%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL051-1 : 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 00:37:11 EDT 2022 % Result : Unsatisfiable 0.15s 0.51s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.10 % Problem : COL051-1 : TPTP v8.1.0. Released v1.0.0. % 0.09/0.11 % Command : moca.sh %s % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 600 % 0.10/0.30 % DateTime : Tue May 31 11:06:58 EDT 2022 % 0.10/0.30 % CPUTime : % 0.15/0.51 % SZS status Unsatisfiable % 0.15/0.51 % SZS output start Proof % 0.15/0.51 The input problem is unsatisfiable because % 0.15/0.51 % 0.15/0.51 [1] the following set of Horn clauses is unsatisfiable: % 0.15/0.51 % 0.15/0.51 response(mocking_bird, Y) = response(Y, Y) % 0.15/0.51 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.15/0.51 response(X, X) = X ==> \bottom % 0.15/0.51 % 0.15/0.51 This holds because % 0.15/0.51 % 0.15/0.51 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.15/0.51 % 0.15/0.51 E: % 0.15/0.51 f1(X, X) = false__ % 0.15/0.51 f1(response(X, X), X) = true__ % 0.15/0.51 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.15/0.51 response(mocking_bird, Y) = response(Y, Y) % 0.15/0.51 G: % 0.15/0.51 true__ = false__ % 0.15/0.51 % 0.15/0.51 This holds because % 0.15/0.51 % 0.15/0.51 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.15/0.51 % 0.15/0.51 response(X0, response(X1, response(Y1, compose(compose(X0, X1), Y1)))) = response(mocking_bird, compose(compose(X0, X1), Y1)) % 0.15/0.51 response(X0, response(X1, response(Y1, response(Y2, compose(compose(compose(X0, X1), Y1), Y2))))) = response(mocking_bird, compose(compose(compose(X0, X1), Y1), Y2)) % 0.15/0.51 response(Y0, response(X0, response(X1, compose(Y0, compose(X0, X1))))) = response(mocking_bird, compose(Y0, compose(X0, X1))) % 0.15/0.51 response(Y0, response(X0, response(X1, response(Y2, compose(Y0, compose(compose(X0, X1), Y2)))))) = response(mocking_bird, compose(Y0, compose(compose(X0, X1), Y2))) % 0.15/0.51 response(Y0, response(X0, response(X1, response(Y2, compose(compose(Y0, compose(X0, X1)), Y2))))) = response(mocking_bird, compose(compose(Y0, compose(X0, X1)), Y2)) % 0.15/0.51 response(Y0, response(Y1, response(X0, response(X1, compose(compose(Y0, Y1), compose(X0, X1)))))) = response(mocking_bird, compose(compose(Y0, Y1), compose(X0, X1))) % 0.15/0.51 response(mocking_bird, Y) = response(Y, Y) % 0.15/0.51 response(mocking_bird, compose(Y0, Y1)) = response(Y0, response(Y1, compose(Y0, Y1))) % 0.15/0.51 f1(X, X) -> false__ % 0.15/0.51 f1(response(X, X), X) -> true__ % 0.15/0.51 f1(response(X0, response(X1, compose(X0, X1))), compose(X0, X1)) -> true__ % 0.15/0.51 f1(response(X0, response(X1, response(Y1, compose(compose(X0, X1), Y1)))), compose(compose(X0, X1), Y1)) -> true__ % 0.15/0.51 f1(response(Y0, response(X0, response(X1, compose(Y0, compose(X0, X1))))), compose(Y0, compose(X0, X1))) -> true__ % 0.15/0.51 f1(response(mocking_bird, Y0), Y0) -> true__ % 0.15/0.51 f1(response(mocking_bird, compose(compose(mocking_bird, X1), X2)), response(X1, response(X2, compose(compose(mocking_bird, X1), X2)))) -> true__ % 0.15/0.51 f1(response(mocking_bird, compose(mocking_bird, X1)), response(X1, compose(mocking_bird, X1))) -> true__ % 0.15/0.51 f1(response(mocking_bird, compose(mocking_bird, compose(X0, X1))), response(X0, response(X1, compose(mocking_bird, compose(X0, X1))))) -> true__ % 0.15/0.51 false__ -> true__ % 0.15/0.51 response(compose(X, Y), W) -> response(X, response(Y, W)) % 0.15/0.51 with the LPO induced by % 0.15/0.51 mocking_bird > f1 > response > compose > false__ > true__ % 0.15/0.51 % 0.15/0.51 % SZS output end Proof % 0.15/0.51 %------------------------------------------------------------------------------