%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT014-1 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 : Sun Jul 17 06:04:07 EDT 2022 % Result : Unsatisfiable 0.48s 0.63s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.11 % Problem : LAT014-1 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n024.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 29 15:40:00 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.63 % SZS status Unsatisfiable % 0.48/0.63 % SZS output start Proof % 0.48/0.63 The input problem is unsatisfiable because % 0.48/0.63 % 0.48/0.63 [1] the following set of Horn clauses is unsatisfiable: % 0.48/0.63 % 0.48/0.63 join(X, meet(Y, meet(X, Z))) = X % 0.48/0.63 meet(X, join(Y, join(X, Z))) = X % 0.48/0.63 join(join(meet(X, Y), meet(Y, Z)), Y) = Y % 0.48/0.63 meet(meet(join(X, Y), join(Y, Z)), Y) = Y % 0.48/0.63 meet(a, join(a, b)) = a ==> \bottom % 0.48/0.63 % 0.48/0.63 This holds because % 0.48/0.63 % 0.48/0.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.48/0.63 % 0.48/0.63 E: % 0.48/0.63 f1(a) = false__ % 0.48/0.63 f1(meet(a, join(a, b))) = true__ % 0.48/0.63 join(X, meet(Y, meet(X, Z))) = X % 0.48/0.63 join(join(meet(X, Y), meet(Y, Z)), Y) = Y % 0.48/0.63 meet(X, join(Y, join(X, Z))) = X % 0.48/0.63 meet(meet(join(X, Y), join(Y, Z)), Y) = Y % 0.48/0.63 G: % 0.48/0.63 true__ = false__ % 0.48/0.63 % 0.48/0.63 This holds because % 0.48/0.63 % 0.48/0.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.48/0.63 % 0.48/0.63 % 0.48/0.63 f1(a) -> false__ % 0.48/0.63 f1(meet(a, join(a, b))) -> true__ % 0.48/0.63 join(X, meet(Y, meet(X, Z))) -> X % 0.48/0.63 join(Y0, Y0) -> Y0 % 0.48/0.63 join(Y0, join(X1, Y0)) -> join(X1, Y0) % 0.48/0.63 join(Y0, join(X1, join(Y0, X2))) -> join(X1, join(Y0, X2)) % 0.48/0.63 join(Y0, join(Y0, X1)) -> join(Y0, X1) % 0.48/0.63 join(Y0, meet(Y0, Y2)) -> Y0 % 0.48/0.63 join(Y0, meet(Y1, Y0)) -> Y0 % 0.48/0.63 join(join(X1, Y1), Y1) -> join(X1, Y1) % 0.48/0.63 join(join(X1, join(Y1, X2)), Y1) -> join(X1, join(Y1, X2)) % 0.48/0.63 join(join(Y0, join(X1, Y0)), join(X1, Y0)) -> join(X1, Y0) % 0.48/0.63 join(join(Y0, meet(join(X1, join(Y0, X2)), Y2)), join(X1, join(Y0, X2))) -> join(X1, join(Y0, X2)) % 0.48/0.63 join(join(Y1, X1), Y1) -> join(Y1, X1) % 0.48/0.63 join(join(Y1, meet(Y1, Y2)), Y1) -> Y1 % 0.48/0.63 join(join(meet(X, Y), meet(Y, Z)), Y) -> Y % 0.48/0.63 join(join(meet(Y0, Y1), Y1), Y1) -> Y1 % 0.48/0.63 join(meet(Y0, Y1), Y1) -> Y1 % 0.48/0.63 meet(X, join(Y, join(X, Z))) -> X % 0.48/0.63 meet(Y0, Y0) -> Y0 % 0.48/0.63 meet(Y0, join(Y0, Y2)) -> Y0 % 0.48/0.63 meet(Y0, join(Y1, Y0)) -> Y0 % 0.48/0.63 meet(Y0, meet(X1, Y0)) -> meet(X1, Y0) % 0.48/0.63 meet(Y0, meet(X1, meet(Y0, X2))) -> meet(X1, meet(Y0, X2)) % 0.48/0.63 meet(Y0, meet(Y0, X1)) -> meet(Y0, X1) % 0.48/0.63 meet(join(X0, Y1), Y1) -> Y1 % 0.48/0.63 meet(meet(X0, Y2), join(Y1, Y2)) -> meet(X0, Y2) % 0.48/0.63 meet(meet(X1, Y1), Y1) -> meet(X1, Y1) % 0.48/0.63 meet(meet(X1, meet(Y1, X2)), Y1) -> meet(X1, meet(Y1, X2)) % 0.48/0.63 meet(meet(Y0, join(meet(X1, meet(Y0, X2)), Y2)), meet(X1, meet(Y0, X2))) -> meet(X1, meet(Y0, X2)) % 0.48/0.63 meet(meet(Y1, X1), Y1) -> meet(Y1, X1) % 0.48/0.63 meet(meet(join(X, Y), join(Y, Z)), Y) -> Y % 0.48/0.63 meet(meet(join(Y0, Y1), Y1), Y1) -> Y1 % 0.48/0.63 true__ -> false__ % 0.48/0.63 with the LPO induced by % 0.48/0.63 b > a > f1 > meet > join > true__ > false__ % 0.48/0.63 % 0.48/0.63 % SZS output end Proof % 0.48/0.63 %------------------------------------------------------------------------------