%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL056-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 00:37:14 EDT 2022 % Result : Unsatisfiable 0.19s 0.38s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL056-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue May 31 12:04:45 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.38 % SZS status Unsatisfiable % 0.19/0.38 % SZS output start Proof % 0.19/0.38 The input problem is unsatisfiable because % 0.19/0.38 % 0.19/0.38 [1] the following set of Horn clauses is unsatisfiable: % 0.19/0.38 % 0.19/0.38 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.19/0.38 response(a, b) = c % 0.19/0.38 response(a, c) = b % 0.19/0.38 response(W, V) = V ==> \bottom % 0.19/0.38 % 0.19/0.38 This holds because % 0.19/0.38 % 0.19/0.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.19/0.38 % 0.19/0.38 E: % 0.19/0.38 f1(V, V) = false__ % 0.19/0.38 f1(response(W, V), V) = true__ % 0.19/0.38 response(a, b) = c % 0.19/0.38 response(a, c) = b % 0.19/0.38 response(compose(X, Y), W) = response(X, response(Y, W)) % 0.19/0.38 G: % 0.19/0.38 true__ = false__ % 0.19/0.38 % 0.19/0.38 This holds because % 0.19/0.38 % 0.19/0.38 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.19/0.38 % 0.19/0.38 % 0.19/0.38 c -> response(a, b) % 0.19/0.38 f1(V, V) -> false__ % 0.19/0.38 f1(b, response(a, b)) -> true__ % 0.19/0.38 f1(response(W, V), V) -> true__ % 0.19/0.38 f1(response(X0, response(X1, Y1)), Y1) -> true__ % 0.19/0.38 f1(response(X0, response(X1, response(Y1, Y2))), Y2) -> true__ % 0.19/0.38 f1(response(Y0, b), response(a, b)) -> true__ % 0.19/0.38 response(a, c) -> b % 0.19/0.38 response(a, response(a, b)) -> b % 0.19/0.38 response(compose(X, Y), W) -> response(X, response(Y, W)) % 0.19/0.38 true__ -> false__ % 0.19/0.38 with the LPO induced by % 0.19/0.38 f1 > c > b > a > compose > response > true__ > false__ % 0.19/0.38 % 0.19/0.38 % SZS output end Proof % 0.19/0.38 %------------------------------------------------------------------------------