%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT040-1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n006.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 06:04:17 EDT 2022 % Result : Unsatisfiable 15.70s 15.79s % Output : Proof 15.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : LAT040-1 : TPTP v8.1.0. Released v2.4.0. % 0.10/0.13 % Command : moca.sh %s % 0.13/0.33 % Computer : n006.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 : Wed Jun 29 17:35:38 EDT 2022 % 0.13/0.34 % CPUTime : % 15.70/15.79 % SZS status Unsatisfiable % 15.70/15.79 % SZS output start Proof % 15.70/15.79 The input problem is unsatisfiable because % 15.70/15.79 % 15.70/15.79 [1] the following set of Horn clauses is unsatisfiable: % 15.70/15.79 % 15.70/15.79 meet(X, X) = X % 15.70/15.79 join(X, X) = X % 15.70/15.79 meet(X, join(X, Y)) = X % 15.70/15.79 join(X, meet(X, Y)) = X % 15.70/15.79 meet(X, Y) = meet(Y, X) % 15.70/15.79 join(X, Y) = join(Y, X) % 15.70/15.79 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 15.70/15.79 join(join(X, Y), Z) = join(X, join(Y, Z)) % 15.70/15.79 join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)) % 15.70/15.79 meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)) % 15.70/15.79 join(xx, yy) = join(xx, zz) % 15.70/15.79 meet(xx, yy) = meet(xx, zz) % 15.70/15.79 yy = zz ==> \bottom % 15.70/15.79 % 15.70/15.79 This holds because % 15.70/15.79 % 15.70/15.79 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 15.70/15.79 % 15.70/15.79 E: % 15.70/15.79 f1(yy) = true__ % 15.70/15.79 f1(zz) = false__ % 15.70/15.79 join(X, X) = X % 15.70/15.79 join(X, Y) = join(Y, X) % 15.70/15.79 join(X, meet(X, Y)) = X % 15.70/15.79 join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)) % 15.70/15.79 join(join(X, Y), Z) = join(X, join(Y, Z)) % 15.70/15.79 join(xx, yy) = join(xx, zz) % 15.70/15.79 meet(X, X) = X % 15.70/15.79 meet(X, Y) = meet(Y, X) % 15.70/15.79 meet(X, join(X, Y)) = X % 15.70/15.79 meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)) % 15.70/15.79 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 15.70/15.79 meet(xx, yy) = meet(xx, zz) % 15.70/15.79 G: % 15.70/15.79 true__ = false__ % 15.70/15.79 % 15.70/15.79 This holds because % 15.70/15.79 % 15.70/15.79 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 15.70/15.79 % 15.70/15.79 join(X, Y) = join(Y, X) % 15.70/15.79 join(Y0, Y1) = join(Y1, join(meet(Y1, X1), Y0)) % 15.70/15.79 join(Y0, join(Y2, Y1)) = join(Y1, join(Y2, Y0)) % 15.70/15.79 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 15.70/15.79 meet(X, Y) = meet(Y, X) % 15.70/15.79 meet(Y0, Y1) = meet(Y1, meet(join(X1, Y1), Y0)) % 15.70/15.79 meet(Y0, meet(Y2, Y1)) = meet(Y1, meet(Y2, Y0)) % 15.70/15.79 meet(Y0, meet(Y2, Y1)) = meet(Y2, meet(Y0, Y1)) % 15.70/15.79 meet(Y0, meet(yy, xx)) = meet(xx, meet(Y0, yy)) % 15.70/15.79 meet(Y0, meet(yy, xx)) = meet(xx, meet(yy, Y0)) % 15.70/15.79 meet(Y0, meet(yy, xx)) = meet(yy, meet(xx, Y0)) % 15.70/15.79 meet(Y2, meet(Y0, Y1)) = meet(Y0, meet(Y1, Y2)) % 15.70/15.79 f1(yy) -> true__ % 15.70/15.79 f1(zz) -> false__ % 15.70/15.79 false__ -> true__ % 15.70/15.79 join(X, X) -> X % 15.70/15.79 join(X, meet(X, Y)) -> X % 15.70/15.79 join(Y0, join(Y1, Y0)) -> join(Y0, Y1) % 15.70/15.79 join(Y0, meet(X1, meet(X2, Y0))) -> Y0 % 15.70/15.79 join(Y0, meet(Y1, Y0)) -> Y0 % 15.70/15.79 join(Y0, meet(Y1, meet(X1, meet(X2, Y0)))) -> Y0 % 15.70/15.79 join(Y0, meet(Y2, meet(Y0, Y1))) -> Y0 % 15.70/15.79 join(Y1, join(Y1, Y2)) -> join(Y1, Y2) % 15.70/15.79 join(join(X, Y), Z) -> join(X, join(Y, Z)) % 15.70/15.79 join(meet(X1, X2), meet(X1, meet(X2, Y1))) -> meet(X1, X2) % 15.70/15.79 join(meet(X1, X2), meet(X1, meet(Y1, X2))) -> meet(X1, X2) % 15.70/15.79 join(meet(X1, X2), meet(X2, meet(X1, Y1))) -> meet(X1, X2) % 15.70/15.79 join(meet(X1, X2), meet(Y1, meet(X1, meet(X2, Y2)))) -> meet(X1, X2) % 15.70/15.79 join(meet(X1, X2), meet(Y1, meet(X2, meet(X1, Y2)))) -> meet(X1, X2) % 15.70/15.79 join(meet(zz, xx), yy) -> yy % 15.70/15.79 join(xx, join(zz, yy)) -> join(yy, xx) % 15.70/15.79 meet(X, X) -> X % 15.70/15.79 meet(X, join(Y, Z)) -> join(meet(X, Y), meet(X, Z)) % 15.70/15.79 meet(Y0, join(Y1, Y0)) -> Y0 % 15.70/15.79 meet(Y0, meet(Y1, meet(Y0, Y1))) -> meet(Y0, Y1) % 15.70/15.79 meet(Y0, meet(join(Y0, Y2), join(Y0, Y1))) -> Y0 % 15.70/15.79 meet(Y1, meet(Y1, Y2)) -> meet(Y1, Y2) % 15.70/15.79 meet(join(X, Y), join(X, Z)) -> join(X, meet(Y, Z)) % 15.70/15.79 meet(join(X1, join(Y2, Y1)), join(Y2, X1)) -> join(X1, Y2) % 15.70/15.79 meet(join(Y2, X1), join(Y2, join(X1, Y1))) -> join(Y2, X1) % 15.70/15.79 meet(join(yy, zz), meet(join(yy, xx), join(zz, Y0))) -> yy % 15.70/15.79 meet(meet(X, Y), Z) -> meet(X, meet(Y, Z)) % 15.70/15.79 meet(xx, meet(join(yy, xx), join(xx, Y1))) -> xx % 15.70/15.79 meet(zz, meet(X0, meet(yy, xx))) -> meet(X0, meet(yy, xx)) % 15.70/15.79 zz -> yy % 15.70/15.79 with the LPO induced by % 15.70/15.79 meet > zz > yy > xx > join > f1 > false__ > true__ % 15.70/15.79 % 15.70/15.79 % SZS output end Proof % 15.70/15.79 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