%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT034-1 : TPTP v8.1.0. Bugfixed v2.5.0. % 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 : Sun Jul 17 06:04:14 EDT 2022 % Result : Unsatisfiable 0.12s 0.40s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : LAT034-1 : TPTP v8.1.0. Bugfixed v2.5.0. % 0.12/0.13 % 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 : Thu Jun 30 07:22:23 EDT 2022 % 0.12/0.34 % CPUTime : % 0.12/0.40 % SZS status Unsatisfiable % 0.12/0.40 % SZS output start Proof % 0.12/0.40 The input problem is unsatisfiable because % 0.12/0.40 % 0.12/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.12/0.40 % 0.12/0.40 meet(X, join(X, Y)) = X % 0.12/0.40 join(X, meet(X, Y)) = X % 0.12/0.40 meet(X, Y) = meet(Y, X) % 0.12/0.40 join(X, Y) = join(Y, X) % 0.12/0.40 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 0.12/0.40 join(join(X, Y), Z) = join(X, join(Y, Z)) % 0.12/0.40 meet(xx, xx) = xx ==> \bottom % 0.12/0.40 % 0.12/0.40 This holds because % 0.12/0.40 % 0.12/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.12/0.40 % 0.12/0.40 E: % 0.12/0.40 f1(meet(xx, xx)) = true__ % 0.12/0.40 f1(xx) = false__ % 0.12/0.40 join(X, Y) = join(Y, X) % 0.12/0.40 join(X, meet(X, Y)) = X % 0.12/0.40 join(join(X, Y), Z) = join(X, join(Y, Z)) % 0.12/0.40 meet(X, Y) = meet(Y, X) % 0.12/0.40 meet(X, join(X, Y)) = X % 0.12/0.40 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 0.12/0.40 G: % 0.12/0.40 true__ = false__ % 0.12/0.40 % 0.12/0.40 This holds because % 0.12/0.40 % 0.12/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.12/0.40 % 0.12/0.40 join(X, Y) = join(Y, X) % 0.12/0.40 join(Y0, Y2) = join(Y2, join(Y2, Y0)) % 0.12/0.40 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 0.12/0.40 meet(X, Y) = meet(Y, X) % 0.12/0.40 meet(Y0, Y2) = meet(Y2, meet(Y2, Y0)) % 0.12/0.40 meet(Y1, meet(Y0, Y2)) = meet(Y0, meet(Y1, Y2)) % 0.12/0.40 meet(Y2, meet(Y0, Y1)) = meet(Y0, meet(Y1, Y2)) % 0.12/0.40 f1(meet(xx, xx)) -> true__ % 0.12/0.40 f1(xx) -> false__ % 0.12/0.40 join(X, meet(X, Y)) -> X % 0.12/0.40 join(Y0, Y0) -> Y0 % 0.12/0.40 join(Y0, meet(Y1, Y0)) -> Y0 % 0.12/0.40 join(Y1, join(Y2, join(Y1, Y2))) -> join(Y1, Y2) % 0.12/0.40 join(join(X, Y), Z) -> join(X, join(Y, Z)) % 0.12/0.40 meet(X, join(X, Y)) -> X % 0.12/0.40 meet(Y0, Y0) -> Y0 % 0.12/0.40 meet(Y0, join(Y1, Y0)) -> Y0 % 0.12/0.40 meet(Y1, meet(Y2, meet(Y1, Y2))) -> meet(Y1, Y2) % 0.12/0.40 meet(Y2, meet(Y0, Y2)) -> meet(Y0, Y2) % 0.12/0.40 meet(Y2, meet(Y1, meet(Y1, Y2))) -> meet(Y1, Y2) % 0.12/0.40 meet(meet(X, Y), Z) -> meet(X, meet(Y, Z)) % 0.12/0.40 true__ -> false__ % 0.12/0.40 with the LPO induced by % 0.12/0.40 xx > f1 > join > meet > true__ > false__ % 0.12/0.40 % 0.12/0.40 % SZS output end Proof % 0.12/0.40 %------------------------------------------------------------------------------