%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL058-1 : 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 00:37:15 EDT 2022 % Result : Unsatisfiable 27.47s 27.66s % Output : Proof 27.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : COL058-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n029.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue May 31 13:10:45 EDT 2022 % 0.13/0.33 % CPUTime : % 27.47/27.66 % SZS status Unsatisfiable % 27.47/27.66 % SZS output start Proof % 27.47/27.66 The input problem is unsatisfiable because % 27.47/27.66 % 27.47/27.66 [1] the following set of Horn clauses is unsatisfiable: % 27.47/27.66 % 27.47/27.66 response(response(lark, X1), X2) = response(X1, response(X2, X2)) % 27.47/27.66 response(X, X) = X ==> \bottom % 27.47/27.66 % 27.47/27.66 This holds because % 27.47/27.66 % 27.47/27.66 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 27.47/27.66 % 27.47/27.66 E: % 27.47/27.66 f1(X, X) = false__ % 27.47/27.66 f1(response(X, X), X) = true__ % 27.47/27.66 response(response(lark, X1), X2) = response(X1, response(X2, X2)) % 27.47/27.66 G: % 27.47/27.66 true__ = false__ % 27.47/27.66 % 27.47/27.66 This holds because % 27.47/27.66 % 27.47/27.66 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 27.47/27.66 % 27.47/27.66 response(X0, response(response(Y1, Y1), response(Y1, Y1))) = response(response(lark, response(lark, X0)), Y1) % 27.47/27.66 response(X0, response(response(response(Y1, Y1), response(Y1, Y1)), response(response(Y1, Y1), response(Y1, Y1)))) = response(response(lark, response(lark, response(lark, X0))), Y1) % 27.47/27.66 response(X0, response(response(response(response(lark, lark), Y1), Y1), response(response(response(lark, lark), Y1), Y1))) = response(response(lark, response(lark, X0)), response(Y1, Y1)) % 27.47/27.66 response(Y0, response(response(response(lark, lark), X0), X0)) = response(response(lark, Y0), response(X0, X0)) % 27.47/27.66 response(Y0, response(response(response(lark, lark), Y1), Y1)) = response(response(lark, response(lark, Y0)), Y1) % 27.47/27.66 response(response(lark, X1), X2) = response(X1, response(X2, X2)) % 27.47/27.66 response(response(lark, response(Y0, Y0)), response(Y1, Y1)) = response(response(lark, response(response(lark, lark), Y0)), Y1) % 27.47/27.66 response(response(lark, response(response(lark, lark), Y0)), X1) = response(response(Y0, Y0), response(response(X1, X1), response(X1, X1))) % 27.47/27.66 response(response(response(lark, lark), X0), response(Y1, Y1)) = response(response(lark, response(lark, response(X0, X0))), Y1) % 27.47/27.66 response(response(response(lark, lark), X1), Y1) = response(response(X1, X1), response(Y1, Y1)) % 27.47/27.66 response(response(response(lark, response(lark, lark)), X1), Y1) = response(response(response(X1, X1), response(X1, X1)), response(Y1, Y1)) % 27.47/27.66 f1(X, X) -> false__ % 27.47/27.66 f1(response(X, X), X) -> true__ % 27.47/27.66 f1(response(response(response(lark, lark), X0), X0), response(X0, X0)) -> true__ % 27.47/27.66 f1(response(response(response(lark, lark), response(X0, X0)), response(X0, X0)), response(response(response(lark, lark), X0), X0)) -> true__ % 27.47/27.66 f1(response(response(response(lark, lark), response(lark, lark)), lark), response(response(lark, lark), response(lark, lark))) -> true__ % 27.47/27.66 f1(response(response(response(lark, response(lark, lark)), X1), response(X1, X1)), response(response(X1, X1), response(X1, X1))) -> true__ % 27.47/27.66 response(response(response(response(lark, lark), X1), X1), response(Y1, Y1)) -> response(response(response(lark, lark), response(X1, X1)), Y1) % 27.47/27.66 true__ -> false__ % 27.47/27.66 with the LPO induced by % 27.47/27.66 lark > response > f1 > true__ > false__ % 27.47/27.66 % 27.47/27.66 % SZS output end Proof % 27.47/27.66 %------------------------------------------------------------------------------