, Y2)), Y2) -> true__ % 8.23/8.16 f1(f1(true__, Y4, Y0, Y1), Y4, multiply(left_solution(X2, Y0), multiply(X2, right_solution(Y1, Y2))), Y2) -> true__ % 8.23/8.16 f1(f1(true__, Y4, Y0, Y1), Y4, multiply(multiply(Y0, left_solution(X2, right_solution(Y1, Y2))), X2), Y2) -> true__ % 8.23/8.16 f1(f1(true__, Y4, Y1, Y1), Y4, Y3, Y3) -> true__ % 8.23/8.16 f1(f1(true__, Y4, left_solution(X0, X0), Y1), Y4, right_solution(Y1, Y2), Y2) -> true__ % 8.23/8.16 f1(f1(true__, Y4, left_solution(left_solution(X0, right_solution(Y1, Y2)), X2), Y1), Y4, multiply(X2, X0), Y2) -> true__ % 8.23/8.16 f1(f1(true__, Y4, left_solution(right_solution(Y1, Y2), Y3), Y1), Y4, Y3, Y2) -> true__ % 8.23/8.16 f1(f1(true__, Y4, multiply(X0, X1), Y1), Y4, multiply(X0, multiply(X1, right_solution(Y1, Y2))), Y2) -> true__ % 8.23/8.16 f1(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 8.23/8.16 f1(true__, Y0, Y2, multiply(multiply(Y0, left_solution(Y1, Y2)), Y1)) -> true__ % 8.23/8.16 f1(true__, Y0, Y3, multiply(Y2, right_solution(right_solution(Y0, Y2), Y3))) -> true__ % 8.23/8.16 f1(true__, Y0, Y3, multiply(multiply(Y0, Y1), right_solution(Y1, Y3))) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(Y1, Y3), multiply(multiply(Y0, Y1), Y3)) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(Y1, Y3), multiply(multiply(left_solution(X2, Y0), multiply(X2, Y1)), Y3)) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(Y1, Y3), multiply(multiply(multiply(Y0, left_solution(X2, Y1)), X2), Y3)) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(Y1, right_solution(multiply(Y0, Y1), Y3)), Y3) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(multiply(X1, X2), Y3), multiply(multiply(multiply(Y0, X1), X2), Y3)) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(right_solution(Y0, Y2), Y3), multiply(Y2, Y3)) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(right_solution(Y0, Y2), right_solution(Y2, Y3)), Y3) -> true__ % 8.23/8.16 f1(true__, Y0, multiply(right_solution(Y0, left_solution(Y2, Y3)), Y2), Y3) -> true__ % 8.23/8.16 f1(true__, Y0, right_solution(Y0, Y2), Y2) -> true__ % 8.23/8.16 f1(true__, Y2, Y3, multiply(Y0, multiply(right_solution(Y0, Y2), Y3))) -> true__ % 8.23/8.16 f1(true__, Y2, Y3, multiply(left_solution(X0, X0), multiply(Y2, Y3))) -> true__ % 8.23/8.16 f1(true__, Y2, Y3, multiply(left_solution(Y1, Y2), multiply(Y1, Y3))) -> true__ % 8.23/8.16 f1(true__, Y2, right_solution(Y1, Y3), multiply(left_solution(Y1, Y2), Y3)) -> true__ % 8.23/8.16 f1(true__, Y2, right_solution(Y2, Y3), multiply(left_solution(X0, X0), Y3)) -> true__ % 8.23/8.16 f1(true__, Y2, right_solution(right_solution(Y0, Y2), Y3), multiply(Y0, Y3)) -> true__ % 8.23/8.16 f1(true__, Y3, Y1, multiply(left_solution(left_solution(Y1, Y2), Y3), Y2)) -> true__ % 8.23/8.16 f1(true__, Y3, right_solution(Y2, Y2), Y3) -> true__ % 8.23/8.16 f1(true__, left_solution(X0, X0), Y2, multiply(left_solution(Y1, Y2), Y1)) -> true__ % 8.23/8.16 f1(true__, left_solution(X0, X0), Y3, multiply(Y2, right_solution(Y2, Y3))) -> true__ % 8.23/8.16 f1(true__, left_solution(X0, X0), multiply(Y2, right_solution(Y2, Y3)), Y3) -> true__ % 8.23/8.16 f1(true__, left_solution(X0, X0), multiply(left_solution(Y2, Y3), Y2), Y3) -> true__ % 8.23/8.16 f1(true__, left_solution(X0, X1), multiply(multiply(X0, X2), Y3), multiply(multiply(X1, X2), Y3)) -> true__ % 8.23/8.16 f1(true__, left_solution(X0, left_solution(X1, multiply(X0, X1))), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, left_solution(X0, left_solution(right_solution(X0, Y1), Y1)), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, Y1), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, Y2), Y1, Y2) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, Y2), Y1, multiply(left_solution(X0, X0), Y2)) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, Y2), Y3, multiply(Y2, right_solution(Y1, Y3))) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, Y2), multiply(Y1, Y3), multiply(Y2, Y3)) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, Y2), multiply(Y1, right_solution(Y2, Y3)), Y3) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, left_solution(Y2, Y3)), multiply(Y1, Y2), Y3) -> true__ % 8.23/8.16 f1(true__, left_solution(Y1, left_solution(right_solution(Y1, Y2), Y3)), Y2, Y3) -> true__ % 8.23/8.16 f1(true__, left_solution(left_solution(X0, multiply(X2, X0)), X2), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, left_solution(left_solution(Y1, Y2), Y3), Y2, multiply(Y3, Y1)) -> true__ % 8.23/8.16 f1(true__, left_solution(left_solution(Y1, Y2), left_solution(Y1, Y3)), Y2, Y3) -> true__ % 8.23/8.16 f1(true__, left_solution(left_solution(right_solution(X0, Y1), Y1), X0), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, left_solution(left_solution(right_solution(Y1, Y2), Y3), Y1), Y3, Y2) -> true__ % 8.23/8.16 f1(true__, left_solution(multiply(left_solution(X2, X2), X1), X1), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(X0, X1), Y2, multiply(multiply(X0, multiply(X1, left_solution(Y1, Y2))), Y1)) -> true__ % 8.23/8.16 f1(true__, multiply(X0, X1), multiply(Y1, Y3), multiply(multiply(X0, multiply(X1, Y1)), Y3)) -> true__ % 8.23/8.16 f1(true__, multiply(X0, left_solution(Y1, right_solution(X0, Y1))), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(X0, left_solution(multiply(X0, X2), X2)), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(X0, multiply(X1, Y1)), Y3, multiply(multiply(X0, X1), multiply(Y1, Y3))) -> true__ % 8.23/8.16 f1(true__, multiply(X1, X2), Y3, multiply(left_solution(X0, X1), multiply(multiply(X0, X2), Y3))) -> true__ % 8.23/8.16 f1(true__, multiply(Y0, Y1), Y3, multiply(Y0, multiply(Y1, Y3))) -> true__ % 8.23/8.16 f1(true__, multiply(Y0, Y1), right_solution(Y1, Y3), multiply(Y0, Y3)) -> true__ % 8.23/8.16 f1(true__, multiply(Y0, left_solution(Y1, Y2)), Y1, multiply(Y0, Y2)) -> true__ % 8.23/8.16 f1(true__, multiply(Y0, left_solution(Y1, right_solution(Y0, Y2))), Y1, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(left_solution(X0, Y1), left_solution(Y1, X0)), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(left_solution(X0, right_solution(X2, X0)), X2), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(left_solution(Y0, Y1), Y2), right_solution(Y2, Y0), Y1) -> true__ % 8.23/8.16 f1(true__, multiply(left_solution(Y0, Y1), left_solution(Y2, Y0)), Y2, Y1) -> true__ % 8.23/8.16 f1(true__, multiply(left_solution(multiply(X0, Y1), Y1), X0), Y2, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(left_solution(multiply(Y0, Y1), Y2), Y0), Y1, Y2) -> true__ % 8.23/8.16 f1(true__, multiply(multiply(Y0, X1), X2), Y3, multiply(Y0, multiply(multiply(X1, X2), Y3))) -> true__ % 8.23/8.16 f1(true__, multiply(multiply(Y0, left_solution(X2, Y1)), X2), Y3, multiply(Y0, multiply(Y1, Y3))) -> true__ % 8.23/8.16 f1(true__, right_solution(X1, X1), Y2, Y2) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(X2, multiply(right_solution(X2, Y0), Y1))) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(left_solution(X2, X2), multiply(Y0, Y1))) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(left_solution(X2, Y0), multiply(X2, Y1))) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(multiply(Y0, left_solution(X2, Y1)), X2)) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, left_solution(Y1, Y2), Y4, Y2) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, left_solution(left_solution(X0, Y1), X2), Y4, multiply(X2, X0)) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, multiply(X0, X1), Y4, multiply(X0, multiply(X1, Y1))) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, multiply(X0, left_solution(Y1, X2)), Y4, multiply(X0, X2)) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y2, Y4), Y5, Y3, left_solution(X0, X0), Y4, Y2) -> true__ % 8.23/8.16 f2(f1(true__, Y3, Y2, Y4), Y5, Y3, left_solution(left_solution(X0, multiply(X1, X0)), X1), Y4, Y2) -> true__ % 8.23/8.16 f2(f1(true__, Y3, multiply(X0, X1), Y4), Y5, Y3, left_solution(X0, left_solution(X1, Y2)), Y4, Y2) -> true__ % 8.23/8.16 f2(f1(true__, Y3, multiply(X0, X2), Y4), Y5, Y3, left_solution(X0, X1), Y4, multiply(X1, X2)) -> true__ % 8.23/8.16 f2(f1(true__, Y3, multiply(X1, X2), Y4), Y5, Y3, Y0, Y4, multiply(multiply(Y0, X1), X2)) -> true__ % 8.23/8.16 f2(f1(true__, Y3, multiply(right_solution(Y0, X1), X2), Y4), Y5, Y3, Y0, Y4, multiply(X1, X2)) -> true__ % 8.23/8.16 f2(f1(true__, Y3, right_solution(X1, X1), Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 8.23/8.16 f2(f1(true__, Y3, right_solution(Y0, Y2), Y4), Y5, Y3, Y0, Y4, Y2) -> true__ % 8.23/8.16 f2(true__, X, Y, U, V, W) -> f1(product(X, Y, U), X, V, W) % 8.23/8.16 f3(f1(true__, Y0, Y1, Y2), Y3, Y1, Y4, Y5, Y0, Y2) -> true__ % 8.23/8.16 f3(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 8.23/8.16 f3(true__, Y, Z, V, X, U, W) -> f2(product(Y, Z, V), X, Y, U, V, W) % 8.23/8.16 f4(f1(true__, Y2, Y0, Y4), Y4, right_solution(Y0, right_solution(Y2, Y3)), Y3) -> true__ % 8.23/8.16 f4(f1(true__, Y2, left_solution(X0, X0), Y4), Y4, right_solution(Y2, Y3), Y3) -> true__ % 8.23/8.16 f4(f1(true__, Y2, left_solution(Y1, right_solution(Y2, Y3)), Y4), Y4, Y1, Y3) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y0, Y4), Y4, Y1, multiply(Y3, multiply(X2, multiply(right_solution(X2, Y0), Y1)))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y0, Y4), Y4, Y1, multiply(Y3, multiply(Y0, Y1))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y0, Y4), Y4, Y1, multiply(Y3, multiply(left_solution(X2, Y0), multiply(X2, Y1)))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y0, Y4), Y4, Y1, multiply(Y3, multiply(multiply(Y0, left_solution(X2, Y1)), X2))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y0, Y4), Y4, multiply(X1, X2), multiply(Y3, multiply(multiply(Y0, X1), X2))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y0, Y4), Y4, multiply(right_solution(Y0, X1), X2), multiply(Y3, multiply(X1, X2))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y0, Y4), Y4, right_solution(Y0, Y2), multiply(Y3, Y2)) -> true__ % 8.23/8.16 f4(f1(true__, Y3, Y2, Y4), Y4, right_solution(X1, X1), multiply(Y3, Y2)) -> true__ % 8.23/8.16 f4(f1(true__, Y3, left_solution(X0, X0), Y4), Y4, Y2, multiply(Y3, Y2)) -> true__ % 8.23/8.16 f4(f1(true__, Y3, left_solution(X0, X1), Y4), Y4, multiply(X0, X2), multiply(Y3, multiply(X1, X2))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, left_solution(Y1, Y2), Y4), Y4, Y1, multiply(Y3, Y2)) -> true__ % 8.23/8.16 f4(f1(true__, Y3, left_solution(left_solution(X0, Y1), X2), Y4), Y4, Y1, multiply(Y3, multiply(X2, X0))) -> true__ % 8.23/8.16 f4(f1(true__, Y3, left_solution(left_solution(X0, multiply(X1, X0)), X1), Y4), Y4, Y2, multiply(Y3, Y2)) -> true__ % 8.23/8.16 f4(f1(true__, Y3, multiply(X0, X1), Y4), Y4, Y1, multiply(Y3, multiply(X0, multiply(X1, Y1)))) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(Y2, Y3), Y0, Y4), Y4, right_solution(Y0, Y2), Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(Y2, Y3), left_solution(X0, X0), Y4), Y4, Y2, Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(Y2, Y3), left_solution(Y1, Y2), Y4), Y4, Y1, Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(X0, multiply(X1, Y1)), Y3), multiply(X0, X1), Y4), Y4, Y1, Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(X1, X2), Y3), Y0, Y4), Y4, multiply(right_solution(Y0, X1), X2), Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(X1, X2), Y3), left_solution(X0, X1), Y4), Y4, multiply(X0, X2), Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(X2, X0), Y3), left_solution(left_solution(X0, Y1), X2), Y4), Y4, Y1, Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(Y0, Y1), Y3), Y0, Y4), Y4, Y1, Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(left_solution(X2, Y0), multiply(X2, Y1)), Y3), Y0, Y4), Y4, Y1, Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(multiply(Y0, X1), X2), Y3), Y0, Y4), Y4, multiply(X1, X2), Y3) -> true__ % 8.23/8.16 f4(f1(true__, left_solution(multiply(multiply(Y0, left_solution(X2, Y1)), X2), Y3), Y0, Y4), Y4, Y1, Y3) -> true__ % 8.23/8.16 f4(true__, U, Z, W) -> product(U, Z, W) % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(X2, multiply(right_solution(X2, Y0), Y1))) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(left_solution(X2, Y0), multiply(X2, Y1))) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(multiply(Y0, left_solution(X2, Y1)), X2)) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), left_solution(Y1, Y2), Y3, Y5, Y4, Y2) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), left_solution(left_solution(X0, Y1), X2), Y3, Y5, Y4, multiply(X2, X0)) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), multiply(X0, X1), Y3, Y5, Y4, multiply(X0, multiply(X1, Y1))) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y1), multiply(X0, left_solution(Y1, X2)), Y3, Y5, Y4, multiply(X0, X2)) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y2), left_solution(X0, X0), Y3, Y5, Y4, Y2) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, Y2), left_solution(left_solution(X0, multiply(X1, X0)), X1), Y3, Y5, Y4, Y2) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, multiply(X0, X1)), left_solution(X0, left_solution(X1, Y2)), Y3, Y5, Y4, Y2) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, multiply(X0, X2)), left_solution(X0, X1), Y3, Y5, Y4, multiply(X1, X2)) -> true__ % 8.23/8.16 f5(f1(true__, Y3, Y4, multiply(X1, X2)), Y0, Y3, Y5, Y4, multiply(multiply(Y0, X1), X2)) -> true__ % 8.28/8.16 f5(f1(true__, Y3, Y4, multiply(right_solution(Y0, X1), X2)), Y0, Y3, Y5, Y4, multiply(X1, X2)) -> true__ % 8.28/8.16 f5(f1(true__, Y3, Y4, right_solution(X1, X1)), Y2, Y3, Y5, Y4, Y2) -> true__ % 8.28/8.16 f5(f1(true__, Y3, Y4, right_solution(Y0, Y2)), Y0, Y3, Y5, Y4, Y2) -> true__ % 8.28/8.16 f5(true__, X, Y, U, Z, W) -> f4(product(X, Y, U), U, Z, W) % 8.28/8.16 f6(f1(true__, Y0, Y1, Y2), Y3, Y4, Y1, Y0, Y5, Y2) -> true__ % 8.28/8.16 f6(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 8.28/8.16 f6(true__, Y, Z, V, X, U, W) -> f5(product(Y, Z, V), X, Y, U, Z, W) % 8.28/8.16 f7(f1(true__, not_identity(Y0), Y0, not_identity(Y0))) -> true__ % 8.28/8.16 f7(product(not_identity(X), X, not_identity(X))) -> true__ % 8.28/8.16 f7(true__) -> false__ % 8.28/8.16 false__ -> true__ % 8.28/8.16 product(X, V, W) -> f1(true__, X, V, W) % 8.28/8.16 product(X, Y, multiply(X, Y)) -> true__ % 8.28/8.16 product(X, right_solution(X, Y), Y) -> true__ % 8.28/8.16 product(left_solution(X, Y), X, Y) -> true__ % 8.28/8.16 with the LPO induced by % 8.28/8.16 not_identity > f7 > right_solution > left_solution > f3 > f2 > f6 > f5 > f4 > product > f1 > multiply > false__ > true__ % 8.28/8.16 % 8.28/8.16 % SZS output end Proof % 8.28/8.16 %------------------------------------------------------------------------------