%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL052-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 : Fri Jul 15 00:37:12 EDT 2022 % Result : Unsatisfiable 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.09 % Problem : COL052-1 : TPTP v8.1.0. Released v1.0.0. % 0.05/0.10 % Command : moca.sh %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 600 % 0.10/0.29 % DateTime : Tue May 31 06:07:28 EDT 2022 % 0.10/0.29 % CPUTime : % 0.36/0.57 % SZS status Unsatisfiable % 0.36/0.57 % SZS output start Proof % 0.36/0.57 The input problem is unsatisfiable because % 0.36/0.57 % 0.36/0.57 [1] the following set of Horn clauses is unsatisfiable: % 0.36/0.57 % 0.36/0.57 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.36/0.57 response(c, common_bird(X)) = response(X, common_bird(X)) % 0.36/0.57 response(a, V) = response(odd_bird, V) ==> \bottom % 0.36/0.57 c = compose(a, b) % 0.36/0.57 % 0.36/0.57 This holds because % 0.36/0.57 % 0.36/0.57 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.36/0.57 % 0.36/0.57 E: % 0.36/0.57 c = compose(a, b) % 0.36/0.57 f1(response(a, V), V) = true__ % 0.36/0.57 f1(response(odd_bird, V), V) = false__ % 0.36/0.57 response(c, common_bird(X)) = response(X, common_bird(X)) % 0.36/0.57 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.36/0.57 G: % 0.36/0.57 true__ = false__ % 0.36/0.57 % 0.36/0.57 This holds because % 0.36/0.57 % 0.36/0.57 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.36/0.57 % 0.36/0.57 response(X0, response(X1, response(Y1, common_bird(compose(compose(X0, X1), Y1))))) = response(a, response(b, common_bird(compose(compose(X0, X1), Y1)))) % 0.36/0.57 response(Y0, response(X0, response(X1, common_bird(compose(Y0, compose(X0, X1)))))) = response(a, response(b, common_bird(compose(Y0, compose(X0, X1))))) % 0.36/0.57 response(a, response(b, common_bird(Y0))) = response(Y0, common_bird(Y0)) % 0.36/0.57 response(a, response(b, common_bird(compose(Y0, Y1)))) = response(Y0, response(Y1, common_bird(compose(Y0, Y1)))) % 0.36/0.57 response(c, common_bird(X)) = response(X, common_bird(X)) % 0.36/0.57 c -> compose(a, b) % 0.36/0.57 f1(response(X0, common_bird(X0)), response(b, common_bird(X0))) -> true__ % 0.36/0.57 f1(response(X0, response(X1, common_bird(compose(X0, X1)))), response(b, common_bird(compose(X0, X1)))) -> true__ % 0.36/0.57 f1(response(X0, response(X1, response(Y1, common_bird(compose(compose(X0, X1), Y1))))), response(b, common_bird(compose(compose(X0, X1), Y1)))) -> true__ % 0.36/0.57 f1(response(Y0, response(X0, response(X1, common_bird(compose(Y0, compose(X0, X1)))))), response(b, common_bird(compose(Y0, compose(X0, X1))))) -> true__ % 0.36/0.57 f1(response(a, V), V) -> true__ % 0.36/0.57 f1(response(a, response(b, common_bird(compose(a, X1)))), response(X1, common_bird(compose(a, X1)))) -> true__ % 0.36/0.57 f1(response(a, response(b, common_bird(compose(a, compose(X1, X2))))), response(X1, response(X2, common_bird(compose(a, compose(X1, X2)))))) -> true__ % 0.36/0.57 f1(response(a, response(b, common_bird(compose(compose(a, X1), X2)))), response(X1, response(X2, common_bird(compose(compose(a, X1), X2))))) -> true__ % 0.36/0.57 f1(response(a, response(b, common_bird(compose(compose(odd_bird, X1), X2)))), response(X1, response(X2, common_bird(compose(compose(odd_bird, X1), X2))))) -> false__ % 0.36/0.57 f1(response(a, response(b, common_bird(compose(odd_bird, X1)))), response(X1, common_bird(compose(odd_bird, X1)))) -> false__ % 0.36/0.57 f1(response(a, response(b, common_bird(compose(odd_bird, compose(X1, X2))))), response(X1, response(X2, common_bird(compose(odd_bird, compose(X1, X2)))))) -> false__ % 0.36/0.57 f1(response(odd_bird, V), V) -> false__ % 0.36/0.57 response(compose(X, Y), W) -> response(X, response(Y, W)) % 0.36/0.57 true__ -> false__ % 0.36/0.57 with the LPO induced by % 0.36/0.57 c > b > a > odd_bird > f1 > common_bird > compose > response > true__ > false__ % 0.36/0.57 % 0.36/0.57 % SZS output end Proof % 0.36/0.57 %------------------------------------------------------------------------------