%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT091-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n012.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 06:04:35 EDT 2022 % Result : Unsatisfiable 34.45s 34.50s % Output : Proof 34.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.07 % Problem : LAT091-1 : TPTP v8.1.0. Released v2.6.0. % 0.02/0.07 % Command : moca.sh %s % 0.06/0.25 % Computer : n012.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 600 % 0.06/0.25 % DateTime : Wed Jun 29 19:10:03 EDT 2022 % 0.06/0.25 % CPUTime : % 34.45/34.50 % SZS status Unsatisfiable % 34.45/34.50 % SZS output start Proof % 34.45/34.50 The input problem is unsatisfiable because % 34.45/34.50 % 34.45/34.50 [1] the following set of Horn clauses is unsatisfiable: % 34.45/34.50 % 34.45/34.50 join(meet(A, B), meet(A, join(A, B))) = A % 34.45/34.50 join(meet(A, A), meet(B, join(A, A))) = A % 34.45/34.50 join(meet(A, B), meet(B, join(A, B))) = B % 34.45/34.50 meet(meet(join(A, B), join(C, A)), A) = A % 34.45/34.50 join(join(meet(A, B), meet(C, A)), A) = A % 34.45/34.50 join(b, a) = join(a, b) ==> \bottom % 34.45/34.50 % 34.45/34.50 This holds because % 34.45/34.50 % 34.45/34.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 34.45/34.50 % 34.45/34.50 E: % 34.45/34.50 f1(join(a, b)) = false__ % 34.45/34.50 f1(join(b, a)) = true__ % 34.45/34.50 join(join(meet(A, B), meet(C, A)), A) = A % 34.45/34.50 join(meet(A, A), meet(B, join(A, A))) = A % 34.45/34.50 join(meet(A, B), meet(A, join(A, B))) = A % 34.45/34.50 join(meet(A, B), meet(B, join(A, B))) = B % 34.45/34.50 meet(meet(join(A, B), join(C, A)), A) = A % 34.45/34.50 G: % 34.45/34.50 true__ = false__ % 34.45/34.50 % 34.45/34.50 This holds because % 34.45/34.50 % 34.45/34.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 34.45/34.50 % 34.45/34.50 join(X0, X1) = join(X1, X0) % 34.45/34.50 meet(X0, X1) = meet(X1, X0) % 34.45/34.50 f1(join(a, b)) -> false__ % 34.45/34.50 f1(join(b, a)) -> true__ % 34.45/34.50 join(X0, meet(X0, join(X0, X1))) -> X0 % 34.45/34.50 join(Y0, join(X1, Y0)) -> join(X1, Y0) % 34.45/34.50 join(Y0, join(Y0, Y0)) -> Y0 % 34.45/34.50 join(Y0, join(join(Y0, X1), Y0)) -> join(join(Y0, X1), Y0) % 34.45/34.50 join(Y0, join(meet(X1, Y0), meet(Y2, Y0))) -> Y0 % 34.45/34.50 join(Y0, join(meet(Y0, Y1), meet(Y0, X1))) -> Y0 % 34.45/34.50 join(Y0, join(meet(Y1, Y0), meet(Y0, X1))) -> Y0 % 34.45/34.50 join(Y0, meet(Y0, X1)) -> Y0 % 34.45/34.50 join(Y0, meet(Y0, meet(X1, Y0))) -> Y0 % 34.45/34.50 join(Y0, meet(Y1, Y0)) -> Y0 % 34.45/34.50 join(Y0, meet(Y1, join(Y0, Y0))) -> Y0 % 34.45/34.50 join(Y1, Y1) -> Y1 % 34.45/34.50 join(Y1, join(Y1, X1)) -> join(Y1, X1) % 34.45/34.50 join(Y1, join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 join(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> Y1 % 34.45/34.50 join(Y1, meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1)) % 34.45/34.50 join(Y1, meet(Y1, join(Y1, Y1))) -> Y1 % 34.45/34.50 join(Y1, meet(Y1, join(join(Y1, X1), Y1))) -> Y1 % 34.45/34.50 join(Y1, meet(Y1, join(meet(Y1, join(X1, Y1)), Y1))) -> Y1 % 34.45/34.50 join(Y1, meet(Y1, join(meet(join(Y1, X1), Y1), Y1))) -> Y1 % 34.45/34.50 join(Y1, meet(Y1, join(meet(join(Y1, X1), join(X2, Y1)), Y1))) -> Y1 % 34.45/34.50 join(Y1, meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1)) % 34.45/34.50 join(Y1, meet(join(X0, Y1), join(Y1, X2))) -> meet(join(X0, Y1), join(Y1, X2)) % 34.45/34.50 join(Y1, meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(Y1, meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2)) % 34.45/34.50 join(Y1, meet(join(Y1, X1), join(join(Y1, X1), Y1))) -> join(Y1, X1) % 34.45/34.50 join(Y1, meet(meet(Y1, join(X1, Y1)), join(meet(Y1, join(X1, Y1)), Y1))) -> meet(Y1, join(X1, Y1)) % 34.45/34.50 join(Y1, meet(meet(join(Y1, X1), Y1), join(meet(join(Y1, X1), Y1), Y1))) -> meet(join(Y1, X1), Y1) % 34.45/34.50 join(Y1, meet(meet(join(Y1, X1), join(X2, Y1)), join(meet(join(Y1, X1), join(X2, Y1)), Y1))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(join(X0, X0), meet(join(X0, X0), join(meet(join(join(X0, X0), Y1), X0), join(X0, X0)))) -> join(X0, X0) % 34.45/34.50 join(join(X0, Y1), join(Y1, meet(Y2, join(X0, Y1)))) -> join(X0, Y1) % 34.45/34.50 join(join(X0, meet(X0, X1)), meet(X0, X1)) -> join(X0, meet(X0, X1)) % 34.45/34.50 join(join(X1, Y1), Y1) -> join(X1, Y1) % 34.45/34.50 join(join(X1, Y1), join(Y1, meet(join(X1, Y1), Y2))) -> join(X1, Y1) % 34.45/34.50 join(join(X1, Y1), meet(join(X1, Y1), Y1)) -> join(X1, Y1) % 34.45/34.50 join(join(X1, Y2), join(meet(Y1, join(X1, Y2)), Y2)) -> join(X1, Y2) % 34.45/34.50 join(join(X1, Y2), join(meet(join(X1, Y2), Y1), Y2)) -> join(X1, Y2) % 34.45/34.50 join(join(Y0, Y2), join(Y2, Y0)) -> join(Y2, Y0) % 34.45/34.50 join(join(Y0, join(X1, Y0)), join(X1, Y0)) -> join(X1, Y0) % 34.45/34.50 join(join(Y0, meet(Y0, X1)), Y0) -> Y0 % 34.45/34.50 join(join(Y1, X1), Y1) -> join(Y1, X1) % 34.45/34.50 join(join(Y1, X1), join(Y1, meet(Y2, join(Y1, X1)))) -> join(Y1, X1) % 34.45/34.50 join(join(Y1, X1), join(Y1, meet(join(Y1, X1), Y2))) -> join(Y1, X1) % 34.45/34.50 join(join(Y1, Y1), Y1) -> Y1 % 34.45/34.50 join(join(Y1, join(Y1, X1)), join(Y1, X1)) -> join(Y1, X1) % 34.45/34.50 join(join(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(Y1, join(meet(Y1, X1), Y1)) % 34.45/34.50 join(join(Y1, meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1)) % 34.45/34.50 join(join(Y1, meet(Y2, Y1)), Y1) -> Y1 % 34.45/34.50 join(join(Y1, meet(Y2, join(X0, Y1))), join(X0, Y1)) -> join(X0, Y1) % 34.45/34.50 join(join(Y1, meet(Y2, join(Y1, X1))), join(Y1, X1)) -> join(Y1, X1) % 34.45/34.50 join(join(Y1, meet(Y2, join(join(Y1, X1), Y1))), join(join(Y1, X1), Y1)) -> join(join(Y1, X1), Y1) % 34.45/34.50 join(join(Y1, meet(Y2, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 join(join(Y1, meet(Y2, meet(Y1, join(X1, Y1)))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1)) % 34.45/34.50 join(join(Y1, meet(Y2, meet(join(X0, Y1), join(X2, Y1)))), meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1)) % 34.45/34.50 join(join(Y1, meet(Y2, meet(join(X0, Y1), join(Y1, X2)))), meet(join(X0, Y1), join(Y1, X2))) -> meet(join(X0, Y1), join(Y1, X2)) % 34.45/34.50 join(join(Y1, meet(Y2, meet(join(Y1, X1), Y1))), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1) % 34.45/34.50 join(join(Y1, meet(Y2, meet(join(Y1, X1), join(X2, Y1)))), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(join(Y1, meet(Y2, meet(join(Y1, X1), join(Y1, X2)))), meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2)) % 34.45/34.50 join(join(Y1, meet(join(X0, Y1), Y2)), join(X0, Y1)) -> join(X0, Y1) % 34.45/34.50 join(join(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1) % 34.45/34.50 join(join(Y1, meet(join(Y1, X1), Y2)), join(Y1, X1)) -> join(Y1, X1) % 34.45/34.50 join(join(Y1, meet(join(Y1, X1), join(X2, Y1))), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(join(Y1, meet(meet(join(X0, Y1), join(X2, Y1)), Y2)), meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1)) % 34.45/34.50 join(join(Y1, meet(meet(join(X0, Y1), join(Y1, X2)), Y2)), meet(join(X0, Y1), join(Y1, X2))) -> meet(join(X0, Y1), join(Y1, X2)) % 34.45/34.50 join(join(Y1, meet(meet(join(Y1, X1), join(X2, Y1)), Y2)), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(join(Y1, meet(meet(join(Y1, X1), join(Y1, X2)), Y2)), meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2)) % 34.45/34.50 join(join(Y2, X1), join(meet(Y1, join(Y2, X1)), Y2)) -> join(Y2, X1) % 34.45/34.50 join(join(Y2, X1), join(meet(join(Y2, X1), Y1), Y2)) -> join(Y2, X1) % 34.45/34.50 join(join(join(X1, Y1), Y1), join(X1, Y1)) -> join(X1, Y1) % 34.45/34.50 join(join(join(Y1, X1), Y1), Y1) -> join(join(Y1, X1), Y1) % 34.45/34.50 join(join(join(Y1, X1), Y1), join(Y1, X1)) -> join(Y1, X1) % 34.45/34.50 join(join(join(Y1, X1), Y1), meet(join(join(Y1, X1), Y1), Y1)) -> join(join(Y1, X1), Y1) % 34.45/34.50 join(join(join(join(Y1, X1), Y1), Y1), join(join(Y1, X1), Y1)) -> join(join(Y1, X1), Y1) % 34.45/34.50 join(join(meet(A, B), meet(C, A)), A) -> A % 34.45/34.50 join(join(meet(X0, X0), meet(X0, meet(X0, X0))), meet(X0, meet(X0, X0))) -> meet(X0, meet(X0, X0)) % 34.45/34.50 join(join(meet(X0, X1), meet(X0, meet(X0, X1))), meet(X0, meet(X0, X1))) -> meet(X0, meet(X0, X1)) % 34.45/34.50 join(join(meet(X0, X1), meet(meet(X0, X1), X1)), meet(meet(X0, X1), X1)) -> meet(meet(X0, X1), X1) % 34.45/34.50 join(join(meet(X0, X2), meet(X0, join(X1, meet(X0, X2)))), meet(X0, join(X1, meet(X0, X2)))) -> meet(X0, join(X1, meet(X0, X2))) % 34.45/34.50 join(join(meet(X1, X0), meet(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 join(join(meet(X1, Y0), Y0), Y0) -> Y0 % 34.45/34.50 join(join(meet(X1, Y0), meet(Y0, Y2)), Y0) -> Y0 % 34.45/34.50 join(join(meet(X1, Y0), meet(Y2, Y0)), Y0) -> Y0 % 34.45/34.50 join(join(meet(X2, X0), meet(X0, join(X1, meet(X2, X0)))), meet(X0, join(X1, meet(X2, X0)))) -> meet(X0, join(X1, meet(X2, X0))) % 34.45/34.50 join(join(meet(Y0, Y1), Y0), Y0) -> Y0 % 34.45/34.50 join(join(meet(Y0, Y1), meet(Y0, X1)), Y0) -> Y0 % 34.45/34.50 join(join(meet(Y0, join(X1, Y2)), Y2), join(X1, Y2)) -> join(X1, Y2) % 34.45/34.50 join(join(meet(Y0, join(Y2, X1)), Y2), join(Y2, X1)) -> join(Y2, X1) % 34.45/34.50 join(join(meet(Y0, join(join(Y2, X1), Y2)), Y2), join(join(Y2, X1), Y2)) -> join(join(Y2, X1), Y2) % 34.45/34.50 join(join(meet(Y0, meet(join(X0, Y2), join(X2, Y2))), Y2), meet(join(X0, Y2), join(X2, Y2))) -> meet(join(X0, Y2), join(X2, Y2)) % 34.45/34.50 join(join(meet(Y0, meet(join(X1, Y2), join(Y2, X2))), Y2), meet(join(X1, Y2), join(Y2, X2))) -> meet(join(X1, Y2), join(Y2, X2)) % 34.45/34.50 join(join(meet(Y0, meet(join(Y2, X1), join(X2, Y2))), Y2), meet(join(Y2, X1), join(X2, Y2))) -> meet(join(Y2, X1), join(X2, Y2)) % 34.45/34.50 join(join(meet(Y0, meet(join(Y2, X1), join(Y2, X2))), Y2), meet(join(Y2, X1), join(Y2, X2))) -> meet(join(Y2, X1), join(Y2, X2)) % 34.45/34.50 join(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1))) -> join(Y1, join(meet(Y1, X1), Y1)) % 34.45/34.50 join(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1)))) -> join(meet(Y1, X1), Y1) % 34.45/34.50 join(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), join(meet(Y1, join(Y2, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)))) -> join(meet(Y1, X1), Y1) % 34.45/34.50 join(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), join(meet(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)))) -> join(meet(Y1, X1), Y1) % 34.45/34.50 join(join(meet(Y1, X1), meet(X2, Y1)), meet(join(meet(Y1, X1), meet(X2, Y1)), join(Y1, join(meet(Y1, X1), meet(X2, Y1))))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 join(join(meet(join(X1, Y2), Y1), Y2), join(X1, Y2)) -> join(X1, Y2) % 34.45/34.50 join(join(meet(join(Y2, X1), Y1), Y2), join(Y2, X1)) -> join(Y2, X1) % 34.45/34.50 join(join(meet(join(join(Y2, X1), Y2), Y1), Y2), join(join(Y2, X1), Y2)) -> join(join(Y2, X1), Y2) % 34.45/34.50 join(join(meet(meet(join(X1, Y2), join(X2, Y2)), Y1), Y2), meet(join(X1, Y2), join(X2, Y2))) -> meet(join(X1, Y2), join(X2, Y2)) % 34.45/34.50 join(join(meet(meet(join(X1, Y2), join(Y2, X2)), Y1), Y2), meet(join(X1, Y2), join(Y2, X2))) -> meet(join(X1, Y2), join(Y2, X2)) % 34.45/34.50 join(join(meet(meet(join(Y2, X1), join(X2, Y2)), Y1), Y2), meet(join(Y2, X1), join(X2, Y2))) -> meet(join(Y2, X1), join(X2, Y2)) % 34.45/34.50 join(join(meet(meet(join(Y2, X1), join(Y2, X2)), Y1), Y2), meet(join(Y2, X1), join(Y2, X2))) -> meet(join(Y2, X1), join(Y2, X2)) % 34.45/34.50 join(meet(A, A), meet(B, join(A, A))) -> A % 34.45/34.50 join(meet(A, B), meet(A, join(A, B))) -> A % 34.45/34.50 join(meet(A, B), meet(B, join(A, B))) -> B % 34.45/34.50 join(meet(X0, X0), meet(meet(X0, X0), join(meet(X0, join(Y2, meet(X0, X0))), meet(X0, X0)))) -> meet(X0, X0) % 34.45/34.50 join(meet(X0, X0), meet(meet(X0, X0), join(meet(X0, meet(X0, X0)), meet(X0, X0)))) -> meet(X0, X0) % 34.45/34.50 join(meet(X0, X0), meet(meet(X0, meet(X0, X0)), join(meet(X0, meet(X0, X0)), meet(X0, X0)))) -> meet(X0, meet(X0, X0)) % 34.45/34.50 join(meet(X0, X1), join(X0, meet(X0, X1))) -> join(X0, meet(X0, X1)) % 34.45/34.50 join(meet(X0, X1), meet(X0, join(meet(X0, X1), X2))) -> meet(X0, join(meet(X0, X1), X2)) % 34.45/34.50 join(meet(X0, X1), meet(X1, X0)) -> meet(X0, X1) % 34.45/34.50 join(meet(X0, X1), meet(X1, join(meet(X0, X1), X2))) -> meet(X1, join(meet(X0, X1), X2)) % 34.45/34.50 join(meet(X0, X1), meet(meet(X0, meet(X0, X1)), join(meet(X0, meet(X0, X1)), meet(X0, X1)))) -> meet(X0, meet(X0, X1)) % 34.45/34.50 join(meet(X0, X2), meet(X0, join(X1, meet(X0, X2)))) -> meet(X0, join(X1, meet(X0, X2))) % 34.45/34.50 join(meet(X0, X2), meet(meet(X0, X2), join(meet(X0, join(X1, meet(X0, X2))), meet(X0, X2)))) -> meet(X0, X2) % 34.45/34.50 join(meet(X0, X2), meet(meet(X0, join(X1, meet(X0, X2))), join(meet(X0, join(X1, meet(X0, X2))), meet(X0, X2)))) -> meet(X0, join(X1, meet(X0, X2))) % 34.45/34.50 join(meet(X0, Y1), meet(meet(X0, Y1), join(meet(Y1, join(Y2, meet(X0, Y1))), meet(X0, Y1)))) -> meet(X0, Y1) % 34.45/34.50 join(meet(X0, join(X0, X1)), join(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1)))) -> meet(X0, join(X0, X1)) % 34.45/34.50 join(meet(X0, join(X0, X1)), meet(meet(X0, X0), join(meet(X0, X0), meet(X0, join(X0, X1))))) -> meet(X0, X0) % 34.45/34.50 join(meet(X0, join(X1, meet(X0, X2))), join(meet(X0, X2), meet(Y2, meet(X0, join(X1, meet(X0, X2)))))) -> meet(X0, join(X1, meet(X0, X2))) % 34.45/34.50 join(meet(X0, join(X1, meet(X0, X2))), meet(X0, X2)) -> meet(X0, join(X1, meet(X0, X2))) % 34.45/34.50 join(meet(X0, join(X1, meet(X2, X0))), meet(X2, X0)) -> meet(X0, join(X1, meet(X2, X0))) % 34.45/34.50 join(meet(X0, join(meet(X0, X1), X2)), meet(X0, X1)) -> meet(X0, join(meet(X0, X1), X2)) % 34.45/34.50 join(meet(X1, X0), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 join(meet(X1, Y0), Y0) -> Y0 % 34.45/34.50 join(meet(X1, Y0), meet(meet(X1, Y0), Y0)) -> meet(X1, Y0) % 34.45/34.50 join(meet(X1, Y1), meet(meet(X1, Y1), join(meet(meet(X1, Y1), Y1), meet(X1, Y1)))) -> meet(X1, Y1) % 34.45/34.50 join(meet(X1, Y2), meet(meet(X1, Y2), join(meet(join(meet(X1, Y2), Y1), Y2), meet(X1, Y2)))) -> meet(X1, Y2) % 34.45/34.50 join(meet(X1, join(meet(X0, X1), X2)), meet(X0, X1)) -> meet(X1, join(meet(X0, X1), X2)) % 34.45/34.50 join(meet(X2, X0), meet(X0, join(X1, meet(X2, X0)))) -> meet(X0, join(X1, meet(X2, X0))) % 34.45/34.50 join(meet(X2, X0), meet(meet(X0, join(X1, meet(X2, X0))), join(meet(X0, join(X1, meet(X2, X0))), meet(X2, X0)))) -> meet(X0, join(X1, meet(X2, X0))) % 34.45/34.50 join(meet(Y0, X1), Y0) -> Y0 % 34.45/34.50 join(meet(Y0, X1), meet(Y0, join(Y0, meet(Y0, X1)))) -> Y0 % 34.45/34.50 join(meet(Y0, X1), meet(meet(Y0, X1), join(Y0, meet(Y0, X1)))) -> meet(Y0, X1) % 34.45/34.50 join(meet(Y0, Y0), join(Y0, Y0)) -> Y0 % 34.45/34.50 join(meet(Y0, join(Y0, Y0)), Y0) -> Y0 % 34.45/34.50 join(meet(Y0, join(Y0, Y0)), Y0) -> join(Y0, Y0) % 34.45/34.50 join(meet(Y0, join(join(Y0, X1), Y0)), Y0) -> Y0 % 34.45/34.50 join(meet(Y0, join(join(Y0, X1), Y0)), Y0) -> meet(Y0, join(join(Y0, X1), Y0)) % 34.45/34.50 join(meet(Y0, meet(X1, Y0)), Y0) -> Y0 % 34.45/34.50 join(meet(Y0, meet(X1, Y0)), meet(meet(X1, Y0), Y0)) -> meet(X1, Y0) % 34.45/34.50 join(meet(Y1, join(X1, Y1)), Y1) -> Y1 % 34.45/34.50 join(meet(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1) % 34.45/34.50 join(meet(join(X0, Y1), join(X2, Y1)), Y1) -> meet(join(X0, Y1), join(X2, Y1)) % 34.45/34.50 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)) % 34.45/34.50 join(meet(join(X0, Y1), join(X2, Y1)), join(Y1, meet(meet(join(X0, Y1), join(X2, Y1)), Y2))) -> meet(join(X0, Y1), join(X2, Y1)) % 34.45/34.50 join(meet(join(X0, Y1), join(Y1, X2)), Y1) -> meet(join(X0, Y1), join(Y1, X2)) % 34.45/34.50 join(meet(join(X0, Y1), join(Y1, X2)), join(Y1, meet(Y2, meet(join(X0, Y1), join(Y1, X2))))) -> meet(join(X0, Y1), join(Y1, X2)) % 34.45/34.50 join(meet(join(X0, Y1), join(Y1, X2)), join(Y1, meet(meet(join(X0, Y1), join(Y1, X2)), Y2))) -> meet(join(X0, Y1), join(Y1, X2)) % 34.45/34.50 join(meet(join(X0, Y2), join(X2, Y2)), join(meet(Y1, meet(join(X0, Y2), join(X2, Y2))), Y2)) -> meet(join(X0, Y2), join(X2, Y2)) % 34.45/34.50 join(meet(join(X0, Y2), join(X2, Y2)), join(meet(meet(join(X0, Y2), join(X2, Y2)), Y1), Y2)) -> meet(join(X0, Y2), join(X2, Y2)) % 34.45/34.50 join(meet(join(X1, Y2), join(Y2, X2)), join(meet(Y1, meet(join(X1, Y2), join(Y2, X2))), Y2)) -> meet(join(X1, Y2), join(Y2, X2)) % 34.45/34.50 join(meet(join(X1, Y2), join(Y2, X2)), join(meet(meet(join(X1, Y2), join(Y2, X2)), Y1), Y2)) -> meet(join(X1, Y2), join(Y2, X2)) % 34.45/34.50 join(meet(join(Y1, X1), join(X2, Y1)), Y1) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(meet(join(Y1, X1), join(X2, Y1)), join(Y1, meet(Y2, meet(join(Y1, X1), join(X2, Y1))))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(meet(join(Y1, X1), join(X2, Y1)), join(Y1, meet(meet(join(Y1, X1), join(X2, Y1)), Y2))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 join(meet(join(Y1, X1), join(Y1, X2)), Y1) -> meet(join(Y1, X1), join(Y1, X2)) % 34.45/34.50 join(meet(join(Y1, X1), join(Y1, X2)), join(Y1, meet(Y2, meet(join(Y1, X1), join(Y1, X2))))) -> meet(join(Y1, X1), join(Y1, X2)) % 34.45/34.50 join(meet(join(Y1, X1), join(Y1, X2)), join(Y1, meet(meet(join(Y1, X1), join(Y1, X2)), Y2))) -> meet(join(Y1, X1), join(Y1, X2)) % 34.45/34.50 join(meet(join(Y1, Y1), Y1), Y1) -> Y1 % 34.45/34.50 join(meet(join(Y1, meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1)) % 34.45/34.50 join(meet(join(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)), meet(meet(join(Y1, X1), Y1), meet(join(Y1, X1), Y1))) -> meet(join(Y1, X1), Y1) % 34.45/34.50 join(meet(join(Y2, X1), join(X2, Y2)), join(meet(Y1, meet(join(Y2, X1), join(X2, Y2))), Y2)) -> meet(join(Y2, X1), join(X2, Y2)) % 34.45/34.50 join(meet(join(Y2, X1), join(X2, Y2)), join(meet(meet(join(Y2, X1), join(X2, Y2)), Y1), Y2)) -> meet(join(Y2, X1), join(X2, Y2)) % 34.45/34.50 join(meet(join(Y2, X1), join(Y2, X2)), join(meet(Y1, meet(join(Y2, X1), join(Y2, X2))), Y2)) -> meet(join(Y2, X1), join(Y2, X2)) % 34.45/34.50 join(meet(join(Y2, X1), join(Y2, X2)), join(meet(meet(join(Y2, X1), join(Y2, X2)), Y1), Y2)) -> meet(join(Y2, X1), join(Y2, X2)) % 34.45/34.50 join(meet(join(join(Y1, X1), Y1), Y1), join(join(Y1, X1), Y1)) -> join(join(Y1, X1), Y1) % 34.45/34.50 join(meet(join(meet(X1, Y0), Y0), Y0), Y0) -> Y0 % 34.45/34.50 join(meet(join(meet(Y0, Y1), Y0), Y0), Y0) -> Y0 % 34.45/34.50 join(meet(join(meet(Y1, X1), Y1), Y1), meet(Y1, Y1)) -> Y1 % 34.45/34.50 join(meet(join(meet(Y1, X1), Y1), Y1), meet(join(meet(Y1, X1), Y1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 join(meet(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 join(meet(join(meet(Y1, X1), meet(X2, Y1)), Y1), meet(Y1, Y1)) -> Y1 % 34.45/34.50 join(meet(join(meet(Y1, X1), meet(X2, Y1)), Y1), meet(join(meet(Y1, X1), meet(X2, Y1)), Y1)) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 join(meet(join(meet(Y1, X1), meet(X2, Y1)), join(Y1, join(meet(Y1, X1), meet(X2, Y1)))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 join(meet(meet(X0, X0), join(X0, X0)), meet(join(X0, X0), X0)) -> join(X0, X0) % 34.45/34.50 join(meet(meet(X0, X0), join(X0, X0)), meet(meet(X0, X0), X0)) -> meet(X0, X0) % 34.45/34.50 join(meet(meet(X0, X0), meet(X1, join(X0, X0))), meet(meet(X0, X0), X0)) -> meet(X0, X0) % 34.45/34.50 join(meet(meet(X0, X0), meet(X1, join(X0, X0))), meet(meet(X1, join(X0, X0)), X0)) -> meet(X1, join(X0, X0)) % 34.45/34.50 join(meet(meet(X0, X1), join(X0, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 join(meet(meet(X0, X1), meet(X0, join(X0, X1))), meet(meet(X0, X1), X0)) -> meet(X0, X1) % 34.45/34.50 join(meet(meet(X0, X1), meet(X0, join(X0, X1))), meet(meet(X0, join(X0, X1)), X0)) -> meet(X0, join(X0, X1)) % 34.45/34.50 join(meet(meet(X0, X1), meet(X1, join(X0, X1))), meet(meet(X0, X1), X1)) -> meet(X0, X1) % 34.45/34.50 join(meet(meet(X0, X1), meet(X1, join(X0, X1))), meet(meet(X1, join(X0, X1)), X1)) -> meet(X1, join(X0, X1)) % 34.45/34.50 join(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1)) % 34.45/34.50 meet(X0, meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 meet(X0, meet(X1, X0)) -> meet(X1, X0) % 34.45/34.50 meet(X1, meet(X1, join(X0, X1))) -> meet(X1, join(X0, X1)) % 34.45/34.50 meet(Y0, join(join(Y0, X1), Y0)) -> Y0 % 34.45/34.50 meet(Y0, meet(Y0, join(Y0, Y1))) -> meet(Y0, join(Y0, Y1)) % 34.45/34.50 meet(Y0, meet(join(X1, Y0), join(Y0, Y2))) -> Y0 % 34.45/34.50 meet(Y0, meet(join(X1, Y0), join(Y2, Y0))) -> Y0 % 34.45/34.50 meet(Y0, meet(join(Y0, Y1), join(Y0, X1))) -> Y0 % 34.45/34.50 meet(Y0, meet(join(Y3, Y0), meet(join(Y0, Y1), join(Y2, Y0)))) -> Y0 % 34.45/34.50 meet(Y0, meet(meet(join(Y0, Y1), join(Y0, Y2)), join(Y3, Y0))) -> Y0 % 34.45/34.50 meet(Y0, meet(meet(join(Y0, Y1), join(Y2, Y0)), join(Y0, Y3))) -> Y0 % 34.45/34.50 meet(Y0, meet(meet(join(Y1, Y0), join(Y2, Y0)), join(Y3, Y0))) -> Y0 % 34.45/34.50 meet(Y0, meet(meet(join(Y2, Y0), join(Y0, Y1)), join(Y3, Y0))) -> Y0 % 34.45/34.50 meet(Y1, Y1) -> Y1 % 34.45/34.50 meet(Y1, join(X1, Y1)) -> Y1 % 34.45/34.50 meet(Y1, join(Y1, X1)) -> Y1 % 34.45/34.50 meet(Y1, join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 meet(Y1, join(meet(X0, Y1), meet(Y1, X2))) -> join(meet(X0, Y1), meet(Y1, X2)) % 34.45/34.50 meet(Y1, join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 meet(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(Y1, join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2)) % 34.45/34.50 meet(Y1, meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1) % 34.45/34.50 meet(Y1, meet(join(Y1, X1), join(X2, Y1))) -> Y1 % 34.45/34.50 meet(Y2, meet(meet(join(Y2, X1), join(X2, Y2)), join(Y1, Y2))) -> Y2 % 34.45/34.50 meet(join(X0, X1), join(X0, join(X0, X1))) -> join(X0, join(X0, X1)) % 34.45/34.50 meet(join(X0, X1), join(X0, meet(join(X0, X1), X2))) -> join(X0, meet(join(X0, X1), X2)) % 34.45/34.50 meet(join(X0, X1), join(X1, X0)) -> join(X0, X1) % 34.45/34.50 meet(join(X0, X1), join(meet(join(X0, X1), X2), X0)) -> join(meet(join(X0, X1), X2), X0) % 34.45/34.50 meet(join(X0, X1), join(meet(join(X0, X1), X2), X1)) -> join(meet(join(X0, X1), X2), X1) % 34.45/34.50 meet(join(X0, X1), meet(join(X1, X0), join(Y2, join(X0, X1)))) -> join(X0, X1) % 34.45/34.50 meet(join(X0, X1), meet(join(X1, X0), join(join(X0, X1), Y2))) -> join(X0, X1) % 34.45/34.50 meet(join(X0, X1), meet(join(Y0, join(X0, X1)), join(X1, X0))) -> join(X0, X1) % 34.45/34.50 meet(join(X0, X2), join(X0, meet(X1, join(X0, X2)))) -> join(X0, meet(X1, join(X0, X2))) % 34.45/34.50 meet(join(X0, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 meet(join(X1, X0), join(X0, X1)) -> join(X0, X1) % 34.45/34.50 meet(join(X1, X0), join(X0, meet(join(X1, X0), X2))) -> join(X0, meet(join(X1, X0), X2)) % 34.45/34.50 meet(join(X1, X2), join(meet(X0, join(X1, X2)), X1)) -> join(meet(X0, join(X1, X2)), X1) % 34.45/34.50 meet(join(X1, X2), join(meet(X0, join(X1, X2)), X2)) -> join(meet(X0, join(X1, X2)), X2) % 34.45/34.50 meet(join(X1, Y1), Y1) -> Y1 % 34.45/34.50 meet(join(X2, X0), join(X0, meet(X1, join(X2, X0)))) -> join(X0, meet(X1, join(X2, X0))) % 34.45/34.50 meet(join(Y1, X1), Y1) -> Y1 % 34.45/34.50 meet(join(Y1, X1), join(join(Y1, X1), Y1)) -> join(Y1, X1) % 34.45/34.50 meet(join(Y1, join(Y1, X1)), join(Y1, X1)) -> join(Y1, X1) % 34.45/34.50 meet(join(Y1, join(meet(X0, Y1), meet(X2, Y1))), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 meet(join(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 meet(join(Y1, join(meet(Y1, X1), meet(X2, Y1))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(join(Y1, meet(X1, Y1)), Y1) -> join(Y1, meet(X1, Y1)) % 34.45/34.50 meet(join(Y1, meet(join(Y1, X1), join(X2, Y1))), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1)) % 34.45/34.50 meet(join(Y2, Y2), Y2) -> Y2 % 34.45/34.50 meet(join(join(Y1, X1), Y1), Y1) -> Y1 % 34.45/34.50 meet(join(meet(X0, Y1), meet(X2, Y1)), Y1) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 meet(join(meet(X0, Y1), meet(X2, Y1)), join(Y1, join(meet(X0, Y1), meet(X2, Y1)))) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 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)) % 34.45/34.50 meet(join(meet(X0, Y1), meet(X2, Y1)), meet(Y1, join(join(meet(X0, Y1), meet(X2, Y1)), Y2))) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 meet(join(meet(X0, Y1), meet(Y1, X2)), Y1) -> join(meet(X0, Y1), meet(Y1, X2)) % 34.45/34.50 meet(join(meet(X0, Y1), meet(Y1, X2)), meet(Y1, join(Y2, join(meet(X0, Y1), meet(Y1, X2))))) -> join(meet(X0, Y1), meet(Y1, X2)) % 34.45/34.50 meet(join(meet(X0, Y1), meet(Y1, X2)), meet(Y1, join(join(meet(X0, Y1), meet(Y1, X2)), Y2))) -> join(meet(X0, Y1), meet(Y1, X2)) % 34.45/34.50 meet(join(meet(X0, Y2), meet(X2, Y2)), meet(join(Y1, join(meet(X0, Y2), meet(X2, Y2))), Y2)) -> join(meet(X0, Y2), meet(X2, Y2)) % 34.45/34.50 meet(join(meet(X0, Y2), meet(X2, Y2)), meet(join(join(meet(X0, Y2), meet(X2, Y2)), Y1), Y2)) -> join(meet(X0, Y2), meet(X2, Y2)) % 34.45/34.50 meet(join(meet(Y0, X1), Y0), Y0) -> Y0 % 34.45/34.50 meet(join(meet(Y1, X1), Y1), Y1) -> join(meet(Y1, X1), Y1) % 34.45/34.50 meet(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1))) -> join(meet(Y1, X1), Y1) % 34.45/34.50 meet(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), Y1)) -> meet(join(meet(Y1, X1), Y1), Y1) % 34.45/34.50 meet(join(meet(Y1, X1), meet(X2, Y1)), Y1) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(join(meet(Y1, X1), meet(X2, Y1)), join(Y1, join(meet(Y1, X1), meet(X2, Y1)))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(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)) % 34.45/34.50 meet(join(meet(Y1, X1), meet(X2, Y1)), meet(Y1, join(join(meet(Y1, X1), meet(X2, Y1)), Y2))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(join(meet(Y1, X1), meet(Y1, X2)), Y1) -> join(meet(Y1, X1), meet(Y1, X2)) % 34.45/34.50 meet(join(meet(Y1, X1), meet(Y1, X2)), meet(Y1, join(Y2, join(meet(Y1, X1), meet(Y1, X2))))) -> join(meet(Y1, X1), meet(Y1, X2)) % 34.45/34.50 meet(join(meet(Y1, X1), meet(Y1, X2)), meet(Y1, join(join(meet(Y1, X1), meet(Y1, X2)), Y2))) -> join(meet(Y1, X1), meet(Y1, X2)) % 34.45/34.50 meet(join(meet(Y2, X1), meet(X2, Y2)), meet(join(Y1, join(meet(Y2, X1), meet(X2, Y2))), Y2)) -> join(meet(Y2, X1), meet(X2, Y2)) % 34.45/34.50 meet(join(meet(Y2, X1), meet(X2, Y2)), meet(join(join(meet(Y2, X1), meet(X2, Y2)), Y1), Y2)) -> join(meet(Y2, X1), meet(X2, Y2)) % 34.45/34.50 meet(meet(X0, X1), join(X0, meet(X0, X1))) -> meet(X0, X1) % 34.45/34.50 meet(meet(X0, Y1), Y1) -> meet(X0, Y1) % 34.45/34.50 meet(meet(X0, Y1), meet(Y1, join(Y2, meet(X0, Y1)))) -> meet(X0, Y1) % 34.45/34.50 meet(meet(X0, Y1), meet(Y1, join(meet(X0, Y1), Y2))) -> meet(X0, Y1) % 34.45/34.50 meet(meet(X0, join(X0, X1)), X0) -> meet(X0, join(X0, X1)) % 34.45/34.50 meet(meet(X0, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 meet(meet(X0, meet(X0, X0)), meet(X0, X0)) -> meet(X0, X0) % 34.45/34.50 meet(meet(X0, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 meet(meet(X1, Y1), meet(meet(X1, Y1), Y1)) -> meet(meet(X1, Y1), Y1) % 34.45/34.50 meet(meet(X1, Y2), meet(join(Y1, meet(X1, Y2)), Y2)) -> meet(X1, Y2) % 34.45/34.50 meet(meet(X1, Y2), meet(join(meet(X1, Y2), Y1), Y2)) -> meet(X1, Y2) % 34.45/34.50 meet(meet(X1, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 meet(meet(X1, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1) % 34.45/34.50 meet(meet(Y0, X0), meet(Y0, join(X0, X0))) -> meet(Y0, join(X0, X0)) % 34.45/34.50 meet(meet(Y0, Y0), meet(Y0, join(X0, Y0))) -> meet(Y0, join(X0, Y0)) % 34.45/34.50 meet(meet(Y0, Y0), meet(Y0, join(Y0, X1))) -> meet(Y0, join(Y0, X1)) % 34.45/34.50 meet(meet(Y0, Y2), meet(Y2, Y0)) -> meet(Y2, Y0) % 34.45/34.50 meet(meet(Y0, join(Y2, Y0)), Y0) -> Y0 % 34.45/34.50 meet(meet(Y1, X1), Y1) -> meet(Y1, X1) % 34.45/34.50 meet(meet(Y1, X1), meet(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1) % 34.45/34.50 meet(meet(Y1, X1), meet(Y1, join(meet(Y1, X1), Y2))) -> meet(Y1, X1) % 34.45/34.50 meet(meet(Y1, join(Y1, Y1)), join(Y1, Y1)) -> join(Y1, Y1) % 34.45/34.50 meet(meet(Y1, join(Y1, meet(X1, Y1))), join(Y1, meet(X1, Y1))) -> join(Y1, meet(X1, Y1)) % 34.45/34.50 meet(meet(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1)))), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 meet(meet(Y1, join(Y2, join(meet(X0, Y1), meet(Y1, X2)))), join(meet(X0, Y1), meet(Y1, X2))) -> join(meet(X0, Y1), meet(Y1, X2)) % 34.45/34.50 meet(meet(Y1, join(Y2, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 meet(meet(Y1, join(Y2, join(meet(Y1, X1), meet(X2, Y1)))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(meet(Y1, join(Y2, join(meet(Y1, X1), meet(Y1, X2)))), join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2)) % 34.45/34.50 meet(meet(Y1, join(join(meet(X0, Y1), meet(X2, Y1)), Y2)), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 meet(meet(Y1, join(join(meet(X0, Y1), meet(Y1, X2)), Y2)), join(meet(X0, Y1), meet(Y1, X2))) -> join(meet(X0, Y1), meet(Y1, X2)) % 34.45/34.50 meet(meet(Y1, join(join(meet(Y1, X1), meet(X2, Y1)), Y2)), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(meet(Y1, join(join(meet(Y1, X1), meet(Y1, X2)), Y2)), join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2)) % 34.45/34.50 meet(meet(Y1, join(meet(X0, Y1), Y2)), meet(X0, Y1)) -> meet(X0, Y1) % 34.45/34.50 meet(meet(Y1, join(meet(X0, Y1), meet(X2, Y1))), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1)) % 34.45/34.50 meet(meet(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1) % 34.45/34.50 meet(meet(Y1, join(meet(Y1, X1), Y2)), meet(Y1, X1)) -> meet(Y1, X1) % 34.45/34.50 meet(meet(Y1, join(meet(Y1, X1), meet(X2, Y1))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1)) % 34.45/34.50 meet(meet(Y1, meet(X1, Y1)), Y1) -> meet(Y1, meet(X1, Y1)) % 34.45/34.50 meet(meet(Y2, X1), meet(join(Y1, meet(Y2, X1)), Y2)) -> meet(Y2, X1) % 34.45/34.50 meet(meet(Y2, X1), meet(join(meet(Y2, X1), Y1), Y2)) -> meet(Y2, X1) % 34.45/34.50 meet(meet(join(A, B), join(C, A)), A) -> A % 34.45/34.50 meet(meet(join(X1, Y0), join(Y0, Y2)), Y0) -> Y0 % 34.45/34.50 meet(meet(join(X1, Y0), join(Y2, Y0)), Y0) -> Y0 % 34.45/34.50 meet(meet(join(Y0, Y1), Y0), Y0) -> Y0 % 34.45/34.50 meet(meet(join(Y0, Y1), join(Y0, X1)), Y0) -> Y0 % 34.45/34.50 meet(meet(join(Y0, join(meet(X0, Y2), meet(X2, Y2))), Y2), join(meet(X0, Y2), meet(X2, Y2))) -> join(meet(X0, Y2), meet(X2, Y2)) % 34.45/34.50 meet(meet(join(Y0, join(meet(Y2, X1), meet(X2, Y2))), Y2), join(meet(Y2, X1), meet(X2, Y2))) -> join(meet(Y2, X1), meet(X2, Y2)) % 34.45/34.50 meet(meet(join(Y0, meet(X1, Y2)), Y2), meet(X1, Y2)) -> meet(X1, Y2) % 34.45/34.50 meet(meet(join(Y0, meet(Y2, X1)), Y2), meet(Y2, X1)) -> meet(Y2, X1) % 34.45/34.50 meet(meet(join(Y2, X1), Y2), meet(Y2, join(Y2, X1))) -> meet(Y2, join(Y2, X1)) % 34.45/34.50 meet(meet(join(join(X0, X0), Y1), X0), join(X0, X0)) -> join(X0, X0) % 34.45/34.50 meet(meet(join(join(meet(X1, Y2), meet(X2, Y2)), Y1), Y2), join(meet(X1, Y2), meet(X2, Y2))) -> join(meet(X1, Y2), meet(X2, Y2)) % 34.45/34.50 meet(meet(join(join(meet(X1, Y2), meet(Y2, X2)), Y1), Y2), join(meet(X1, Y2), meet(Y2, X2))) -> join(meet(X1, Y2), meet(Y2, X2)) % 34.45/34.50 meet(meet(join(join(meet(Y2, X1), meet(X2, Y2)), Y1), Y2), join(meet(Y2, X1), meet(X2, Y2))) -> join(meet(Y2, X1), meet(X2, Y2)) % 34.45/34.50 meet(meet(join(join(meet(Y2, X1), meet(Y2, X2)), Y1), Y2), join(meet(Y2, X1), meet(Y2, X2))) -> join(meet(Y2, X1), meet(Y2, X2)) % 34.45/34.50 meet(meet(join(meet(X0, join(X0, X1)), Y1), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1)) % 34.45/34.50 meet(meet(join(meet(X1, Y2), Y1), Y2), meet(X1, Y2)) -> meet(X1, Y2) % 34.45/34.50 meet(meet(join(meet(X1, join(X0, X0)), Y1), X0), meet(X1, join(X0, X0))) -> meet(X1, join(X0, X0)) % 34.45/34.50 meet(meet(join(meet(X1, join(X0, X1)), Y1), X1), meet(X1, join(X0, X1))) -> meet(X1, join(X0, X1)) % 34.45/34.50 meet(meet(join(meet(Y1, X1), Y1), Y1), Y1) -> meet(join(meet(Y1, X1), Y1), Y1) % 34.45/34.50 meet(meet(join(meet(Y2, X1), Y1), Y2), meet(Y2, X1)) -> meet(Y2, X1) % 34.45/34.50 meet(meet(meet(X0, X0), meet(X0, X0)), meet(meet(X0, X0), X0)) -> meet(meet(X0, X0), X0) % 34.45/34.50 meet(meet(meet(X0, X1), meet(X0, X1)), meet(meet(X0, X1), X0)) -> meet(meet(X0, X1), X0) % 34.45/34.50 meet(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1)) % 34.45/34.50 meet(meet(meet(X1, Y1), Y1), meet(X1, Y1)) -> meet(X1, Y1) % 34.45/34.50 true__ -> false__ % 34.45/34.50 with the LPO induced by % 34.45/34.50 b > a > f1 > meet > join > true__ > false__ % 34.45/34.50 % 34.45/34.50 % SZS output end Proof % 34.45/34.50 %------------------------------------------------------------------------------