%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT039-2 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 06:04:16 EDT 2022 % Result : Unsatisfiable 4.42s 4.60s % Output : Proof 4.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : LAT039-2 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.13 % Command : moca.sh %s % 0.12/0.32 % Computer : n007.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Thu Jun 30 14:26:23 EDT 2022 % 0.12/0.32 % CPUTime : % 4.42/4.60 % SZS status Unsatisfiable % 4.42/4.60 % SZS output start Proof % 4.42/4.60 The input problem is unsatisfiable because % 4.42/4.60 % 4.42/4.60 [1] the following set of Horn clauses is unsatisfiable: % 4.42/4.60 % 4.42/4.60 meet(X, X) = X % 4.42/4.60 join(X, X) = X % 4.42/4.60 meet(X, join(X, Y)) = X % 4.42/4.60 join(X, meet(X, Y)) = X % 4.42/4.60 meet(X, Y) = meet(Y, X) % 4.42/4.60 join(X, Y) = join(Y, X) % 4.42/4.60 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 4.42/4.60 join(join(X, Y), Z) = join(X, join(Y, Z)) % 4.42/4.60 join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)) % 4.42/4.60 meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)) % 4.42/4.60 join(xx, yy) = yy % 4.42/4.60 join(xx, meet(yy, zz)) = meet(join(xx, yy), join(xx, zz)) ==> \bottom % 4.42/4.60 % 4.42/4.60 This holds because % 4.42/4.60 % 4.42/4.60 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.42/4.60 % 4.42/4.60 E: % 4.42/4.60 f1(join(xx, meet(yy, zz))) = true__ % 4.42/4.60 f1(meet(join(xx, yy), join(xx, zz))) = false__ % 4.42/4.60 join(X, X) = X % 4.42/4.60 join(X, Y) = join(Y, X) % 4.42/4.60 join(X, meet(X, Y)) = X % 4.42/4.60 join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)) % 4.42/4.60 join(join(X, Y), Z) = join(X, join(Y, Z)) % 4.42/4.60 join(xx, yy) = yy % 4.42/4.60 meet(X, X) = X % 4.42/4.60 meet(X, Y) = meet(Y, X) % 4.42/4.60 meet(X, join(X, Y)) = X % 4.42/4.60 meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)) % 4.42/4.60 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 4.42/4.60 G: % 4.42/4.60 true__ = false__ % 4.42/4.60 % 4.42/4.60 This holds because % 4.42/4.60 % 4.42/4.60 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.42/4.60 % 4.42/4.60 join(X, Y) = join(Y, X) % 4.42/4.60 join(Y1, join(Y0, Y2)) = join(Y0, join(Y1, Y2)) % 4.42/4.60 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 4.42/4.60 meet(X, Y) = meet(Y, X) % 4.42/4.60 meet(Y1, meet(Y0, Y2)) = meet(Y0, meet(Y1, Y2)) % 4.42/4.60 meet(Y2, meet(Y0, Y1)) = meet(Y0, meet(Y1, Y2)) % 4.42/4.60 meet(join(Y1, Y2), Y0) = join(meet(Y0, Y1), meet(Y0, Y2)) % 4.42/4.60 f1(join(meet(xx, yy), meet(yy, zz))) -> false__ % 4.42/4.60 f1(join(xx, join(meet(xx, yy), meet(yy, zz)))) -> false__ % 4.42/4.60 f1(join(xx, meet(yy, zz))) -> true__ % 4.42/4.60 f1(meet(join(xx, yy), join(xx, zz))) -> false__ % 4.42/4.60 join(X, X) -> X % 4.42/4.60 join(X, meet(X, Y)) -> X % 4.42/4.60 join(X0, join(X1, join(X0, meet(X1, X2)))) -> join(X0, X1) % 4.42/4.60 join(X0, join(X1, join(meet(X1, Y1), meet(join(X0, join(X1, Y1)), Y2)))) -> join(X0, join(X1, meet(Y1, Y2))) % 4.42/4.60 join(X0, join(meet(X0, X1), join(meet(X0, Y1), join(meet(X1, X0), join(X1, join(meet(X1, Y1), meet(join(X0, join(X1, Y1)), Y2))))))) -> join(X0, join(X1, meet(Y1, Y2))) % 4.42/4.60 join(Y0, join(Y1, join(Y0, Y1))) -> join(Y0, Y1) % 4.42/4.60 join(Y0, join(Y1, meet(join(Y0, Y1), X1))) -> join(Y0, Y1) % 4.42/4.60 join(Y0, join(meet(Y0, X1), Y2)) -> join(Y0, Y2) % 4.42/4.60 join(Y0, join(meet(Y0, X1), meet(Y0, X2))) -> Y0 % 4.42/4.60 join(Y0, join(meet(Y0, Y1), meet(join(Y0, Y1), Y2))) -> join(Y0, meet(Y1, Y2)) % 4.42/4.60 join(Y0, meet(Y1, Y0)) -> Y0 % 4.42/4.60 join(Y0, meet(Y1, meet(Y0, X1))) -> Y0 % 4.42/4.60 join(Y1, join(Y1, Y2)) -> join(Y1, Y2) % 4.42/4.60 join(Y1, join(Y2, meet(Y1, Y2))) -> join(Y1, Y2) % 4.42/4.60 join(join(X, Y), Z) -> join(X, join(Y, Z)) % 4.42/4.60 join(meet(X0, X1), meet(X0, meet(X1, Y1))) -> meet(X0, X1) % 4.42/4.60 join(meet(Y0, Y1), join(Y0, meet(join(Y1, Y0), Y2))) -> join(Y0, meet(Y1, Y2)) % 4.42/4.60 join(meet(Y0, xx), meet(Y0, yy)) -> meet(Y0, yy) % 4.42/4.60 join(meet(xx, yy), meet(yy, Y2)) -> join(xx, meet(yy, Y2)) % 4.42/4.60 join(xx, join(yy, Y2)) -> join(yy, Y2) % 4.42/4.60 join(xx, yy) -> yy % 4.42/4.60 meet(X, X) -> X % 4.42/4.60 meet(X, join(Y, Z)) -> join(meet(X, Y), meet(X, Z)) % 4.42/4.60 meet(Y0, meet(Y1, meet(Y0, Y1))) -> meet(Y0, Y1) % 4.42/4.60 meet(Y1, meet(Y1, Y2)) -> meet(Y1, Y2) % 4.42/4.60 meet(join(X, Y), join(X, Z)) -> join(X, meet(Y, Z)) % 4.42/4.60 meet(join(X0, meet(X1, X2)), Y2) -> meet(join(X0, X1), meet(join(X0, X2), Y2)) % 4.42/4.60 meet(join(meet(Y0, X1), meet(Y0, X2)), Y2) -> meet(Y0, meet(join(X1, X2), Y2)) % 4.42/4.60 meet(join(xx, Y1), yy) -> join(xx, meet(Y1, yy)) % 4.42/4.60 meet(meet(X, Y), Z) -> meet(X, meet(Y, Z)) % 4.42/4.60 true__ -> false__ % 4.42/4.60 with the LPO induced by % 4.42/4.60 zz > f1 > yy > xx > meet > join > true__ > false__ % 4.42/4.60 % 4.42/4.60 % SZS output end Proof % 4.42/4.60 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