%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP028-2 : TPTP v8.1.0. Released v1.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 5.27s 5.29s % Output : Proof 5.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GRP028-2 : TPTP v8.1.0. Released v1.1.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 13 15:16:48 EDT 2022 % 0.12/0.33 % CPUTime : % 5.27/5.29 % SZS status Unsatisfiable % 5.27/5.29 % SZS output start Proof % 5.27/5.29 The input problem is unsatisfiable because % 5.27/5.29 % 5.27/5.29 [1] the following set of Horn clauses is unsatisfiable: % 5.27/5.29 % 5.27/5.29 product(X, Y, multiply(X, Y)) % 5.27/5.29 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 5.27/5.29 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 5.27/5.29 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 5.27/5.29 product(left_solution(X, Y), X, Y) % 5.27/5.29 product(X, right_solution(X, Y), Y) % 5.27/5.29 product(not_identity(X), X, not_identity(X)) ==> \bottom % 5.27/5.29 % 5.27/5.29 This holds because % 5.27/5.29 % 5.27/5.29 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.27/5.29 % 5.27/5.29 E: % 5.27/5.29 f1(true__, Z, W) = Z % 5.27/5.29 f2(product(X, Y, W), X, Y, Z, W) = W % 5.27/5.29 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 5.27/5.29 f3(true__, X, V, W) = product(X, V, W) % 5.27/5.29 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 5.27/5.29 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 5.27/5.29 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 5.27/5.29 f6(true__, U, Z, W) = product(U, Z, W) % 5.27/5.29 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 5.27/5.29 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 5.27/5.29 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 5.27/5.29 f9(product(not_identity(X), X, not_identity(X))) = true__ % 5.27/5.29 f9(true__) = false__ % 5.27/5.29 product(X, Y, multiply(X, Y)) = true__ % 5.27/5.29 product(X, right_solution(X, Y), Y) = true__ % 5.27/5.29 product(left_solution(X, Y), X, Y) = true__ % 5.27/5.29 G: % 5.27/5.29 true__ = false__ % 5.27/5.29 % 5.27/5.29 This holds because % 5.27/5.29 % 5.27/5.29 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.27/5.29 % 5.27/5.29 % 5.27/5.29 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 5.27/5.29 f1(f3(true__, Y0, right_solution(Y0, Y2), Y3), Y3, Y2) -> Y2 % 5.27/5.29 f1(f3(true__, left_solution(Y1, Y2), Y1, Y3), Y3, Y2) -> Y2 % 5.27/5.29 f1(true__, Z, W) -> Z % 5.27/5.29 f2(f3(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> Y2 % 5.27/5.29 f2(product(X, Y, W), X, Y, Z, W) -> W % 5.27/5.29 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 5.27/5.29 f3(f3(true__, Y0, Y1, Y2), Y0, X1, multiply(Y2, right_solution(Y1, X1))) -> true__ % 5.27/5.29 f3(f3(true__, Y0, Y1, Y2), Y0, multiply(Y1, right_solution(Y2, X1)), X1) -> true__ % 5.27/5.29 f3(f3(true__, Y0, Y1, left_solution(Y3, X1)), Y0, multiply(Y1, Y3), X1) -> true__ % 5.27/5.29 f3(f3(true__, Y0, Y1, left_solution(right_solution(Y1, X1), Y3)), Y0, X1, Y3) -> true__ % 5.27/5.29 f3(f3(true__, Y0, left_solution(Y1, Y2), left_solution(Y1, X1)), Y0, Y2, X1) -> true__ % 5.27/5.29 f3(f3(true__, Y0, left_solution(right_solution(Y3, X1), Y2), Y3), Y0, Y2, X1) -> true__ % 5.27/5.29 f3(f3(true__, Y3, Y0, Y4), Y3, multiply(Y0, Y1), multiply(Y4, Y1)) -> true__ % 5.27/5.29 f3(f3(true__, Y3, left_solution(Y1, Y2), Y4), Y3, Y2, multiply(Y4, Y1)) -> true__ % 5.27/5.29 f3(f3(true__, Y4, Y1, Y1), Y4, Y3, Y3) -> true__ % 5.27/5.29 f3(true__, Y0, X1, multiply(multiply(Y0, Y1), right_solution(Y1, X1))) -> true__ % 5.27/5.29 f3(true__, Y0, X1, multiply(multiply(Y0, left_solution(Y2, X1)), Y2)) -> true__ % 5.27/5.29 f3(true__, Y0, Y1, multiply(X1, right_solution(right_solution(Y0, X1), Y1))) -> true__ % 5.27/5.29 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 5.27/5.29 f3(true__, Y0, multiply(Y1, Y3), multiply(multiply(Y0, Y1), Y3)) -> true__ % 5.27/5.29 f3(true__, Y0, multiply(Y1, right_solution(multiply(Y0, Y1), X1)), X1) -> true__ % 5.27/5.29 f3(true__, Y0, multiply(right_solution(X1, X1), Y2), multiply(Y0, Y2)) -> true__ % 5.27/5.29 f3(true__, Y0, multiply(right_solution(Y0, X1), Y2), multiply(X1, Y2)) -> true__ % 5.27/5.29 f3(true__, Y0, multiply(right_solution(Y0, X1), right_solution(X1, Y2)), Y2) -> true__ % 5.27/5.29 f3(true__, Y0, multiply(right_solution(Y0, left_solution(Y2, X1)), Y2), X1) -> true__ % 5.27/5.29 f3(true__, Y0, right_solution(X1, X1), Y0) -> true__ % 5.27/5.29 f3(true__, Y0, right_solution(Y0, Y2), Y2) -> true__ % 5.27/5.29 f3(true__, Y0, right_solution(right_solution(left_solution(X1, X2), Y0), X1), X2) -> true__ % 5.27/5.29 f3(true__, left_solution(Y0, Y1), multiply(Y0, right_solution(Y1, X1)), X1) -> true__ % 5.27/5.29 f3(true__, left_solution(Y0, left_solution(Y2, X1)), multiply(Y0, Y2), X1) -> true__ % 5.27/5.29 f3(true__, left_solution(Y1, X1), multiply(Y1, Y2), multiply(X1, Y2)) -> true__ % 5.27/5.29 f3(true__, left_solution(Y1, Y1), Y2, Y2) -> true__ % 5.27/5.29 f3(true__, left_solution(Y1, Y2), Y1, Y2) -> true__ % 5.27/5.29 f3(true__, left_solution(Y2, X1), Y1, multiply(X1, right_solution(Y2, Y1))) -> true__ % 5.27/5.29 f3(true__, left_solution(left_solution(Y2, Y1), X1), Y1, multiply(X1, Y2)) -> true__ % 5.27/5.29 f3(true__, left_solution(multiply(right_solution(X0, X0), Y1), X2), Y1, X2) -> true__ % 5.27/5.29 f3(true__, multiply(left_solution(X0, X1), X2), right_solution(X2, X0), X1) -> true__ % 5.27/5.29 f3(true__, multiply(left_solution(X0, X1), left_solution(Y1, X0)), Y1, X1) -> true__ % 5.27/5.29 f3(true__, multiply(left_solution(multiply(X0, Y1), X2), X0), Y1, X2) -> true__ % 5.27/5.29 f3(true__, right_solution(X0, X0), Y1, Y1) -> true__ % 5.27/5.29 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 5.27/5.29 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, left_solution(Y1, Y2), Y4, Y2) -> true__ % 5.27/5.29 f4(f3(true__, Y3, right_solution(Y0, Y2), Y4), Y5, Y3, Y0, Y4, Y2) -> true__ % 5.27/5.29 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 5.27/5.29 f5(f3(true__, Y0, Y1, Y2), Y3, Y1, Y4, Y5, Y0, Y2) -> true__ % 5.27/5.29 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 5.27/5.29 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 5.27/5.29 f6(f3(true__, Y0, Y1, Y2), Y2, right_solution(Y1, X1), multiply(Y0, X1)) -> true__ % 5.27/5.29 f6(f3(true__, Y0, left_solution(Y1, right_solution(Y0, X1)), Y3), Y3, Y1, X1) -> true__ % 5.27/5.29 f6(f3(true__, Y0, left_solution(Y3, X1), Y2), Y2, Y3, multiply(Y0, X1)) -> true__ % 5.27/5.29 f6(f3(true__, Y3, Y0, Y4), Y4, Y1, multiply(Y3, multiply(Y0, Y1))) -> true__ % 5.27/5.29 f6(f3(true__, left_solution(X1, Y2), Y0, Y3), Y3, right_solution(Y0, X1), Y2) -> true__ % 5.27/5.29 f6(f3(true__, left_solution(X1, Y2), left_solution(Y1, X1), Y3), Y3, Y1, Y2) -> true__ % 5.27/5.29 f6(f3(true__, left_solution(multiply(Y1, Y3), X1), Y1, Y2), Y2, Y3, X1) -> true__ % 5.27/5.29 f6(true__, U, Z, W) -> product(U, Z, W) % 5.27/5.29 f7(f3(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 5.27/5.29 f7(f3(true__, Y3, Y4, Y1), left_solution(Y1, Y2), Y3, Y5, Y4, Y2) -> true__ % 5.27/5.29 f7(f3(true__, Y3, Y4, right_solution(Y0, Y2)), Y0, Y3, Y5, Y4, Y2) -> true__ % 5.27/5.29 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 5.27/5.29 f8(f3(true__, Y0, Y1, Y2), Y3, Y4, Y1, Y0, Y5, Y2) -> true__ % 5.27/5.29 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 5.27/5.29 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 5.27/5.29 f9(f3(true__, not_identity(Y0), Y0, not_identity(Y0))) -> true__ % 5.27/5.29 f9(product(not_identity(X), X, not_identity(X))) -> true__ % 5.27/5.29 f9(true__) -> false__ % 5.27/5.29 false__ -> true__ % 5.27/5.29 left_solution(right_solution(Y1, Y1), X1) -> X1 % 5.27/5.29 multiply(X1, right_solution(right_solution(left_solution(Y0, Y1), X1), Y0)) -> Y1 % 5.27/5.29 multiply(Y0, right_solution(Y0, Y1)) -> Y1 % 5.27/5.29 multiply(Y0, right_solution(right_solution(Y2, Y0), right_solution(X0, X0))) -> Y2 % 5.27/5.29 multiply(Y1, right_solution(Y2, Y2)) -> Y1 % 5.27/5.29 multiply(Y1, right_solution(right_solution(Y2, Y2), right_solution(X0, X0))) -> Y1 % 5.27/5.29 multiply(left_solution(Y0, Y1), Y0) -> Y1 % 5.27/5.29 multiply(left_solution(Y0, Y1), left_solution(right_solution(X1, X1), Y0)) -> Y1 % 5.27/5.29 multiply(left_solution(Y0, Y1), right_solution(right_solution(X1, X1), Y0)) -> Y1 % 5.27/5.29 multiply(left_solution(multiply(right_solution(X1, X1), Y1), Y2), Y1) -> Y2 % 5.27/5.29 multiply(multiply(Y1, Y2), right_solution(Y2, right_solution(X0, X0))) -> Y1 % 5.27/5.29 multiply(multiply(Y1, left_solution(Y2, right_solution(X0, X0))), Y2) -> Y1 % 5.27/5.29 multiply(multiply(left_solution(X1, Y2), Y0), right_solution(Y0, X1)) -> Y2 % 5.27/5.29 multiply(multiply(left_solution(X1, Y2), left_solution(Y1, X1)), Y1) -> Y2 % 5.27/5.29 multiply(multiply(left_solution(multiply(X1, X2), Y1), X1), X2) -> Y1 % 5.27/5.29 product(X, V, W) -> f3(true__, X, V, W) % 5.27/5.29 product(X, Y, multiply(X, Y)) -> true__ % 5.27/5.29 product(X, right_solution(X, Y), Y) -> true__ % 5.27/5.29 product(left_solution(X, Y), X, Y) -> true__ % 5.27/5.29 with the LPO induced by % 5.27/5.29 not_identity > f9 > right_solution > left_solution > f2 > f1 > f8 > f7 > f6 > f5 > f4 > product > f3 > multiply > false__ > true__ % 5.27/5.29 % 5.27/5.29 % SZS output end Proof % 5.27/5.29 %------------------------------------------------------------------------------