%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP028-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 10:51:58 EDT 2022 % Result : Unsatisfiable 0.72s 0.87s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP028-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue Jun 14 11:56:09 EDT 2022 % 0.13/0.35 % CPUTime : % 0.72/0.87 % SZS status Unsatisfiable % 0.72/0.87 % SZS output start Proof % 0.72/0.87 The input problem is unsatisfiable because % 0.72/0.87 % 0.72/0.87 [1] the following set of Horn clauses is unsatisfiable: % 0.72/0.87 % 0.72/0.87 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 0.72/0.87 product(left_solution(X, Y), X, Y) % 0.72/0.87 product(X, right_solution(X, Y), Y) % 0.72/0.87 product(not_identity(X), X, not_identity(X)) ==> \bottom % 0.72/0.87 % 0.72/0.87 This holds because % 0.72/0.87 % 0.72/0.87 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.72/0.87 % 0.72/0.87 E: % 0.72/0.87 f1(true__, U, Z, W) = product(U, Z, W) % 0.72/0.87 f2(true__, X, Y, U, Z, W) = f1(product(X, Y, U), U, Z, W) % 0.72/0.87 f3(product(X, V, W), Y, Z, V, X, U, W) = true__ % 0.72/0.87 f3(true__, Y, Z, V, X, U, W) = f2(product(Y, Z, V), X, Y, U, Z, W) % 0.72/0.87 f4(product(not_identity(X), X, not_identity(X))) = true__ % 0.72/0.87 f4(true__) = false__ % 0.72/0.87 product(X, right_solution(X, Y), Y) = true__ % 0.72/0.87 product(left_solution(X, Y), X, Y) = true__ % 0.72/0.87 G: % 0.72/0.87 true__ = false__ % 0.72/0.87 % 0.72/0.87 This holds because % 0.72/0.87 % 0.72/0.87 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.72/0.87 % 0.72/0.87 % 0.72/0.87 f1(f1(true__, Y2, Y0, Y4), Y4, right_solution(Y0, right_solution(Y2, Y3)), Y3) -> true__ % 0.72/0.87 f1(f1(true__, Y2, left_solution(Y1, right_solution(Y2, Y3)), Y4), Y4, Y1, Y3) -> true__ % 0.72/0.87 f1(f1(true__, Y2, right_solution(Y2, Y3), Y4), Y4, right_solution(X1, X1), Y3) -> true__ % 0.72/0.87 f1(f1(true__, left_solution(Y2, Y3), Y0, Y4), Y4, right_solution(X1, right_solution(left_solution(X1, Y0), Y2)), Y3) -> true__ % 0.72/0.87 f1(f1(true__, left_solution(Y2, Y3), Y0, Y4), Y4, right_solution(Y0, Y2), Y3) -> true__ % 0.72/0.87 f1(f1(true__, left_solution(Y2, Y3), Y2, Y4), Y4, right_solution(X1, X1), Y3) -> true__ % 0.72/0.87 f1(f1(true__, left_solution(Y2, Y3), left_solution(Y1, Y2), Y4), Y4, Y1, Y3) -> true__ % 0.72/0.87 f1(true__, Y0, right_solution(Y0, Y2), Y2) -> true__ % 0.72/0.87 f1(true__, Y2, right_solution(Y1, right_solution(left_solution(Y1, Y2), Y3)), Y3) -> true__ % 0.72/0.87 f1(true__, Y2, right_solution(right_solution(Y0, Y2), right_solution(Y0, Y3)), Y3) -> true__ % 0.72/0.87 f1(true__, Y3, right_solution(Y2, Y2), Y3) -> true__ % 0.72/0.87 f1(true__, Y3, right_solution(right_solution(left_solution(Y0, Y1), Y3), Y0), Y1) -> true__ % 0.72/0.87 f1(true__, left_solution(Y0, Y1), right_solution(right_solution(X1, X1), Y0), Y1) -> true__ % 0.72/0.87 f1(true__, left_solution(Y1, Y2), Y1, Y2) -> true__ % 0.72/0.87 f2(f1(true__, Y3, Y4, Y1), left_solution(Y1, Y2), Y3, Y5, Y4, Y2) -> true__ % 0.72/0.87 f2(f1(true__, Y3, Y4, right_solution(X1, X1)), Y2, Y3, Y5, Y4, Y2) -> true__ % 0.72/0.87 f2(f1(true__, Y3, Y4, right_solution(X1, right_solution(left_solution(X1, Y0), Y2))), Y0, Y3, Y5, Y4, Y2) -> true__ % 0.72/0.87 f2(f1(true__, Y3, Y4, right_solution(Y0, Y2)), Y0, Y3, Y5, Y4, Y2) -> true__ % 0.72/0.87 f2(true__, X, Y, U, Z, W) -> f1(product(X, Y, U), U, Z, W) % 0.72/0.87 f3(f1(true__, Y0, Y1, Y2), Y3, Y4, Y1, Y0, Y5, Y2) -> true__ % 0.72/0.87 f3(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 0.72/0.87 f3(true__, Y, Z, V, X, U, W) -> f2(product(Y, Z, V), X, Y, U, Z, W) % 0.72/0.87 f4(f1(true__, not_identity(Y0), Y0, not_identity(Y0))) -> true__ % 0.72/0.87 f4(product(not_identity(X), X, not_identity(X))) -> true__ % 0.72/0.87 f4(true__) -> false__ % 0.72/0.87 false__ -> true__ % 0.72/0.87 product(U, Z, W) -> f1(true__, U, Z, W) % 0.72/0.87 product(X, right_solution(X, Y), Y) -> true__ % 0.72/0.87 product(left_solution(X, Y), X, Y) -> true__ % 0.72/0.87 with the LPO induced by % 0.72/0.87 not_identity > f4 > right_solution > left_solution > f3 > f2 > product > f1 > false__ > true__ % 0.72/0.87 % 0.72/0.87 % SZS output end Proof % 0.72/0.87 %------------------------------------------------------------------------------