%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL053-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 00:37:13 EDT 2022 % Result : Unsatisfiable 0.49s 0.63s % Output : Proof 0.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COL053-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Tue May 31 04:38:07 EDT 2022 % 0.14/0.34 % CPUTime : % 0.49/0.63 % SZS status Unsatisfiable % 0.49/0.63 % SZS output start Proof % 0.49/0.63 The input problem is unsatisfiable because % 0.49/0.63 % 0.49/0.63 [1] the following set of Horn clauses is unsatisfiable: % 0.49/0.63 % 0.49/0.63 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.49/0.63 response(U, f(U)) = response(a, response(b, response(c, f(U)))) ==> \bottom % 0.49/0.63 % 0.49/0.63 This holds because % 0.49/0.63 % 0.49/0.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.49/0.63 % 0.49/0.63 E: % 0.49/0.63 f1(response(U, f(U)), U) = true__ % 0.49/0.63 f1(response(a, response(b, response(c, f(U)))), U) = false__ % 0.49/0.63 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.49/0.63 G: % 0.49/0.63 true__ = false__ % 0.49/0.63 % 0.49/0.63 This holds because % 0.49/0.63 % 0.49/0.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.49/0.63 % 0.49/0.63 % 0.49/0.63 f1(response(U, f(U)), U) -> true__ % 0.49/0.63 f1(response(X0, response(X1, f(compose(X0, X1)))), compose(X0, X1)) -> true__ % 0.49/0.63 f1(response(X0, response(X1, response(Y1, f(compose(compose(X0, X1), Y1))))), compose(compose(X0, X1), Y1)) -> true__ % 0.49/0.63 f1(response(X0, response(X1, response(Y1, response(Y2, f(compose(compose(compose(X0, X1), Y1), Y2)))))), compose(compose(compose(X0, X1), Y1), Y2)) -> true__ % 0.49/0.63 f1(response(Y0, response(X0, response(X1, f(compose(Y0, compose(X0, X1)))))), compose(Y0, compose(X0, X1))) -> true__ % 0.49/0.63 f1(response(Y0, response(X0, response(X1, response(Y2, f(compose(Y0, compose(compose(X0, X1), Y2))))))), compose(Y0, compose(compose(X0, X1), Y2))) -> true__ % 0.49/0.63 f1(response(Y0, response(X0, response(X1, response(Y2, f(compose(compose(Y0, compose(X0, X1)), Y2)))))), compose(compose(Y0, compose(X0, X1)), Y2)) -> true__ % 0.49/0.63 f1(response(Y0, response(Y1, response(X0, response(X1, f(compose(Y0, compose(Y1, compose(X0, X1)))))))), compose(Y0, compose(Y1, compose(X0, X1)))) -> true__ % 0.49/0.63 f1(response(Y0, response(Y1, response(X0, response(X1, f(compose(compose(Y0, Y1), compose(X0, X1))))))), compose(compose(Y0, Y1), compose(X0, X1))) -> true__ % 0.49/0.63 f1(response(a, response(b, response(c, f(U)))), U) -> false__ % 0.49/0.63 false__ -> true__ % 0.49/0.63 response(compose(X, Y), W) -> response(X, response(Y, W)) % 0.49/0.63 with the LPO induced by % 0.49/0.63 compose > f1 > c > a > response > f > b > false__ > true__ % 0.49/0.63 % 0.49/0.63 % SZS output end Proof % 0.49/0.63 %------------------------------------------------------------------------------