%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n010.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 06:04:19 EDT 2022 % Result : Unsatisfiable 21.54s 21.48s % Output : Proof 21.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.33 % Computer : n010.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 29 21:05:49 EDT 2022 % 0.12/0.34 % CPUTime : % 21.54/21.48 % SZS status Unsatisfiable % 21.54/21.48 % SZS output start Proof % 21.54/21.48 The input problem is unsatisfiable because % 21.54/21.48 % 21.54/21.48 [1] the following set of Horn clauses is unsatisfiable: % 21.54/21.48 % 21.54/21.48 meet(X, X) = X % 21.54/21.48 join(X, X) = X % 21.54/21.48 meet(X, join(X, Y)) = X % 21.54/21.48 join(X, meet(X, Y)) = X % 21.54/21.48 meet(X, Y) = meet(Y, X) % 21.54/21.48 join(X, Y) = join(Y, X) % 21.54/21.48 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 21.54/21.48 join(join(X, Y), Z) = join(X, join(Y, Z)) % 21.54/21.48 complement(join(X, Y)) = meet(complement(X), complement(Y)) % 21.54/21.48 complement(meet(X, Y)) = join(complement(X), complement(Y)) % 21.54/21.48 join(complement(X), X) = n1 % 21.54/21.48 meet(complement(X), X) = n0 % 21.54/21.48 complement(complement(X)) = X % 21.54/21.48 join(X, meet(Y, join(X, Z))) = meet(join(X, Y), join(X, Z)) % 21.54/21.48 join(a, meet(complement(a), join(a, b))) = join(a, b) ==> \bottom % 21.54/21.48 % 21.54/21.48 This holds because % 21.54/21.48 % 21.54/21.48 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 21.54/21.48 % 21.54/21.48 E: % 21.54/21.48 complement(complement(X)) = X % 21.54/21.48 complement(join(X, Y)) = meet(complement(X), complement(Y)) % 21.54/21.48 complement(meet(X, Y)) = join(complement(X), complement(Y)) % 21.54/21.48 f1(join(a, b)) = false__ % 21.54/21.48 f1(join(a, meet(complement(a), join(a, b)))) = true__ % 21.54/21.48 join(X, X) = X % 21.54/21.48 join(X, Y) = join(Y, X) % 21.54/21.48 join(X, meet(X, Y)) = X % 21.54/21.48 join(X, meet(Y, join(X, Z))) = meet(join(X, Y), join(X, Z)) % 21.54/21.48 join(complement(X), X) = n1 % 21.54/21.48 join(join(X, Y), Z) = join(X, join(Y, Z)) % 21.54/21.48 meet(X, X) = X % 21.54/21.48 meet(X, Y) = meet(Y, X) % 21.54/21.48 meet(X, join(X, Y)) = X % 21.54/21.48 meet(complement(X), X) = n0 % 21.54/21.48 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 21.54/21.48 G: % 21.54/21.48 true__ = false__ % 21.54/21.48 % 21.54/21.48 This holds because % 21.54/21.48 % 21.54/21.48 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 21.54/21.48 % 21.54/21.48 complement(n0) = join(Y1, complement(Y1)) % 21.54/21.48 complement(n1) = meet(Y1, complement(Y1)) % 21.54/21.48 join(X, Y) = join(Y, X) % 21.54/21.48 join(Y0, Y1) = join(Y1, join(meet(X1, Y1), Y0)) % 21.54/21.48 join(Y0, Y1) = join(Y1, join(meet(X1, meet(X2, Y1)), Y0)) % 21.54/21.48 join(Y0, Y1) = join(Y1, join(meet(X1, meet(Y1, X2)), Y0)) % 21.54/21.48 join(Y0, complement(X0)) = join(n0, join(complement(X0), Y0)) % 21.54/21.48 join(Y0, join(X2, Y0)) = join(Y0, join(meet(X1, Y0), X2)) % 21.54/21.48 join(Y0, join(Y1, complement(Y0))) = join(n1, Y1) % 21.54/21.48 join(Y0, n1) = join(Y2, join(complement(Y2), Y0)) % 21.54/21.48 join(Y1, join(Y0, Y2)) = join(Y0, join(Y1, Y2)) % 21.54/21.48 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 21.54/21.48 join(false__, join(complement(false__), Y2)) = join(Y0, join(complement(Y0), Y2)) % 21.54/21.48 join(false__, join(complement(false__), complement(X1))) = join(X0, join(complement(X0), complement(X1))) % 21.54/21.48 join(n1, join(complement(X0), X1)) = join(X0, join(complement(X0), X1)) % 21.54/21.48 meet(X, Y) = meet(Y, X) % 21.54/21.48 meet(Y0, Y1) = meet(Y1, meet(join(X1, Y1), Y0)) % 21.54/21.48 meet(Y0, Y1) = meet(Y1, meet(join(X1, join(X2, Y1)), Y0)) % 21.54/21.48 meet(Y0, Y1) = meet(Y1, meet(join(X1, join(Y1, X2)), Y0)) % 21.54/21.48 meet(Y0, complement(X0)) = meet(n1, meet(complement(X0), Y0)) % 21.54/21.48 meet(Y0, meet(X2, Y0)) = meet(Y0, meet(join(X1, Y0), X2)) % 21.54/21.48 meet(Y0, meet(Y1, complement(Y0))) = meet(n0, Y1) % 21.54/21.48 meet(Y0, n0) = meet(Y2, meet(complement(Y2), Y0)) % 21.54/21.48 meet(Y1, meet(Y0, Y2)) = meet(Y0, meet(Y1, Y2)) % 21.54/21.48 meet(Y2, meet(Y0, Y1)) = meet(Y0, meet(Y1, Y2)) % 21.54/21.48 meet(false__, meet(complement(false__), Y2)) = meet(Y0, meet(complement(Y0), Y2)) % 21.54/21.48 meet(false__, meet(complement(false__), complement(X1))) = meet(X0, meet(complement(X0), complement(X1))) % 21.54/21.48 meet(n0, meet(complement(X0), X1)) = meet(X0, meet(complement(X0), X1)) % 21.54/21.48 complement(complement(X)) -> X % 21.54/21.48 complement(join(X, Y)) -> meet(complement(X), complement(Y)) % 21.54/21.48 complement(meet(X, Y)) -> join(complement(X), complement(Y)) % 21.54/21.48 f1(join(a, b)) -> false__ % 21.54/21.48 f1(join(a, meet(complement(a), join(a, b)))) -> true__ % 21.54/21.48 f1(meet(join(a, complement(a)), join(a, b))) -> true__ % 21.54/21.48 join(X, X) -> X % 21.54/21.48 join(X, meet(X, Y)) -> X % 21.54/21.48 join(X, meet(Y, join(X, Z))) -> meet(join(X, Y), join(X, Z)) % 21.54/21.48 join(X0, complement(X0)) -> n1 % 21.54/21.48 join(X0, join(X1, join(Y1, meet(complement(X0), complement(X1))))) -> n1 % 21.54/21.48 join(X0, join(X1, join(meet(Y2, join(X0, X1)), complement(X0)))) -> n1 % 21.54/21.48 join(X0, join(X1, join(meet(complement(X0), complement(X1)), Y1))) -> join(n1, Y1) % 21.54/21.48 join(X0, join(X1, meet(Y1, join(X0, join(X1, Y2))))) -> meet(join(X0, join(X1, Y1)), join(X0, join(X1, Y2))) % 21.54/21.48 join(X0, join(X1, meet(complement(X0), complement(X1)))) -> n1 % 21.54/21.48 join(X0, join(complement(X0), Y1)) -> join(n1, Y1) % 21.54/21.48 join(X1, join(X0, meet(complement(X0), complement(X1)))) -> n1 % 21.54/21.48 join(Y0, join(X1, join(X0, meet(complement(Y0), meet(complement(X0), complement(X1)))))) -> n1 % 21.54/21.48 join(Y0, join(X1, join(complement(Y0), complement(Y1)))) -> n1 % 21.54/21.48 join(Y0, join(X1, join(meet(false__, join(Y0, X1)), meet(complement(Y0), complement(X1))))) -> n1 % 21.54/21.48 join(Y0, join(Y1, join(Y0, Y1))) -> join(Y0, Y1) % 21.54/21.48 join(Y0, join(Y1, join(meet(X2, Y1), Y0))) -> join(Y0, Y1) % 21.54/21.48 join(Y0, join(Y1, join(meet(X2, Y1), complement(Y0)))) -> n1 % 21.54/21.48 join(Y0, join(Y1, meet(X1, meet(X2, join(Y0, Y1))))) -> join(Y0, Y1) % 21.54/21.48 join(Y0, join(Y1, meet(X1, meet(join(Y0, Y1), X2)))) -> join(Y0, Y1) % 21.54/21.48 join(Y0, join(Y1, meet(join(Y0, Y1), X1))) -> join(Y0, Y1) % 21.54/21.48 join(Y0, join(complement(X0), meet(X0, complement(Y0)))) -> n1 % 21.54/21.48 join(Y0, join(complement(X0), meet(complement(Y0), X0))) -> n1 % 21.54/21.48 join(Y0, join(complement(X1), Y0)) -> join(Y0, complement(X1)) % 21.54/21.48 join(Y0, join(complement(Y0), X1)) -> join(n1, join(Y0, X1)) % 21.54/21.48 join(Y0, join(complement(Y0), complement(Y1))) -> join(Y0, n1) % 21.54/21.48 join(Y0, join(meet(X1, meet(X2, Y0)), Y2)) -> join(Y0, Y2) % 21.54/21.48 join(Y0, join(meet(X1, meet(Y0, X2)), Y2)) -> join(Y0, Y2) % 21.54/21.48 join(Y0, join(meet(Y0, X1), Y2)) -> join(Y0, Y2) % 21.54/21.48 join(Y0, join(meet(complement(Y0), X0), complement(X0))) -> n1 % 21.54/21.48 join(Y0, join(meet(false__, Y0), join(complement(Y0), complement(Y2)))) -> n1 % 21.54/21.48 join(Y0, join(meet(false__, Y0), join(complement(Y2), complement(Y0)))) -> n1 % 21.54/21.48 join(Y0, join(n0, Y2)) -> join(Y0, Y2) % 21.54/21.48 join(Y0, meet(X0, meet(X1, join(Y0, Y2)))) -> meet(join(Y0, meet(X0, X1)), join(Y0, Y2)) % 21.54/21.48 join(Y0, meet(X1, meet(X2, Y0))) -> Y0 % 21.54/21.48 join(Y0, meet(X1, meet(Y0, X2))) -> Y0 % 21.54/21.48 join(Y0, meet(Y1, Y0)) -> Y0 % 21.54/21.48 join(Y0, meet(Y1, join(Y2, Y0))) -> meet(join(Y0, Y1), join(Y0, Y2)) % 21.54/21.48 join(Y0, meet(Y1, meet(X1, meet(X2, Y0)))) -> Y0 % 21.54/21.48 join(Y0, meet(Y1, meet(X1, meet(Y0, X2)))) -> Y0 % 21.54/21.48 join(Y0, meet(Y1, meet(Y2, meet(join(X2, Y2), Y0)))) -> Y0 % 21.54/21.48 join(Y0, meet(Y1, meet(join(Y0, X1), join(Y0, X2)))) -> meet(join(Y0, Y1), meet(join(Y0, X1), join(Y0, X2))) % 21.54/21.48 join(Y0, meet(join(Y0, Y2), Y1)) -> meet(join(Y0, Y1), join(Y0, Y2)) % 21.54/21.48 join(Y0, n0) -> Y0 % 21.54/21.48 join(Y0, n1) -> n1 % 21.54/21.48 join(Y1, join(X1, join(X0, meet(complement(X0), meet(complement(X1), complement(Y1)))))) -> n1 % 21.54/21.48 join(Y1, join(X1, join(complement(Y1), Y0))) -> n1 % 21.54/21.48 join(Y1, join(Y0, join(X1, complement(Y1)))) -> n1 % 21.54/21.48 join(Y1, join(Y0, meet(X1, Y1))) -> join(Y0, Y1) % 21.54/21.48 join(Y1, join(Y0, meet(X1, meet(X2, Y1)))) -> join(Y0, Y1) % 21.54/21.48 join(Y1, join(Y0, meet(X1, meet(Y1, X2)))) -> join(Y0, Y1) % 21.54/21.48 join(Y1, join(Y0, meet(Y1, X1))) -> join(Y0, Y1) % 21.54/21.48 join(Y1, join(Y1, Y2)) -> join(Y1, Y2) % 21.54/21.48 join(Y1, join(meet(X0, X1), meet(join(complement(X0), complement(X1)), complement(Y1)))) -> n1 % 21.54/21.48 join(Y1, join(meet(X0, complement(Y1)), complement(X0))) -> n1 % 21.54/21.48 join(Y1, join(meet(Y2, Y1), Y0)) -> join(Y1, Y0) % 21.54/21.48 join(Y1, join(meet(false__, Y1), X1)) -> join(Y1, X1) % 21.54/21.48 join(Y1, join(meet(false__, Y1), join(X1, join(X2, Y1)))) -> join(X1, join(X2, Y1)) % 21.54/21.48 join(Y1, join(meet(false__, Y1), join(X1, join(Y1, X2)))) -> join(X1, join(Y1, X2)) % 21.54/21.48 join(Y1, join(meet(false__, Y1), meet(join(Y1, X1), join(Y1, X2)))) -> meet(join(Y1, X1), join(Y1, X2)) % 21.54/21.48 join(Y1, join(n1, meet(X0, meet(complement(X0), complement(Y1))))) -> n1 % 21.54/21.48 join(Y2, join(Y0, complement(Y2))) -> join(Y0, n1) % 21.54/21.48 join(Y2, join(meet(false__, Y2), meet(X1, join(Y2, X2)))) -> meet(join(Y2, X1), join(Y2, X2)) % 21.54/21.48 join(complement(X), X) -> n1 % 21.54/21.48 join(complement(X0), join(Y1, meet(X0, complement(Y1)))) -> n1 % 21.54/21.48 join(complement(X0), join(Y1, meet(complement(Y1), X0))) -> n1 % 21.54/21.48 join(complement(X0), join(meet(X0, Y1), complement(Y1))) -> n1 % 21.54/21.48 join(complement(X0), join(meet(Y1, X0), complement(Y1))) -> n1 % 21.54/21.48 join(complement(X0), meet(n0, X1)) -> complement(X0) % 21.54/21.48 join(complement(Y0), join(Y1, join(meet(X2, Y1), Y0))) -> n1 % 21.54/21.48 join(complement(Y1), join(Y1, Y2)) -> join(n1, Y2) % 21.54/21.48 join(complement(Y2), meet(Y1, n1)) -> meet(join(Y2, complement(Y2)), join(complement(Y2), Y1)) % 21.54/21.48 join(false__, join(complement(Y0), complement(false__))) -> join(n1, complement(Y0)) % 21.54/21.48 join(false__, join(complement(false__), complement(X0))) -> join(n1, complement(X0)) % 21.54/21.48 join(join(X, Y), Z) -> join(X, join(Y, Z)) % 21.54/21.49 join(meet(X0, X1), join(Y0, meet(complement(Y0), join(complement(X0), complement(X1))))) -> n1 % 21.54/21.49 join(meet(X0, X1), join(Y1, join(complement(X0), complement(X1)))) -> n1 % 21.54/21.49 join(meet(X0, X1), join(complement(X0), complement(X1))) -> n1 % 21.54/21.49 join(meet(X0, X1), join(complement(X0), join(complement(X1), Y1))) -> join(n1, Y1) % 21.54/21.49 join(meet(X0, X1), join(meet(false__, meet(X0, X1)), join(complement(X0), complement(X1)))) -> n1 % 21.54/21.49 join(meet(X0, X1), meet(X0, meet(X1, Y1))) -> meet(X0, X1) % 21.54/21.49 join(meet(X0, X1), meet(n0, X1)) -> meet(X0, X1) % 21.54/21.49 join(meet(X1, X2), meet(X1, meet(Y1, X2))) -> meet(X1, X2) % 21.54/21.49 join(meet(X1, X2), meet(X2, meet(Y1, X1))) -> meet(X1, X2) % 21.54/21.49 join(meet(X1, X2), meet(Y1, meet(X1, meet(X2, Y2)))) -> meet(X1, X2) % 21.54/21.49 join(meet(X1, X2), meet(Y1, meet(X1, meet(Y2, X2)))) -> meet(X1, X2) % 21.54/21.49 join(meet(X1, X2), meet(Y1, meet(X2, meet(Y2, X1)))) -> meet(X1, X2) % 21.54/21.49 join(meet(X1, Y1), meet(X1, join(Y1, X2))) -> meet(X1, join(Y1, X2)) % 21.54/21.49 join(meet(X1, join(Y2, X2)), meet(Y1, meet(X1, Y2))) -> meet(X1, join(Y2, X2)) % 21.54/21.49 join(meet(Y1, X2), join(meet(false__, meet(Y1, X2)), meet(join(Y1, X1), X2))) -> meet(join(Y1, X1), X2) % 21.54/21.49 join(meet(Y1, Y0), join(complement(Y0), complement(Y1))) -> n1 % 21.54/21.49 join(meet(complement(X0), X1), meet(X1, complement(X0))) -> meet(complement(X0), X1) % 21.54/21.49 join(meet(complement(X0), X1), meet(Y1, meet(X1, complement(X0)))) -> meet(complement(X0), X1) % 21.54/21.49 join(meet(complement(X0), complement(X1)), join(X0, X1)) -> n1 % 21.54/21.49 join(meet(complement(Y0), complement(X1)), meet(complement(Y0), complement(X2))) -> meet(complement(Y0), join(complement(X1), meet(complement(Y0), complement(X2)))) % 21.54/21.49 join(meet(join(X1, Y1), X2), meet(X2, Y1)) -> meet(join(X1, Y1), X2) % 21.54/21.49 join(meet(join(X1, Y2), X2), meet(Y1, meet(X2, Y2))) -> meet(join(X1, Y2), X2) % 21.54/21.49 join(meet(join(Y0, X1), join(Y0, X2)), Y2) -> join(Y0, join(meet(X1, join(Y0, X2)), Y2)) % 21.54/21.49 join(meet(join(Y2, X1), X2), meet(Y1, meet(Y2, X2))) -> meet(join(Y2, X1), X2) % 21.54/21.49 join(n0, X0) -> X0 % 21.54/21.49 join(n0, complement(Y1)) -> complement(Y1) % 21.54/21.49 join(n0, join(X0, join(complement(X0), Y1))) -> join(n1, Y1) % 21.54/21.49 join(n0, join(Y0, complement(X0))) -> join(Y0, complement(X0)) % 21.54/21.49 join(n0, join(complement(X0), complement(X1))) -> join(complement(X0), complement(X1)) % 21.54/21.49 join(n0, join(complement(Y1), Y2)) -> join(complement(Y1), Y2) % 21.54/21.49 join(n0, join(meet(Y0, n1), complement(Y0))) -> n1 % 21.54/21.49 join(n0, join(meet(n1, Y1), complement(Y1))) -> n1 % 21.54/21.49 join(n0, meet(Y1, meet(complement(Y1), Y2))) -> n0 % 21.54/21.49 join(n0, meet(complement(X0), complement(X1))) -> meet(complement(X0), complement(X1)) % 21.54/21.49 join(n1, Y1) -> n1 % 21.54/21.49 join(n1, complement(Y1)) -> n1 % 21.54/21.49 join(n1, join(Y0, meet(n0, complement(Y0)))) -> n1 % 21.54/21.49 join(n1, join(n0, Y1)) -> join(n1, Y1) % 21.54/21.49 join(n1, meet(Y0, X1)) -> n1 % 21.54/21.49 join(n1, n0) -> n1 % 21.54/21.49 meet(X, X) -> X % 21.54/21.49 meet(X, join(X, Y)) -> X % 21.54/21.49 meet(X0, complement(X0)) -> n0 % 21.54/21.49 meet(X0, meet(X1, join(complement(X0), complement(X1)))) -> n0 % 21.54/21.49 meet(X0, meet(X1, meet(Y1, join(complement(X0), complement(X1))))) -> n0 % 21.54/21.49 meet(X0, meet(X1, meet(join(Y2, meet(X0, X1)), complement(X0)))) -> n0 % 21.54/21.49 meet(X0, meet(X1, meet(join(complement(X0), complement(X1)), Y1))) -> meet(n0, Y1) % 21.54/21.49 meet(X0, meet(X1, meet(join(false__, meet(X0, X1)), join(complement(X0), complement(X1))))) -> n0 % 21.54/21.49 meet(X0, meet(complement(X0), Y1)) -> meet(n0, Y1) % 21.54/21.49 meet(X0, meet(complement(X0), meet(join(n1, Y1), complement(Y1)))) -> n0 % 21.54/21.49 meet(X0, meet(complement(Y1), join(Y1, complement(X0)))) -> n0 % 21.54/21.49 meet(X0, meet(complement(Y1), join(complement(X0), Y1))) -> n0 % 21.54/21.49 meet(X0, meet(join(Y0, complement(X0)), complement(Y0))) -> n0 % 21.54/21.49 meet(X0, meet(join(complement(X0), Y1), complement(Y1))) -> n0 % 21.54/21.49 meet(Y0, join(X1, join(X2, Y0))) -> Y0 % 21.54/21.49 meet(Y0, join(X1, join(Y0, X2))) -> Y0 % 21.54/21.49 meet(Y0, join(Y1, Y0)) -> Y0 % 21.54/21.49 meet(Y0, join(Y1, join(X1, join(X2, Y0)))) -> Y0 % 21.54/21.49 meet(Y0, join(Y1, join(X1, join(Y0, X2)))) -> Y0 % 21.54/21.49 meet(Y0, join(Y1, join(Y2, join(meet(X2, Y2), Y0)))) -> Y0 % 21.54/21.49 meet(Y0, meet(X1, meet(complement(Y0), complement(Y1)))) -> n0 % 21.54/21.49 meet(Y0, meet(Y1, join(X1, join(X2, meet(Y0, Y1))))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y0, meet(Y1, join(X1, join(meet(Y0, Y1), X2)))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y0, meet(Y1, join(X1, meet(Y0, Y1)))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y0, meet(Y1, join(meet(Y0, Y1), X1))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y0, meet(Y1, meet(Y0, Y1))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y0, meet(Y1, meet(join(X2, Y1), Y0))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y0, meet(Y1, meet(join(X2, Y1), complement(Y0)))) -> n0 % 21.54/21.49 meet(Y0, meet(Y2, join(Y0, Y1))) -> meet(Y0, Y2) % 21.54/21.49 meet(Y0, meet(complement(X1), Y0)) -> meet(Y0, complement(X1)) % 21.54/21.49 meet(Y0, meet(complement(Y0), X1)) -> meet(n0, meet(Y0, X1)) % 21.54/21.49 meet(Y0, meet(complement(Y0), complement(Y1))) -> meet(Y0, n0) % 21.54/21.49 meet(Y0, meet(false__, meet(complement(Y0), complement(false__)))) -> n0 % 21.54/21.49 meet(Y0, meet(join(X1, join(X2, Y0)), Y2)) -> meet(Y0, Y2) % 21.54/21.49 meet(Y0, meet(join(X1, join(Y0, X2)), Y2)) -> meet(Y0, Y2) % 21.54/21.49 meet(Y0, meet(join(Y0, X1), Y2)) -> meet(Y0, Y2) % 21.54/21.49 meet(Y0, meet(join(Y0, X1), join(Y0, X2))) -> Y0 % 21.54/21.49 meet(Y0, meet(join(false__, Y0), meet(complement(Y0), complement(Y2)))) -> n0 % 21.54/21.49 meet(Y0, meet(join(false__, Y0), meet(complement(Y2), complement(Y0)))) -> n0 % 21.54/21.49 meet(Y0, meet(n1, Y2)) -> meet(Y0, Y2) % 21.54/21.49 meet(Y0, meet(n1, join(Y0, Y2))) -> Y0 % 21.54/21.49 meet(Y0, n0) -> n0 % 21.54/21.49 meet(Y0, n1) -> Y0 % 21.54/21.49 meet(Y1, meet(X1, meet(complement(Y1), Y0))) -> n0 % 21.54/21.49 meet(Y1, meet(Y0, join(X1, Y1))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y1, meet(Y0, join(X1, join(X2, Y1)))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y1, meet(Y0, join(X1, join(Y1, X2)))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y1, meet(Y0, join(Y1, X1))) -> meet(Y0, Y1) % 21.54/21.49 meet(Y1, meet(Y0, meet(X1, complement(Y1)))) -> n0 % 21.54/21.49 meet(Y1, meet(Y1, Y2)) -> meet(Y1, Y2) % 21.54/21.49 meet(Y1, meet(complement(Y1), join(n0, Y2))) -> n0 % 21.54/21.49 meet(Y1, meet(join(Y2, Y1), Y0)) -> meet(Y1, Y0) % 21.54/21.49 meet(Y2, meet(Y0, complement(Y2))) -> meet(Y0, n0) % 21.54/21.49 meet(Y2, meet(Y1, join(complement(Y1), complement(Y2)))) -> n0 % 21.54/21.49 meet(complement(X), X) -> n0 % 21.54/21.49 meet(complement(X0), join(n1, X1)) -> complement(X0) % 21.54/21.49 meet(complement(X0), meet(Y1, complement(X0))) -> meet(Y1, complement(X0)) % 21.54/21.49 meet(complement(X0), meet(complement(X1), join(X0, X1))) -> n0 % 21.54/21.49 meet(complement(X0), meet(complement(X1), meet(join(X0, X1), Y1))) -> meet(n0, Y1) % 21.54/21.49 meet(complement(Y0), meet(X0, join(Y0, complement(X0)))) -> n0 % 21.54/21.49 meet(complement(Y0), meet(X0, join(complement(X0), Y0))) -> n0 % 21.54/21.49 meet(complement(Y0), meet(X0, meet(join(false__, X0), join(Y0, complement(X0))))) -> n0 % 21.54/21.49 meet(complement(Y0), meet(X0, meet(join(false__, X0), join(complement(X0), Y0)))) -> n0 % 21.54/21.49 meet(complement(Y0), meet(Y1, meet(join(X2, Y1), Y0))) -> n0 % 21.54/21.49 meet(complement(Y0), meet(complement(Y1), join(Y1, Y0))) -> n0 % 21.54/21.49 meet(complement(Y0), meet(join(Y0, Y1), complement(Y1))) -> n0 % 21.54/21.49 meet(complement(Y1), meet(Y1, Y2)) -> meet(n0, Y2) % 21.54/21.49 meet(complement(Y1), meet(join(Y0, Y1), complement(Y0))) -> n0 % 21.54/21.49 meet(false__, meet(complement(Y0), complement(false__))) -> meet(n0, complement(Y0)) % 21.54/21.49 meet(false__, meet(complement(false__), complement(X0))) -> meet(n0, complement(X0)) % 21.54/21.49 meet(join(X0, X1), join(X0, join(X1, Y1))) -> join(X0, X1) % 21.54/21.49 meet(join(X0, X1), join(n1, X1)) -> join(X0, X1) % 21.54/21.49 meet(join(X0, X1), meet(Y1, meet(complement(X0), complement(X1)))) -> n0 % 21.54/21.49 meet(join(X0, X1), meet(complement(X0), complement(X1))) -> n0 % 21.54/21.49 meet(join(X0, X1), meet(complement(X0), meet(complement(X1), Y1))) -> n0 % 21.54/21.49 meet(join(X1, X2), join(X1, join(Y1, X2))) -> join(X1, X2) % 21.54/21.49 meet(join(X1, X2), join(Y1, join(X1, join(X2, Y2)))) -> join(X1, X2) % 21.54/21.49 meet(join(X1, X2), join(Y1, join(X1, join(Y2, X2)))) -> join(X1, X2) % 21.54/21.49 meet(join(X1, X2), join(Y1, join(X2, join(Y2, X1)))) -> join(X1, X2) % 21.54/21.49 meet(join(X1, Y1), join(X1, meet(Y1, X2))) -> join(X1, meet(Y1, X2)) % 21.54/21.49 meet(join(Y0, Y2), join(Y0, join(Y0, Y2))) -> join(Y0, join(Y0, Y2)) % 21.54/21.49 meet(join(Y0, Y2), join(Y0, meet(complement(Y0), complement(Y2)))) -> join(Y0, n0) % 21.54/21.49 meet(join(Y0, n1), join(Y0, complement(Y2))) -> join(Y0, complement(Y2)) % 21.54/21.49 meet(join(Y1, X2), meet(join(false__, join(Y1, X2)), join(meet(Y1, X1), X2))) -> join(meet(Y1, X1), X2) % 21.54/21.49 meet(join(complement(X0), X1), join(X1, complement(X0))) -> join(complement(X0), X1) % 21.54/21.49 meet(join(complement(X0), X1), join(Y1, join(X1, complement(X0)))) -> join(complement(X0), X1) % 21.54/21.49 meet(join(meet(X1, Y1), X2), join(X2, Y1)) -> join(meet(X1, Y1), X2) % 21.54/21.49 meet(join(meet(X1, Y2), X2), join(Y1, join(X2, Y2))) -> join(meet(X1, Y2), X2) % 21.54/21.49 meet(join(meet(Y2, X1), X2), join(Y1, join(Y2, X2))) -> join(meet(Y2, X1), X2) % 21.54/21.49 meet(meet(X, Y), Z) -> meet(X, meet(Y, Z)) % 21.54/21.49 meet(n0, Y1) -> n0 % 21.54/21.49 meet(n0, complement(Y1)) -> n0 % 21.54/21.49 meet(n0, join(Y0, X1)) -> n0 % 21.54/21.49 meet(n0, meet(join(Y0, n1), complement(Y0))) -> n0 % 21.54/21.49 meet(n1, X0) -> X0 % 21.54/21.49 meet(n1, complement(Y1)) -> complement(Y1) % 21.54/21.49 meet(n1, join(Y1, join(complement(Y1), Y2))) -> n1 % 21.54/21.49 meet(n1, join(Y1, meet(complement(Y1), complement(Y2)))) -> join(Y1, meet(complement(Y1), complement(Y2))) % 21.54/21.49 meet(n1, join(complement(X0), complement(X1))) -> join(complement(X0), complement(X1)) % 21.54/21.49 meet(n1, meet(X0, meet(complement(X0), Y1))) -> meet(n0, Y1) % 21.54/21.49 meet(n1, meet(Y0, complement(X0))) -> meet(Y0, complement(X0)) % 21.54/21.49 meet(n1, meet(complement(X0), complement(X1))) -> meet(complement(X0), complement(X1)) % 21.54/21.49 meet(n1, meet(complement(Y1), Y2)) -> meet(complement(Y1), Y2) % 21.54/21.49 meet(n1, meet(join(Y0, n0), complement(Y0))) -> n0 % 21.54/21.49 meet(n1, meet(join(n0, Y1), complement(Y1))) -> n0 % 21.54/21.49 meet(n1, meet(n0, Y1)) -> meet(n0, Y1) % 21.54/21.49 meet(n1, n0) -> n0 % 21.54/21.49 true__ -> false__ % 21.54/21.49 with the LPO induced by % 21.54/21.49 b > a > f1 > complement > join > meet > n0 > n1 > true__ > false__ % 21.54/21.49 % 21.54/21.49 % SZS output end Proof % 21.54/21.49 %------------------------------------------------------------------------------