%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0. % 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 06:04:12 EDT 2022 % Result : Unsatisfiable 45.32s 45.39s % Output : Proof 45.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n029.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 29 23:59:38 EDT 2022 % 0.13/0.34 % CPUTime : % 45.32/45.39 % SZS status Unsatisfiable % 45.32/45.39 % SZS output start Proof % 45.32/45.39 The input problem is unsatisfiable because % 45.32/45.39 % 45.32/45.39 [1] the following set of Horn clauses is unsatisfiable: % 45.32/45.39 % 45.32/45.39 meet(X, X) = X % 45.32/45.39 join(X, X) = X % 45.32/45.39 meet(X, Y) = meet(Y, X) % 45.32/45.39 join(X, Y) = join(Y, X) % 45.32/45.39 meet(meet(join(X, Y), join(Z, Y)), Y) = Y % 45.32/45.39 join(join(meet(X, Y), meet(Z, Y)), Y) = Y % 45.32/45.39 meet2(X, X) = X % 45.32/45.39 meet2(X, Y) = meet2(Y, X) % 45.32/45.39 meet2(meet2(join(X, Y), join(Z, Y)), Y) = Y % 45.32/45.39 join(join(meet2(X, Y), meet2(Z, Y)), Y) = Y % 45.32/45.39 meet(a, b) = meet2(a, b) ==> \bottom % 45.32/45.39 % 45.32/45.39 This holds because % 45.32/45.39 % 45.32/45.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 45.32/45.39 % 45.32/45.39 E: % 45.32/45.39 f1(meet(a, b)) = true__ % 45.32/45.39 f1(meet2(a, b)) = false__ % 45.32/45.39 join(X, X) = X % 45.32/45.39 join(X, Y) = join(Y, X) % 45.32/45.39 join(join(meet(X, Y), meet(Z, Y)), Y) = Y % 45.32/45.39 join(join(meet2(X, Y), meet2(Z, Y)), Y) = Y % 45.32/45.39 meet(X, X) = X % 45.32/45.39 meet(X, Y) = meet(Y, X) % 45.32/45.39 meet(meet(join(X, Y), join(Z, Y)), Y) = Y % 45.32/45.39 meet2(X, X) = X % 45.32/45.39 meet2(X, Y) = meet2(Y, X) % 45.32/45.39 meet2(meet2(join(X, Y), join(Z, Y)), Y) = Y % 45.32/45.39 G: % 45.32/45.39 true__ = false__ % 45.32/45.39 % 45.32/45.39 This holds because % 45.32/45.39 % 45.32/45.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 45.32/45.39 % 45.32/45.39 join(X, Y) = join(Y, X) % 45.32/45.39 join(meet(Y0, Y1), meet2(Y0, Y1)) = meet2(Y1, Y0) % 45.32/45.39 meet(X, Y) = meet(Y, X) % 45.32/45.39 meet2(X, Y) = meet2(Y, X) % 45.32/45.39 meet2(Y0, meet2(Y0, Y1)) = meet2(Y1, Y0) % 45.32/45.39 f1(meet(a, b)) -> true__ % 45.32/45.39 f1(meet2(a, b)) -> false__ % 45.32/45.39 join(X, X) -> X % 45.32/45.39 join(Y0, join(Y0, meet(Y0, Y1))) -> Y0 % 45.32/45.39 join(Y0, join(meet(Y0, Y1), meet(Y0, Y2))) -> Y0 % 45.32/45.39 join(Y0, join(meet(Y0, Y1), meet2(Y0, Y2))) -> Y0 % 45.32/45.39 join(Y0, join(meet(Y0, Y1), meet2(Y2, Y0))) -> Y0 % 45.32/45.39 join(Y0, join(meet(Y1, Y0), meet2(X1, Y0))) -> Y0 % 45.32/45.39 join(Y0, join(meet(Y1, Y0), meet2(Y0, Y2))) -> Y0 % 45.32/45.39 join(Y0, join(meet2(X1, Y0), meet(Y2, Y0))) -> Y0 % 45.32/45.39 join(Y0, join(meet2(Y0, Y1), meet(Y0, Y2))) -> Y0 % 45.32/45.39 join(Y0, join(meet2(Y0, Y1), meet(Y2, Y0))) -> Y0 % 45.32/45.39 join(Y0, join(meet2(Y0, Y1), meet2(Y0, Y2))) -> Y0 % 45.32/45.39 join(Y0, join(meet2(Y1, Y0), meet(Y0, Y2))) -> Y0 % 45.32/45.39 join(Y0, meet(Y0, Y1)) -> Y0 % 45.32/45.39 join(Y0, meet2(Y0, Y1)) -> Y0 % 45.32/45.39 join(Y1, join(X1, Y1)) -> join(X1, Y1) % 45.32/45.39 join(Y1, join(Y1, X1)) -> join(Y1, X1) % 45.32/45.39 join(Y1, join(Y1, meet(Y2, Y1))) -> Y1 % 45.32/45.39 join(Y1, join(meet(Y0, Y1), meet(Y1, Y2))) -> Y1 % 45.32/45.39 join(Y1, join(meet(Y0, Y1), meet(Y2, Y1))) -> Y1 % 45.32/45.39 join(Y1, join(meet(Y1, Y0), meet(Y2, Y1))) -> Y1 % 45.32/45.39 join(Y1, join(meet2(Y0, Y1), meet2(Y1, Y2))) -> Y1 % 45.32/45.39 join(Y1, join(meet2(Y0, Y1), meet2(Y2, Y1))) -> Y1 % 45.32/45.39 join(Y1, join(meet2(Y1, Y0), meet2(Y2, Y1))) -> Y1 % 45.32/45.39 join(Y1, meet(Y2, Y1)) -> Y1 % 45.32/45.39 join(Y1, meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1)) % 45.32/45.39 join(Y1, meet(join(X1, Y1), join(Y1, X2))) -> meet(join(X1, Y1), join(Y1, X2)) % 45.32/45.39 join(Y1, meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1)) % 45.32/45.39 join(Y1, meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2)) % 45.32/45.39 join(Y1, meet2(Y2, Y1)) -> Y1 % 45.32/45.39 join(Y1, meet2(join(X0, Y1), join(X2, Y1))) -> meet2(join(X0, Y1), join(X2, Y1)) % 45.32/45.39 join(Y1, meet2(join(X1, Y1), join(Y1, X2))) -> meet2(join(X1, Y1), join(Y1, X2)) % 45.32/45.39 join(Y1, meet2(join(Y1, X1), join(X2, Y1))) -> meet2(join(Y1, X1), join(X2, Y1)) % 45.32/45.39 join(Y1, meet2(join(Y1, X1), join(Y1, X2))) -> meet2(join(Y1, X1), join(Y1, X2)) % 45.32/45.39 join(join(X1, Y0), join(Y0, meet(Y2, join(X1, Y0)))) -> join(X1, Y0) % 45.32/45.39 join(join(X1, Y0), join(Y0, meet2(Y2, join(X1, Y0)))) -> join(X1, Y0) % 45.32/45.39 join(join(X1, Y2), join(Y2, meet(join(X1, Y2), Y1))) -> join(X1, Y2) % 45.32/45.39 join(join(X1, Y2), join(Y2, meet2(join(X1, Y2), Y1))) -> join(X1, Y2) % 45.32/45.39 join(join(Y0, X1), join(Y0, meet(Y2, join(Y0, X1)))) -> join(Y0, X1) % 45.32/45.39 join(join(Y0, X1), join(Y0, meet2(Y2, join(Y0, X1)))) -> join(Y0, X1) % 45.32/45.39 join(join(Y2, X1), join(Y2, meet(join(Y2, X1), Y1))) -> join(Y2, X1) % 45.32/45.39 join(join(Y2, X1), join(Y2, meet2(join(Y2, X1), Y1))) -> join(Y2, X1) % 45.32/45.39 join(join(meet(X, Y), meet(Z, Y)), Y) -> Y % 45.32/45.39 join(join(meet2(X, Y), meet2(Z, Y)), Y) -> Y % 45.32/45.39 join(meet(X0, X1), meet(X0, join(X2, meet(X0, X1)))) -> meet(X0, join(X2, meet(X0, X1))) % 45.32/45.39 join(meet(X0, X1), meet(X1, join(X2, meet(X0, X1)))) -> meet(X1, join(X2, meet(X0, X1))) % 45.32/45.39 join(meet(X0, X1), meet(X1, join(meet(X0, X1), X2))) -> meet(X1, join(meet(X0, X1), X2)) % 45.32/45.39 join(meet(X0, X1), meet2(X1, X0)) -> meet2(X1, X0) % 45.32/45.39 join(meet(X0, X1), meet2(X1, join(X2, meet(X0, X1)))) -> meet2(X1, join(X2, meet(X0, X1))) % 45.32/45.39 join(meet(X1, X0), meet(X1, join(meet(X1, X0), X2))) -> meet(X1, join(meet(X1, X0), X2)) % 45.32/45.39 join(meet(X1, join(X2, meet(X0, X1))), join(meet(X0, X1), meet(Y2, meet(X1, join(X2, meet(X0, X1)))))) -> meet(X1, join(X2, meet(X0, X1))) % 45.32/45.39 join(meet(X1, join(X2, meet(X1, X0))), join(meet(X1, X0), meet(Y2, meet(X1, join(X2, meet(X1, X0)))))) -> meet(X1, join(X2, meet(X1, X0))) % 45.32/45.39 join(meet(Y1, Y0), meet2(Y1, Y0)) -> meet2(Y1, Y0) % 45.32/45.39 join(meet(join(X0, Y1), join(X2, Y1)), join(Y1, meet(Y2, meet(join(X0, Y1), join(X2, Y1))))) -> meet(join(X0, Y1), join(X2, Y1)) % 45.32/45.39 join(meet(join(X0, Y2), join(X2, Y2)), join(Y2, meet2(Y1, meet(join(X0, Y2), join(X2, Y2))))) -> meet(join(X0, Y2), join(X2, Y2)) % 45.32/45.39 join(meet(join(X1, Y0), join(Y0, X2)), join(Y0, meet(Y2, meet(join(X1, Y0), join(Y0, X2))))) -> meet(join(X1, Y0), join(Y0, X2)) % 45.32/45.39 join(meet(join(X1, Y2), join(X2, Y2)), join(Y2, meet(meet(join(X1, Y2), join(X2, Y2)), Y1))) -> meet(join(X1, Y2), join(X2, Y2)) % 45.32/45.39 join(meet(join(X1, Y2), join(Y2, X2)), join(Y2, meet(meet(join(X1, Y2), join(Y2, X2)), Y1))) -> meet(join(X1, Y2), join(Y2, X2)) % 45.32/45.39 join(meet(join(Y0, X1), join(X2, Y0)), join(Y0, meet(Y2, meet(join(Y0, X1), join(X2, Y0))))) -> meet(join(Y0, X1), join(X2, Y0)) % 45.32/45.39 join(meet(join(Y0, X1), join(Y0, X2)), join(Y0, meet(Y2, meet(join(Y0, X1), join(Y0, X2))))) -> meet(join(Y0, X1), join(Y0, X2)) % 45.32/45.39 join(meet(join(Y2, X1), join(X2, Y2)), join(Y2, meet(meet(join(Y2, X1), join(X2, Y2)), Y1))) -> meet(join(Y2, X1), join(X2, Y2)) % 45.32/45.39 join(meet(join(Y2, X1), join(X2, Y2)), join(Y2, meet2(Y1, meet(join(Y2, X1), join(X2, Y2))))) -> meet(join(Y2, X1), join(X2, Y2)) % 45.32/45.39 join(meet(join(Y2, X1), join(Y2, X2)), join(Y2, meet(meet(join(Y2, X1), join(Y2, X2)), Y1))) -> meet(join(Y2, X1), join(Y2, X2)) % 45.32/45.39 join(meet2(X0, X1), meet(X1, join(X2, meet2(X0, X1)))) -> meet(X1, join(X2, meet2(X0, X1))) % 45.32/45.39 join(meet2(X0, X1), meet2(X1, join(X2, meet2(X0, X1)))) -> meet2(X1, join(X2, meet2(X0, X1))) % 45.32/45.39 join(meet2(join(X0, Y1), join(X2, Y1)), join(Y1, meet2(meet2(join(X0, Y1), join(X2, Y1)), Y2))) -> meet2(join(X0, Y1), join(X2, Y1)) % 45.32/45.39 join(meet2(join(X1, Y0), join(X2, Y0)), join(Y0, meet2(Y2, meet2(join(X1, Y0), join(X2, Y0))))) -> meet2(join(X1, Y0), join(X2, Y0)) % 45.32/45.39 join(meet2(join(X1, Y0), join(Y0, X2)), join(Y0, meet2(Y2, meet2(join(X1, Y0), join(Y0, X2))))) -> meet2(join(X1, Y0), join(Y0, X2)) % 45.32/45.39 join(meet2(join(X1, Y2), join(Y2, X2)), join(Y2, meet2(meet2(join(X1, Y2), join(Y2, X2)), Y1))) -> meet2(join(X1, Y2), join(Y2, X2)) % 45.32/45.39 join(meet2(join(Y0, X1), join(X2, Y0)), join(Y0, meet2(Y2, meet2(join(Y0, X1), join(X2, Y0))))) -> meet2(join(Y0, X1), join(X2, Y0)) % 45.32/45.39 join(meet2(join(Y0, X1), join(Y0, X2)), join(Y0, meet2(Y2, meet2(join(Y0, X1), join(Y0, X2))))) -> meet2(join(Y0, X1), join(Y0, X2)) % 45.32/45.39 join(meet2(join(Y2, X1), join(X2, Y2)), join(Y2, meet2(meet2(join(Y2, X1), join(X2, Y2)), Y1))) -> meet2(join(Y2, X1), join(X2, Y2)) % 45.32/45.39 meet(X, X) -> X % 45.32/45.39 meet(Y0, join(Y0, Y1)) -> Y0 % 45.32/45.39 meet(Y0, meet(join(Y0, Y1), join(Y0, Y2))) -> Y0 % 45.32/45.39 meet(Y0, meet2(join(Y0, Y1), join(Y0, Y2))) -> Y0 % 45.32/45.39 meet(Y1, join(Y2, Y1)) -> Y1 % 45.32/45.39 meet(Y1, join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet(X1, Y1), meet(Y1, X2))) -> join(meet(X1, Y1), meet(Y1, X2)) % 45.32/45.39 meet(Y1, join(meet(X1, Y1), meet2(X2, Y1))) -> join(meet(X1, Y1), meet2(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet(X1, Y1), meet2(Y1, X2))) -> join(meet(X1, Y1), meet2(Y1, X2)) % 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2)) % 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet2(X2, Y1))) -> join(meet(Y1, X1), meet2(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet2(Y1, X2))) -> join(meet(Y1, X1), meet2(Y1, X2)) % 45.32/45.39 meet(Y1, join(meet2(X0, Y1), meet2(X2, Y1))) -> join(meet2(X0, Y1), meet2(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet2(X1, Y1), meet(X2, Y1))) -> join(meet2(X1, Y1), meet(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet2(X1, Y1), meet(Y1, X2))) -> join(meet2(X1, Y1), meet(Y1, X2)) % 45.32/45.39 meet(Y1, join(meet2(X1, Y1), meet2(Y1, X2))) -> join(meet2(X1, Y1), meet2(Y1, X2)) % 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet(X2, Y1))) -> join(meet2(Y1, X1), meet(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet(Y1, X2))) -> join(meet2(Y1, X1), meet(Y1, X2)) % 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet2(X2, Y1))) -> join(meet2(Y1, X1), meet2(X2, Y1)) % 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet2(Y1, X2))) -> join(meet2(Y1, X1), meet2(Y1, X2)) % 45.32/45.39 meet(Y1, meet(X1, Y1)) -> meet(X1, Y1) % 45.32/45.39 meet(Y1, meet(Y1, X1)) -> meet(Y1, X1) % 45.32/45.39 meet(Y1, meet(Y1, join(Y2, Y1))) -> Y1 % 45.32/45.39 meet(Y1, meet(join(Y0, Y1), join(Y1, Y2))) -> Y1 % 45.32/45.39 meet(Y1, meet(join(Y0, Y1), join(Y2, Y1))) -> Y1 % 45.32/45.39 meet(Y1, meet(join(Y1, Y0), join(Y2, Y1))) -> Y1 % 45.32/45.39 meet(Y1, meet2(X1, Y1)) -> meet2(X1, Y1) % 45.32/45.39 meet(Y1, meet2(Y1, X1)) -> meet2(Y1, X1) % 45.32/45.39 meet(Y1, meet2(join(X0, Y1), join(X2, Y1))) -> Y1 % 45.32/45.39 meet(Y1, meet2(join(X1, Y1), join(Y1, X2))) -> Y1 % 45.32/45.39 meet(Y1, meet2(join(Y1, X1), join(X2, Y1))) -> Y1 % 45.32/45.39 meet(join(X0, X1), join(X0, meet(X2, join(X0, X1)))) -> join(X0, meet(X2, join(X0, X1))) % 45.32/45.39 meet(join(X0, X1), join(X0, meet(join(X0, X1), X2))) -> join(X0, meet(join(X0, X1), X2)) % 45.32/45.39 meet(join(X0, X1), join(X1, meet(X2, join(X0, X1)))) -> join(X1, meet(X2, join(X0, X1))) % 45.32/45.39 meet(join(X0, X1), join(X1, meet(join(X0, X1), X2))) -> join(X1, meet(join(X0, X1), X2)) % 45.32/45.39 meet(join(X0, X1), join(X1, meet2(X2, join(X0, X1)))) -> join(X1, meet2(X2, join(X0, X1))) % 45.32/45.39 meet(join(X1, meet(X2, join(X0, X1))), meet(join(X0, X1), join(Y2, join(X1, meet(X2, join(X0, X1)))))) -> join(X1, meet(X2, join(X0, X1))) % 45.32/45.39 meet(join(meet(X0, Y1), meet(X2, Y1)), meet(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1))))) -> join(meet(X0, Y1), meet(X2, Y1)) % 45.32/45.39 meet(join(meet(X1, Y0), meet(Y0, X2)), meet(Y0, join(Y2, join(meet(X1, Y0), meet(Y0, X2))))) -> join(meet(X1, Y0), meet(Y0, X2)) % 45.32/45.39 meet(join(meet(X1, Y0), meet2(X2, Y0)), meet(Y0, join(Y2, join(meet(X1, Y0), meet2(X2, Y0))))) -> join(meet(X1, Y0), meet2(X2, Y0)) % 45.32/45.39 meet(join(meet(X1, Y2), meet(X2, Y2)), meet(Y2, join(join(meet(X1, Y2), meet(X2, Y2)), Y1))) -> join(meet(X1, Y2), meet(X2, Y2)) % 45.32/45.39 meet(join(meet(X1, Y2), meet(Y2, X2)), meet(Y2, join(join(meet(X1, Y2), meet(Y2, X2)), Y1))) -> join(meet(X1, Y2), meet(Y2, X2)) % 45.32/45.39 meet(join(meet(Y0, X1), meet(X2, Y0)), meet(Y0, join(Y2, join(meet(Y0, X1), meet(X2, Y0))))) -> join(meet(Y0, X1), meet(X2, Y0)) % 45.32/45.39 meet(join(meet(Y0, X1), meet(Y0, X2)), meet(Y0, join(Y2, join(meet(Y0, X1), meet(Y0, X2))))) -> join(meet(Y0, X1), meet(Y0, X2)) % 45.32/45.39 meet(join(meet(Y0, X1), meet2(X2, Y0)), meet(Y0, join(Y2, join(meet(Y0, X1), meet2(X2, Y0))))) -> join(meet(Y0, X1), meet2(X2, Y0)) % 45.32/45.39 meet(join(meet(Y2, X1), meet(X2, Y2)), meet(Y2, join(join(meet(Y2, X1), meet(X2, Y2)), Y1))) -> join(meet(Y2, X1), meet(X2, Y2)) % 45.32/45.39 meet(join(meet(Y2, X1), meet(Y2, X2)), meet(Y2, join(join(meet(Y2, X1), meet(Y2, X2)), Y1))) -> join(meet(Y2, X1), meet(Y2, X2)) % 45.32/45.39 meet(join(meet2(X0, Y1), meet2(X2, Y1)), meet(Y1, join(Y2, join(meet2(X0, Y1), meet2(X2, Y1))))) -> join(meet2(X0, Y1), meet2(X2, Y1)) % 45.32/45.39 meet(join(meet2(X1, Y0), meet(X2, Y0)), meet(Y0, join(Y2, join(meet2(X1, Y0), meet(X2, Y0))))) -> join(meet2(X1, Y0), meet(X2, Y0)) % 45.32/45.39 meet(join(meet2(X1, Y0), meet(Y0, X2)), meet(Y0, join(Y2, join(meet2(X1, Y0), meet(Y0, X2))))) -> join(meet2(X1, Y0), meet(Y0, X2)) % 45.32/45.39 meet(join(meet2(X1, Y0), meet2(Y0, X2)), meet(Y0, join(Y2, join(meet2(X1, Y0), meet2(Y0, X2))))) -> join(meet2(X1, Y0), meet2(Y0, X2)) % 45.32/45.39 meet(join(meet2(X1, Y2), meet(X2, Y2)), meet(Y2, join(join(meet2(X1, Y2), meet(X2, Y2)), Y1))) -> join(meet2(X1, Y2), meet(X2, Y2)) % 45.32/45.39 meet(join(meet2(X1, Y2), meet2(X2, Y2)), meet(Y2, join(join(meet2(X1, Y2), meet2(X2, Y2)), Y1))) -> join(meet2(X1, Y2), meet2(X2, Y2)) % 45.32/45.39 meet(join(meet2(X1, Y2), meet2(Y2, X2)), meet(Y2, join(join(meet2(X1, Y2), meet2(Y2, X2)), Y1))) -> join(meet2(X1, Y2), meet2(Y2, X2)) % 45.32/45.39 meet(join(meet2(Y0, X1), meet(X2, Y0)), meet(Y0, join(Y2, join(meet2(Y0, X1), meet(X2, Y0))))) -> join(meet2(Y0, X1), meet(X2, Y0)) % 45.32/45.39 meet(join(meet2(Y0, X1), meet2(X2, Y0)), meet(Y0, join(Y2, join(meet2(Y0, X1), meet2(X2, Y0))))) -> join(meet2(Y0, X1), meet2(X2, Y0)) % 45.32/45.39 meet(join(meet2(Y0, X1), meet2(Y0, X2)), meet(Y0, join(Y2, join(meet2(Y0, X1), meet2(Y0, X2))))) -> join(meet2(Y0, X1), meet2(Y0, X2)) % 45.32/45.39 meet(join(meet2(Y2, X1), meet2(X2, Y2)), meet(Y2, join(join(meet2(Y2, X1), meet2(X2, Y2)), Y1))) -> join(meet2(Y2, X1), meet2(X2, Y2)) % 45.32/45.39 meet(join(meet2(Y2, X1), meet2(Y2, X2)), meet(Y2, join(join(meet2(Y2, X1), meet2(Y2, X2)), Y1))) -> join(meet2(Y2, X1), meet2(Y2, X2)) % 45.32/45.39 meet(meet(X0, X1), meet(join(Y1, meet(X0, X1)), meet2(X1, X0))) -> meet(X0, X1) % 45.32/45.39 meet(meet(X0, X1), meet(join(meet(X0, X1), Y1), meet2(X1, X0))) -> meet(X0, X1) % 45.32/45.39 meet(meet(X0, X1), meet(meet2(X1, X0), join(Y2, meet(X0, X1)))) -> meet(X0, X1) % 45.32/45.39 meet(meet(X0, X1), meet(meet2(X1, X0), join(meet(X0, X1), Y2))) -> meet(X0, X1) % 45.32/45.39 meet(meet(X0, X1), meet2(X1, X0)) -> meet(X0, X1) % 45.32/45.39 meet(meet(X1, Y0), meet(Y0, join(Y2, meet(X1, Y0)))) -> meet(X1, Y0) % 45.32/45.39 meet(meet(X1, Y1), meet2(Y1, join(Y2, meet(X1, Y1)))) -> meet(X1, Y1) % 45.32/45.39 meet(meet(X1, Y2), meet(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2) % 45.32/45.39 meet(meet(X1, Y2), meet2(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2) % 45.32/45.39 meet(meet(Y0, X1), meet(Y0, join(Y2, meet(Y0, X1)))) -> meet(Y0, X1) % 45.32/45.39 meet(meet(Y0, Y1), meet2(Y0, Y1)) -> meet(Y0, Y1) % 45.32/45.39 meet(meet(Y1, X1), meet2(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1) % 45.32/45.39 meet(meet(Y1, Y0), meet2(Y1, Y0)) -> meet(Y0, Y1) % 45.32/45.39 meet(meet(Y2, X1), meet(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1) % 45.32/45.39 meet(meet(Y2, X1), meet2(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1) % 45.32/45.39 meet(meet(join(X, Y), join(Z, Y)), Y) -> Y % 45.32/45.39 meet(meet2(X1, Y0), meet(Y0, join(Y2, meet2(X1, Y0)))) -> meet2(X1, Y0) % 45.32/45.39 meet(meet2(X1, Y1), meet2(Y1, join(Y2, meet2(X1, Y1)))) -> meet2(X1, Y1) % 45.32/45.39 meet(meet2(X1, Y2), meet(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2) % 45.32/45.39 meet(meet2(X1, Y2), meet2(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2) % 45.32/45.39 meet(meet2(Y0, X1), meet(Y0, join(Y2, meet2(Y0, X1)))) -> meet2(Y0, X1) % 45.32/45.39 meet(meet2(Y0, Y1), meet(Y1, join(Y2, meet2(Y1, Y0)))) -> meet2(Y0, Y1) % 45.32/45.39 meet(meet2(Y1, X1), meet2(Y1, join(Y2, meet2(Y1, X1)))) -> meet2(Y1, X1) % 45.32/45.39 meet(meet2(Y1, Y0), meet(Y1, join(Y2, meet2(Y0, Y1)))) -> meet2(Y0, Y1) % 45.32/45.39 meet(meet2(Y2, X1), meet(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1) % 45.32/45.39 meet(meet2(Y2, X1), meet2(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1) % 45.32/45.39 meet2(X, X) -> X % 45.32/45.39 meet2(Y0, Y1) -> meet(Y1, Y0) % 45.32/45.39 meet2(Y0, join(Y0, Y1)) -> Y0 % 45.32/45.39 meet2(Y0, meet(join(Y0, Y1), join(Y0, Y2))) -> Y0 % 45.32/45.39 meet2(Y0, meet(join(Y0, Y1), join(Y2, Y0))) -> Y0 % 45.32/45.39 meet2(Y0, meet(join(Y1, Y0), join(Y0, Y2))) -> Y0 % 45.32/45.39 meet2(Y0, meet2(join(Y0, Y1), join(Y0, Y2))) -> Y0 % 45.32/45.39 meet2(Y1, join(Y2, Y1)) -> Y1 % 45.32/45.39 meet2(Y1, join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet(X1, Y1), meet(Y1, X2))) -> join(meet(X1, Y1), meet(Y1, X2)) % 45.32/45.39 meet2(Y1, join(meet(X1, Y1), meet2(X2, Y1))) -> join(meet(X1, Y1), meet2(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet(X1, Y1), meet2(Y1, X2))) -> join(meet(X1, Y1), meet2(Y1, X2)) % 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2)) % 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet2(X2, Y1))) -> join(meet(Y1, X1), meet2(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet2(Y1, X2))) -> join(meet(Y1, X1), meet2(Y1, X2)) % 45.32/45.39 meet2(Y1, join(meet2(X0, Y1), meet2(X2, Y1))) -> join(meet2(X0, Y1), meet2(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet2(X1, Y1), meet(X2, Y1))) -> join(meet2(X1, Y1), meet(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet2(X1, Y1), meet(Y1, X2))) -> join(meet2(X1, Y1), meet(Y1, X2)) % 45.32/45.39 meet2(Y1, join(meet2(X1, Y1), meet2(Y1, X2))) -> join(meet2(X1, Y1), meet2(Y1, X2)) % 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet(X2, Y1))) -> join(meet2(Y1, X1), meet(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet(Y1, X2))) -> join(meet2(Y1, X1), meet(Y1, X2)) % 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet2(X2, Y1))) -> join(meet2(Y1, X1), meet2(X2, Y1)) % 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet2(Y1, X2))) -> join(meet2(Y1, X1), meet2(Y1, X2)) % 45.32/45.39 meet2(Y1, meet(X1, Y1)) -> meet(X1, Y1) % 45.32/45.39 meet2(Y1, meet(Y1, X1)) -> meet(Y1, X1) % 45.32/45.39 meet2(Y1, meet(join(X0, Y1), join(X2, Y1))) -> Y1 % 45.32/45.39 meet2(Y1, meet2(X1, Y1)) -> meet2(X1, Y1) % 45.32/45.39 meet2(Y1, meet2(Y1, X1)) -> meet2(Y1, X1) % 45.32/45.39 meet2(Y1, meet2(Y1, join(Y2, Y1))) -> Y1 % 45.32/45.40 meet2(Y1, meet2(join(Y0, Y1), join(Y1, Y2))) -> Y1 % 45.32/45.40 meet2(Y1, meet2(join(Y0, Y1), join(Y2, Y1))) -> Y1 % 45.32/45.40 meet2(Y1, meet2(join(Y1, Y0), join(Y2, Y1))) -> Y1 % 45.32/45.40 meet2(join(X0, X1), join(X1, meet(X2, join(X0, X1)))) -> join(X1, meet(X2, join(X0, X1))) % 45.32/45.40 meet2(join(X0, X1), join(X1, meet(join(X0, X1), X2))) -> join(X1, meet(join(X0, X1), X2)) % 45.32/45.40 meet2(join(meet(X0, Y1), meet(X2, Y1)), meet(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1))))) -> join(meet(X0, Y1), meet(X2, Y1)) % 45.32/45.40 meet2(join(meet(X0, Y1), meet(X2, Y1)), meet2(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1))))) -> join(meet(X0, Y1), meet(X2, Y1)) % 45.32/45.40 meet2(join(meet(X0, Y1), meet(X2, Y1)), meet2(Y1, join(join(meet(X0, Y1), meet(X2, Y1)), Y2))) -> join(meet(X0, Y1), meet(X2, Y1)) % 45.32/45.40 meet2(join(meet(X1, Y0), meet(Y0, X2)), meet2(Y0, join(Y2, join(meet(X1, Y0), meet(Y0, X2))))) -> join(meet(X1, Y0), meet(Y0, X2)) % 45.32/45.40 meet2(join(meet(X1, Y0), meet2(X2, Y0)), meet2(Y0, join(Y2, join(meet(X1, Y0), meet2(X2, Y0))))) -> join(meet(X1, Y0), meet2(X2, Y0)) % 45.32/45.40 meet2(join(meet(X1, Y1), meet(Y1, X2)), meet(Y1, join(Y2, join(meet(X1, Y1), meet(Y1, X2))))) -> join(meet(X1, Y1), meet(Y1, X2)) % 45.32/45.40 meet2(join(meet(X1, Y2), meet(Y2, X2)), meet2(Y2, join(join(meet(X1, Y2), meet(Y2, X2)), Y1))) -> join(meet(X1, Y2), meet(Y2, X2)) % 45.32/45.40 meet2(join(meet(Y0, X1), meet(X2, Y0)), meet2(Y0, join(Y2, join(meet(Y0, X1), meet(X2, Y0))))) -> join(meet(Y0, X1), meet(X2, Y0)) % 45.32/45.40 meet2(join(meet(Y0, X1), meet(Y0, X2)), meet2(Y0, join(Y2, join(meet(Y0, X1), meet(Y0, X2))))) -> join(meet(Y0, X1), meet(Y0, X2)) % 45.32/45.40 meet2(join(meet(Y0, X1), meet2(X2, Y0)), meet2(Y0, join(Y2, join(meet(Y0, X1), meet2(X2, Y0))))) -> join(meet(Y0, X1), meet2(X2, Y0)) % 45.32/45.40 meet2(join(meet(Y1, X1), meet(X2, Y1)), meet(Y1, join(Y2, join(meet(Y1, X1), meet(X2, Y1))))) -> join(meet(Y1, X1), meet(X2, Y1)) % 45.32/45.40 meet2(join(meet(Y2, X1), meet(X2, Y2)), meet2(Y2, join(join(meet(Y2, X1), meet(X2, Y2)), Y1))) -> join(meet(Y2, X1), meet(X2, Y2)) % 45.32/45.40 meet2(join(meet(Y2, X1), meet(Y2, X2)), meet2(Y2, join(join(meet(Y2, X1), meet(Y2, X2)), Y1))) -> join(meet(Y2, X1), meet(Y2, X2)) % 45.32/45.40 meet2(join(meet2(X0, Y1), meet2(X2, Y1)), meet2(Y1, join(Y2, join(meet2(X0, Y1), meet2(X2, Y1))))) -> join(meet2(X0, Y1), meet2(X2, Y1)) % 45.32/45.40 meet2(join(meet2(X0, Y1), meet2(X2, Y1)), meet2(Y1, join(join(meet2(X0, Y1), meet2(X2, Y1)), Y2))) -> join(meet2(X0, Y1), meet2(X2, Y1)) % 45.32/45.40 meet2(join(meet2(X1, Y0), meet(X2, Y0)), meet2(Y0, join(Y2, join(meet2(X1, Y0), meet(X2, Y0))))) -> join(meet2(X1, Y0), meet(X2, Y0)) % 45.32/45.40 meet2(join(meet2(X1, Y0), meet(Y0, X2)), meet2(Y0, join(Y2, join(meet2(X1, Y0), meet(Y0, X2))))) -> join(meet2(X1, Y0), meet(Y0, X2)) % 45.32/45.40 meet2(join(meet2(X1, Y0), meet2(Y0, X2)), meet2(Y0, join(Y2, join(meet2(X1, Y0), meet2(Y0, X2))))) -> join(meet2(X1, Y0), meet2(Y0, X2)) % 45.32/45.40 meet2(join(meet2(X1, Y2), meet2(Y2, X2)), meet2(Y2, join(join(meet2(X1, Y2), meet2(Y2, X2)), Y1))) -> join(meet2(X1, Y2), meet2(Y2, X2)) % 45.32/45.40 meet2(join(meet2(Y0, X1), meet2(X2, Y0)), meet2(Y0, join(Y2, join(meet2(Y0, X1), meet2(X2, Y0))))) -> join(meet2(Y0, X1), meet2(X2, Y0)) % 45.32/45.40 meet2(join(meet2(Y0, X1), meet2(Y0, X2)), meet2(Y0, join(Y2, join(meet2(Y0, X1), meet2(Y0, X2))))) -> join(meet2(Y0, X1), meet2(Y0, X2)) % 45.32/45.40 meet2(join(meet2(Y2, X1), meet2(X2, Y2)), meet2(Y2, join(join(meet2(Y2, X1), meet2(X2, Y2)), Y1))) -> join(meet2(Y2, X1), meet2(X2, Y2)) % 45.32/45.40 meet2(meet(X0, X1), meet(join(Y1, meet(X0, X1)), meet2(X1, X0))) -> meet(X0, X1) % 45.32/45.40 meet2(meet(X0, X1), meet(meet2(X1, X0), join(Y2, meet(X0, X1)))) -> meet(X0, X1) % 45.32/45.40 meet2(meet(X0, X1), meet2(join(Y1, meet(X0, X1)), meet2(X1, X0))) -> meet(X0, X1) % 45.32/45.40 meet2(meet(X0, X1), meet2(join(meet(X0, X1), Y1), meet2(X1, X0))) -> meet(X0, X1) % 45.32/45.40 meet2(meet(X0, X1), meet2(meet2(X1, X0), join(Y2, meet(X0, X1)))) -> meet(X0, X1) % 45.32/45.40 meet2(meet(X0, X1), meet2(meet2(X1, X0), join(meet(X0, X1), Y2))) -> meet(X0, X1) % 45.32/45.40 meet2(meet(X1, Y0), meet2(Y0, join(Y2, meet(X1, Y0)))) -> meet(X1, Y0) % 45.32/45.40 meet2(meet(X1, Y1), meet(Y1, join(Y2, meet(X1, Y1)))) -> meet(X1, Y1) % 45.32/45.40 meet2(meet(X1, Y2), meet(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2) % 45.32/45.40 meet2(meet(X1, Y2), meet2(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2) % 45.32/45.40 meet2(meet(Y0, X1), meet2(Y0, join(Y2, meet(Y0, X1)))) -> meet(Y0, X1) % 45.32/45.40 meet2(meet(Y0, Y1), meet2(Y0, Y1)) -> meet(Y0, Y1) % 45.32/45.40 meet2(meet(Y0, Y1), meet2(Y1, Y0)) -> meet(Y0, Y1) % 45.32/45.40 meet2(meet(Y0, Y1), meet2(Y1, join(Y2, meet(Y1, Y0)))) -> meet(Y0, Y1) % 45.32/45.40 meet2(meet(Y1, X1), meet(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1) % 45.32/45.40 meet2(meet(Y1, Y0), meet2(Y1, Y0)) -> meet(Y0, Y1) % 45.32/45.40 meet2(meet(Y1, Y0), meet2(Y1, join(Y2, meet(Y0, Y1)))) -> meet(Y0, Y1) % 45.32/45.40 meet2(meet(Y2, X1), meet(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1) % 45.32/45.40 meet2(meet(Y2, X1), meet2(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1) % 45.32/45.40 meet2(meet2(X1, Y0), meet2(Y0, join(Y2, meet2(X1, Y0)))) -> meet2(X1, Y0) % 45.32/45.40 meet2(meet2(X1, Y1), meet(Y1, join(Y2, meet2(X1, Y1)))) -> meet2(X1, Y1) % 45.32/45.40 meet2(meet2(X1, Y2), meet(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2) % 45.32/45.40 meet2(meet2(X1, Y2), meet2(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2) % 45.32/45.40 meet2(meet2(Y0, X1), meet2(Y0, join(Y2, meet2(Y0, X1)))) -> meet2(Y0, X1) % 45.32/45.40 meet2(meet2(Y1, X1), meet(Y1, join(Y2, meet2(Y1, X1)))) -> meet2(Y1, X1) % 45.32/45.40 meet2(meet2(Y2, X1), meet(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1) % 45.32/45.40 meet2(meet2(Y2, X1), meet2(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1) % 45.32/45.40 meet2(meet2(join(X, Y), join(Z, Y)), Y) -> Y % 45.32/45.40 true__ -> false__ % 45.32/45.40 with the LPO induced by % 45.32/45.40 b > a > f1 > meet2 > join > meet > true__ > false__ % 45.32/45.40 % 45.32/45.40 % SZS output end Proof % 45.32/45.40 %------------------------------------------------------------------------------