%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT008-1 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n004.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 06:04:05 EDT 2022 % Result : Unsatisfiable 11.36s 11.46s % Output : Proof 11.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : LAT008-1 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Thu Jun 30 06:19:08 EDT 2022 % 0.13/0.35 % CPUTime : % 11.36/11.46 % SZS status Unsatisfiable % 11.36/11.46 % SZS output start Proof % 11.36/11.46 The input problem is unsatisfiable because % 11.36/11.46 % 11.36/11.46 [1] the following set of Horn clauses is unsatisfiable: % 11.36/11.46 % 11.36/11.46 meet(X, join(X, Y)) = X % 11.36/11.46 meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X)) % 11.36/11.46 join(a, meet(a, b)) = a ==> \bottom % 11.36/11.46 % 11.36/11.46 This holds because % 11.36/11.46 % 11.36/11.46 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 11.36/11.46 % 11.36/11.46 E: % 11.36/11.46 f1(a) = false__ % 11.36/11.46 f1(join(a, meet(a, b))) = true__ % 11.36/11.46 meet(X, join(X, Y)) = X % 11.36/11.46 meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X)) % 11.36/11.46 G: % 11.36/11.46 true__ = false__ % 11.36/11.46 % 11.36/11.46 This holds because % 11.36/11.46 % 11.36/11.46 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 11.36/11.46 % 11.36/11.46 join(Y0, meet(Y2, join(Y0, X1))) = meet(join(Y0, X1), join(Y2, Y0)) % 11.36/11.46 join(Y0, meet(Y2, meet(join(Y0, X1), join(X2, Y0)))) = meet(meet(join(Y0, X1), join(X2, Y0)), join(Y2, Y0)) % 11.36/11.46 join(Y1, Y0) = join(Y0, Y1) % 11.36/11.46 join(join(X0, X0), meet(Y2, join(X0, X0))) = meet(join(X0, X0), join(Y2, join(X0, X1))) % 11.36/11.46 join(join(X0, X0), meet(Y2, join(X0, X0))) = meet(join(X0, X0), join(Y2, join(join(X0, X0), X1))) % 11.36/11.46 join(join(X0, X0), meet(Y2, join(join(X0, X1), X2))) = meet(join(join(X0, X1), X2), join(Y2, join(X0, X0))) % 11.36/11.46 join(join(meet(X2, Y0), meet(X1, Y0)), meet(Y2, join(X1, X2))) = meet(join(X1, X2), join(Y2, Y0)) % 11.36/11.46 join(join(meet(X2, Y0), meet(X1, Y0)), meet(Y2, join(X1, X2))) = meet(join(X1, X2), join(Y2, meet(Y0, join(X1, X2)))) % 11.36/11.46 join(join(meet(X2, Y0), meet(X1, Y0)), meet(Y2, join(X1, X2))) = meet(join(X1, X2), join(meet(Y2, join(X1, X2)), Y0)) % 11.36/11.46 join(meet(X0, X1), meet(Y1, meet(X1, join(X2, X0)))) = meet(join(meet(X0, X1), meet(X2, X1)), join(Y1, meet(X0, X1))) % 11.36/11.46 join(meet(X0, X1), meet(Y2, meet(X1, join(X2, X0)))) = meet(meet(X1, join(X2, X0)), join(Y2, meet(X0, X1))) % 11.36/11.46 join(meet(X0, Y1), meet(Y2, Y1)) = meet(Y1, join(Y2, meet(X0, Y1))) % 11.36/11.46 join(meet(Y0, Y0), meet(Y2, join(X1, Y0))) = meet(join(X1, Y0), join(Y2, Y0)) % 11.36/11.46 join(meet(Y0, Y1), meet(X0, Y1)) = meet(Y1, join(meet(X0, Y1), Y0)) % 11.36/11.46 join(meet(Y0, Y1), meet(X0, Y1)) = meet(Y1, join(meet(X0, Y1), meet(Y0, Y1))) % 11.36/11.46 join(meet(Y0, join(X0, X0)), join(X0, X0)) = meet(join(X0, X0), join(join(X0, X1), Y0)) % 11.36/11.46 join(meet(Y0, join(X0, X0)), join(X0, X0)) = meet(join(X0, X0), join(join(X0, X1), meet(Y0, join(X0, X0)))) % 11.36/11.46 join(meet(Y0, join(X1, X2)), join(meet(X2, Y2), meet(X1, Y2))) = meet(join(X1, X2), join(Y2, Y0)) % 11.36/11.46 join(meet(Y0, join(X1, X2)), join(meet(X2, Y2), meet(X1, Y2))) = meet(join(X1, X2), join(Y2, meet(Y0, join(X1, X2)))) % 11.36/11.46 join(meet(Y0, join(X1, X2)), join(meet(X2, Y2), meet(X1, Y2))) = meet(join(X1, X2), join(meet(Y2, join(X1, X2)), Y0)) % 11.36/11.46 join(meet(Y0, join(X1, X2)), meet(Y2, join(X1, meet(X2, Y0)))) = meet(join(X1, meet(X2, Y0)), join(Y2, Y0)) % 11.36/11.46 join(meet(Y0, join(X1, X2)), meet(Y2, join(meet(X1, Y0), X2))) = meet(join(meet(X1, Y0), X2), join(Y2, Y0)) % 11.36/11.46 join(meet(Y0, meet(X1, join(X2, X0))), meet(X0, X1)) = meet(meet(X1, join(X2, X0)), join(meet(X0, X1), Y0)) % 11.36/11.46 join(meet(Y1, Y0), meet(Y2, Y1)) = meet(Y1, join(Y2, Y0)) % 11.36/11.46 meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X)) % 11.36/11.46 meet(Y0, meet(Y0, join(Y2, X0))) = meet(Y0, join(X0, Y2)) % 11.36/11.46 meet(Y1, X0) = meet(X0, Y1) % 11.36/11.46 meet(join(X0, X0), join(Y1, join(X0, X0))) = meet(join(X0, X0), join(Y1, join(X0, X1))) % 11.36/11.46 meet(join(X1, X1), join(X0, X0)) = meet(join(X0, X0), join(X1, X1)) % 11.36/11.46 meet(join(X1, X1), join(join(X0, X0), meet(join(X0, X0), join(X1, X1)))) = meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(join(Y1, Y2), Y0) = join(meet(Y2, Y0), meet(Y1, Y0)) % 11.36/11.46 meet(join(Y1, Y2), Y0) = meet(Y0, join(Y2, Y1)) % 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(X1, join(X0, X0))) = meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(X1, join(X0, meet(X0, X1)))) = meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 meet(meet(X0, join(Y1, Y2)), meet(X0, join(Y1, Y2))) = meet(meet(X0, join(Y1, Y2)), join(Y2, Y1)) % 11.36/11.46 meet(meet(X2, X1), meet(X1, join(X2, X0))) = meet(meet(X2, X1), meet(X2, X1)) % 11.36/11.46 f1(a) -> false__ % 11.36/11.46 f1(join(a, meet(a, b))) -> true__ % 11.36/11.46 join(Y0, Y0) -> Y0 % 11.36/11.46 join(Y0, join(X1, Y0)) -> join(X1, Y0) % 11.36/11.46 join(Y0, join(Y0, Y1)) -> join(Y0, Y1) % 11.36/11.46 join(Y0, join(meet(Y2, Y1), meet(Y0, Y1))) -> meet(join(Y0, Y2), join(Y1, Y0)) % 11.36/11.46 join(Y0, meet(Y0, Y1)) -> Y0 % 11.36/11.46 join(Y0, meet(Y1, Y0)) -> Y0 % 11.36/11.46 join(Y0, meet(join(Y0, X1), join(X2, Y0))) -> meet(join(Y0, X1), join(X2, Y0)) % 11.36/11.46 join(Y0, meet(join(Y0, X1), join(Y0, join(Y0, X1)))) -> join(Y0, X1) % 11.36/11.46 join(Y0, meet(join(Y0, Y1), join(Y0, Y1))) -> join(Y0, Y1) % 11.36/11.46 join(Y1, join(Y1, Y1)) -> join(Y1, Y1) % 11.36/11.46 join(join(X0, X0), join(join(X0, X1), join(X0, X1))) -> join(join(X0, X1), join(X0, X1)) % 11.36/11.46 join(join(X0, X1), join(X1, X0)) -> join(X1, X0) % 11.36/11.46 join(join(X0, X1), meet(Y1, join(X1, X0))) -> join(X0, X1) % 11.36/11.46 join(join(X1, X0), join(X0, X1)) -> join(X1, X0) % 11.36/11.46 join(join(X1, Y1), Y1) -> join(X1, Y1) % 11.36/11.46 join(join(Y1, X1), Y1) -> join(Y1, X1) % 11.36/11.46 join(join(Y1, Y1), join(Y1, Y1)) -> join(Y1, Y1) % 11.36/11.46 join(meet(X0, X1), meet(X1, join(X0, X0))) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 join(meet(X0, X1), meet(X1, join(X0, meet(X0, X1)))) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 join(meet(X0, X1), meet(join(meet(X0, X1), meet(X2, X1)), meet(X1, join(X2, X0)))) -> join(meet(X0, X1), meet(X2, X1)) % 11.36/11.46 join(meet(X0, X1), meet(meet(X1, join(X2, X0)), join(meet(X0, X1), meet(X2, X1)))) -> join(meet(X0, X1), meet(X2, X1)) % 11.36/11.46 join(meet(X1, join(X0, meet(X0, X1))), meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 join(meet(Y0, Y1), Y1) -> Y1 % 11.36/11.46 join(meet(Y0, join(X0, X0)), join(X0, X0)) -> join(X0, X0) % 11.36/11.46 join(meet(Y0, join(X1, Y2)), meet(Y2, Y2)) -> meet(join(X1, Y2), join(Y2, Y0)) % 11.36/11.46 join(meet(Y0, join(X1, meet(X2, Y2))), meet(Y2, join(X1, X2))) -> meet(join(X1, meet(X2, Y2)), join(Y2, Y0)) % 11.36/11.46 join(meet(Y0, join(Y2, X1)), Y2) -> meet(join(Y2, X1), join(Y2, Y0)) % 11.36/11.46 join(meet(Y0, join(join(X0, X1), X2)), join(X0, X0)) -> meet(join(join(X0, X1), X2), join(join(X0, X0), Y0)) % 11.36/11.46 join(meet(Y0, meet(X1, join(X0, X0))), meet(X1, join(meet(X0, X1), X0))) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 join(meet(Y0, meet(X1, join(meet(X0, X1), X0))), meet(X1, join(X0, X0))) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 join(meet(Y0, meet(join(Y2, X1), join(X2, Y2))), Y2) -> meet(meet(join(Y2, X1), join(X2, Y2)), join(Y2, Y0)) % 11.36/11.46 join(meet(Y1, Y0), Y1) -> Y1 % 11.36/11.46 join(meet(Y2, Y0), meet(Y1, Y0)) -> meet(Y0, join(Y2, Y1)) % 11.36/11.46 join(meet(Y2, Y2), meet(Y1, Y2)) -> meet(Y2, Y2) % 11.36/11.46 join(meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))), meet(X1, join(X0, meet(X0, X1)))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 join(meet(join(X1, X1), Y0), meet(meet(X0, join(X1, X1)), Y0)) -> meet(Y0, join(X1, X1)) % 11.36/11.46 join(meet(join(Y1, X1), join(X2, Y1)), Y1) -> meet(join(Y1, X1), join(X2, Y1)) % 11.36/11.46 join(meet(meet(X2, X1), Y0), meet(meet(X0, X1), Y0)) -> meet(Y0, meet(X1, join(X2, X0))) % 11.36/11.46 meet(X, join(X, Y)) -> X % 11.36/11.46 meet(X1, join(meet(X0, X1), X0)) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(Y0, Y0) -> Y0 % 11.36/11.46 meet(Y0, join(join(Y1, Y1), Y1)) -> meet(Y0, join(Y1, Y1)) % 11.36/11.46 meet(Y0, meet(X1, join(X2, meet(X0, X1)))) -> meet(Y0, meet(X1, join(X2, X0))) % 11.36/11.46 meet(Y0, meet(X1, join(meet(X2, X1), X0))) -> meet(Y0, meet(X1, join(X2, X0))) % 11.36/11.46 meet(Y0, meet(Y0, Y0)) -> Y0 % 11.36/11.46 meet(Y0, meet(Y0, Y2)) -> meet(Y0, Y2) % 11.36/11.46 meet(Y0, meet(join(Y0, X1), join(Y2, Y0))) -> Y0 % 11.36/11.46 meet(Y0, meet(join(Y0, Y1), Y0)) -> Y0 % 11.36/11.46 meet(Y0, meet(join(Y0, Y1), join(Y0, Y2))) -> Y0 % 11.36/11.46 meet(Y0, meet(join(Y0, Y1), meet(join(Y0, Y1), join(Y0, Y2)))) -> Y0 % 11.36/11.46 meet(Y0, meet(join(Y1, Y0), join(Y2, Y0))) -> Y0 % 11.36/11.46 meet(Y0, meet(join(Y1, Y1), join(Y0, Y1))) -> meet(Y0, join(Y1, Y1)) % 11.36/11.46 meet(Y0, meet(join(Y2, Y0), join(Y0, Y1))) -> Y0 % 11.36/11.46 meet(Y0, meet(meet(join(Y0, X1), join(X2, Y0)), join(Y2, Y0))) -> Y0 % 11.36/11.46 meet(Y1, join(Y2, Y1)) -> meet(Y1, Y1) % 11.36/11.46 meet(Y1, join(Y2, meet(Y0, Y1))) -> meet(Y1, join(Y2, Y0)) % 11.36/11.46 meet(Y1, join(meet(Y2, Y1), Y0)) -> meet(Y1, join(Y2, Y0)) % 11.36/11.46 meet(Y1, meet(X0, Y1)) -> meet(X0, Y1) % 11.36/11.46 meet(Y1, meet(Y1, join(Y2, Y1))) -> Y1 % 11.36/11.46 meet(join(X0, X0), join(join(X0, X1), Y0)) -> join(X0, X0) % 11.36/11.46 meet(join(X0, X0), join(join(X0, X1), meet(Y0, join(X0, X0)))) -> join(X0, X0) % 11.36/11.46 meet(join(X0, X0), join(join(X1, meet(X1, join(X0, X0))), meet(join(X1, meet(X1, join(X0, X0))), join(X0, X0)))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(join(X0, X0), join(join(join(X0, X0), Y1), Y2)) -> join(X0, X0) % 11.36/11.46 meet(join(X0, X0), meet(join(X0, X0), join(Y2, join(X0, X1)))) -> join(X0, X0) % 11.36/11.46 meet(join(X0, X0), meet(join(X0, X0), join(Y2, join(join(X0, X0), X1)))) -> join(X0, X0) % 11.36/11.46 meet(join(X0, X0), meet(join(join(X0, X1), X2), join(Y2, join(X0, X0)))) -> join(X0, X0) % 11.36/11.46 meet(join(X0, meet(X2, join(X0, X1))), join(X2, X0)) -> meet(join(X0, X1), join(X2, X0)) % 11.36/11.46 meet(join(X1, X1), join(join(meet(X0, X1), X0), meet(join(meet(X0, X1), X0), join(X1, X1)))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(join(X1, X2), join(Y1, join(meet(X2, Y2), meet(X1, Y2)))) -> meet(join(X1, X2), join(Y1, Y2)) % 11.36/11.46 meet(join(X1, X2), join(join(meet(X2, Y1), meet(X1, Y1)), Y2)) -> meet(join(X1, X2), join(Y1, Y2)) % 11.36/11.46 meet(join(X1, Y0), Y0) -> Y0 % 11.36/11.46 meet(join(Y0, Y1), Y0) -> Y0 % 11.36/11.46 meet(join(Y0, Y2), join(Y0, Y0)) -> join(Y0, Y0) % 11.36/11.46 meet(join(Y1, Y2), join(Y2, Y1)) -> join(Y1, Y2) % 11.36/11.46 meet(join(Y2, X1), join(Y2, meet(Y0, join(Y2, X1)))) -> meet(join(Y2, X1), join(Y2, Y0)) % 11.36/11.46 meet(join(Y2, Y2), meet(join(join(Y2, Y2), Y1), join(Y2, Y2))) -> join(Y2, Y2) % 11.36/11.46 meet(join(join(X0, X0), Y1), join(X0, X0)) -> join(X0, X0) % 11.36/11.46 meet(join(meet(X0, X1), X0), join(X1, meet(X0, X1))) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(X1, join(X0, X0))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(join(X0, X0), join(X1, X1))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(join(meet(X1, join(X0, X0)), Y1), meet(X1, join(X0, X0))) -> meet(join(X0, X0), join(X1, X1)) % 11.36/11.46 meet(join(meet(X1, join(X0, X0)), Y1), meet(join(X0, X0), join(X1, X1))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), join(X1, X2)) -> meet(Y0, join(X1, X2)) % 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), join(X1, meet(X2, Y0))) -> meet(Y0, join(X1, meet(X2, Y0))) % 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), join(meet(X1, Y0), X2)) -> meet(Y0, join(meet(X1, Y0), X2)) % 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), meet(join(X1, X2), join(Y2, Y0))) -> meet(Y0, join(X1, X2)) % 11.36/11.46 meet(join(meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))), Y1), meet(X1, join(X0, X0))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))) % 11.36/11.46 meet(meet(X0, X1), meet(X1, join(X2, X0))) -> meet(X0, X1) % 11.36/11.46 meet(meet(X0, X1), meet(meet(X1, join(X2, X0)), join(Y2, meet(X0, X1)))) -> meet(X0, X1) % 11.36/11.46 meet(meet(X0, X1), meet(meet(X1, join(X2, meet(X0, X1))), join(Y2, meet(X0, X1)))) -> meet(X0, X1) % 11.36/11.46 meet(meet(X0, Y1), meet(Y1, join(Y2, meet(X0, Y1)))) -> meet(X0, Y1) % 11.36/11.46 meet(meet(X0, Y1), meet(Y1, meet(X0, Y1))) -> meet(X0, Y1) % 11.36/11.46 meet(meet(X0, join(Y1, Y2)), join(Y2, Y1)) -> meet(X0, join(Y1, Y2)) % 11.36/11.46 meet(meet(X1, X0), meet(join(meet(X1, X0), Y1), X0)) -> meet(X1, X0) % 11.36/11.46 meet(meet(X1, join(X0, X0)), join(join(meet(X0, X1), Y1), Y2)) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 meet(meet(X1, join(X2, X0)), meet(X1, join(meet(X0, X1), X0))) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 meet(meet(X1, join(X2, meet(X0, X1))), meet(X1, join(meet(X0, X1), X0))) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 meet(meet(X1, join(meet(X0, X1), X0)), join(meet(X1, join(X2, X0)), Y2)) -> meet(X1, join(meet(X0, X1), X0)) % 11.36/11.46 meet(meet(X2, X1), meet(join(meet(X2, X1), Y1), meet(X1, join(X2, X0)))) -> meet(X2, X1) % 11.36/11.46 meet(meet(X2, X1), meet(join(meet(X2, X1), Y1), meet(X1, join(meet(X2, X1), X0)))) -> meet(X2, X1) % 11.36/11.46 meet(meet(Y0, Y0), join(X1, Y0)) -> meet(Y0, Y0) % 11.36/11.46 meet(meet(Y0, Y2), Y2) -> meet(Y0, Y2) % 11.36/11.46 meet(meet(Y0, join(X1, X2)), join(X1, meet(X2, Y0))) -> meet(Y0, join(X1, X2)) % 11.36/11.46 meet(meet(Y0, join(X1, X2)), join(meet(X1, Y0), X2)) -> meet(Y0, join(X1, X2)) % 11.36/11.46 meet(meet(Y0, join(X1, X2)), meet(join(X1, meet(X2, Y0)), join(Y2, Y0))) -> meet(Y0, join(X1, X2)) % 11.36/11.46 meet(meet(Y0, join(X2, X1)), meet(Y0, join(X1, X2))) -> meet(Y0, meet(Y0, join(X1, X2))) % 11.36/11.46 meet(meet(Y0, join(join(Y0, Y0), X1)), join(Y0, Y0)) -> meet(Y0, join(join(Y0, Y0), X1)) % 11.36/11.46 meet(meet(Y0, meet(Y0, join(X2, X1))), join(X1, X2)) -> meet(Y0, join(X1, X2)) % 11.36/11.46 meet(meet(Y1, X1), meet(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1) % 11.36/11.46 meet(meet(Y2, X1), meet(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1) % 11.36/11.46 meet(meet(join(X0, X0), join(join(X1, X1), meet(join(X1, X1), join(X0, X0)))), join(join(X1, X1), Y2)) -> meet(join(X0, X0), join(join(X1, X1), meet(join(X1, X1), join(X0, X0)))) % 11.36/11.46 meet(meet(join(X1, X1), join(X0, X0)), join(X1, X1)) -> meet(join(X0, X0), join(X1, X1)) % 11.36/11.46 meet(meet(join(Y0, X2), join(X1, Y0)), join(Y0, Y0)) -> join(Y0, Y0) % 11.36/11.46 meet(meet(join(Y2, X1), join(X2, Y2)), join(Y2, meet(Y0, meet(join(Y2, X1), join(X2, Y2))))) -> meet(meet(join(Y2, X1), join(X2, Y2)), join(Y2, Y0)) % 11.36/11.46 meet(meet(join(Y2, X1), join(Y2, X1)), meet(join(meet(join(Y2, X1), join(Y2, X1)), Y1), join(Y2, X1))) -> meet(join(Y2, X1), join(Y2, X1)) % 11.36/11.46 meet(meet(join(Y2, Y2), Y1), meet(Y1, join(Y2, Y2))) -> meet(join(Y2, Y2), Y1) % 11.36/11.46 meet(meet(meet(X2, X1), Y1), meet(Y1, meet(X1, join(X2, X0)))) -> meet(meet(X2, X1), Y1) % 11.36/11.46 meet(meet(meet(join(Y2, X1), join(Y2, X1)), Y1), meet(Y1, join(Y2, X1))) -> meet(meet(join(Y2, X1), join(Y2, X1)), Y1) % 11.36/11.46 true__ -> false__ % 11.36/11.46 with the LPO induced by % 11.36/11.46 b > a > f1 > join > meet > true__ > false__ % 11.36/11.46 % 11.36/11.46 % SZS output end Proof % 11.36/11.46 %------------------------------------------------------------------------------