%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT039-1 : TPTP v8.1.0. Released v2.4.0. % 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 06:04:16 EDT 2022 % Result : Unsatisfiable 31.05s 31.12s % Output : Proof 31.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : LAT039-1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n012.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 : Thu Jun 30 10:44:33 EDT 2022 % 0.12/0.33 % CPUTime : % 31.05/31.12 % SZS status Unsatisfiable % 31.05/31.12 % SZS output start Proof % 31.05/31.12 The input problem is unsatisfiable because % 31.05/31.12 % 31.05/31.12 [1] the following set of Horn clauses is unsatisfiable: % 31.05/31.12 % 31.05/31.12 meet(X, X) = X % 31.05/31.12 join(X, X) = X % 31.05/31.12 meet(X, join(X, Y)) = X % 31.05/31.12 join(X, meet(X, Y)) = X % 31.05/31.12 meet(X, Y) = meet(Y, X) % 31.05/31.12 join(X, Y) = join(Y, X) % 31.05/31.12 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 31.05/31.12 join(join(X, Y), Z) = join(X, join(Y, Z)) % 31.05/31.12 join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)) % 31.05/31.12 meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)) % 31.05/31.12 join(xx, yy) = yy % 31.05/31.12 join(xx, meet(yy, zz)) = meet(yy, join(xx, zz)) ==> \bottom % 31.05/31.12 % 31.05/31.12 This holds because % 31.05/31.12 % 31.05/31.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 31.05/31.12 % 31.05/31.12 E: % 31.05/31.12 f1(join(xx, meet(yy, zz))) = true__ % 31.05/31.12 f1(meet(yy, join(xx, zz))) = false__ % 31.05/31.12 join(X, X) = X % 31.05/31.12 join(X, Y) = join(Y, X) % 31.05/31.12 join(X, meet(X, Y)) = X % 31.05/31.12 join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)) % 31.05/31.12 join(join(X, Y), Z) = join(X, join(Y, Z)) % 31.05/31.12 join(xx, yy) = yy % 31.05/31.12 meet(X, X) = X % 31.05/31.12 meet(X, Y) = meet(Y, X) % 31.05/31.12 meet(X, join(X, Y)) = X % 31.05/31.12 meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)) % 31.05/31.12 meet(meet(X, Y), Z) = meet(X, meet(Y, Z)) % 31.05/31.12 G: % 31.05/31.12 true__ = false__ % 31.05/31.12 % 31.05/31.12 This holds because % 31.05/31.12 % 31.05/31.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 31.05/31.12 % 31.05/31.12 join(X, Y) = join(Y, X) % 31.05/31.12 join(X2, join(Y0, Y1)) = join(Y0, join(Y1, join(meet(X1, Y0), join(meet(X1, Y1), X2)))) % 31.05/31.12 join(Y0, Y1) = join(Y1, join(meet(X1, Y1), Y0)) % 31.05/31.12 join(Y0, Y1) = join(Y1, join(meet(X1, meet(Y1, X2)), Y0)) % 31.05/31.12 join(Y0, join(X1, join(meet(Y1, Y0), X2))) = join(X1, join(X2, Y0)) % 31.05/31.12 join(Y0, join(X2, join(meet(Y1, Y0), X1))) = join(X1, join(X2, Y0)) % 31.05/31.12 join(Y0, join(Y1, X1)) = join(Y1, join(X1, join(meet(Y1, X1), Y0))) % 31.05/31.12 join(Y0, join(Y1, join(meet(Y3, Y0), join(meet(Y3, Y1), meet(Y3, Y2))))) = join(Y0, join(Y1, meet(Y2, Y3))) % 31.05/31.12 join(Y0, join(Y2, yy)) = join(yy, join(Y2, Y0)) % 31.05/31.12 join(Y0, join(meet(Y2, Y0), meet(Y2, Y1))) = join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(Y0, join(meet(Y2, Y1), meet(Y2, Y0))) = join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(Y0, join(yy, X0)) = join(X0, join(yy, Y0)) % 31.05/31.12 join(Y0, join(yy, X0)) = join(xx, join(Y0, join(X0, yy))) % 31.05/31.12 join(Y0, meet(X0, yy)) = join(meet(X0, xx), join(Y0, meet(yy, X0))) % 31.05/31.12 join(Y0, meet(X0, yy)) = join(meet(X0, xx), join(meet(X0, yy), Y0)) % 31.05/31.12 join(Y0, meet(X0, yy)) = join(meet(X0, xx), join(meet(yy, X0), Y0)) % 31.05/31.12 join(Y0, meet(X0, yy)) = join(meet(yy, X0), join(Y0, meet(X0, xx))) % 31.05/31.12 join(Y0, yy) = join(yy, join(Y0, meet(xx, X0))) % 31.05/31.12 join(Y0, yy) = join(yy, join(meet(xx, X0), Y0)) % 31.05/31.12 join(Y1, join(Y0, Y2)) = join(Y0, join(Y1, Y2)) % 31.05/31.12 join(Y2, join(Y0, Y1)) = join(Y0, join(Y1, Y2)) % 31.05/31.12 join(meet(X0, X1), meet(join(X1, X2), X0)) = join(meet(X0, X1), meet(X0, X2)) % 31.05/31.12 join(meet(X0, meet(X1, xx)), meet(yy, meet(X0, X1))) = meet(X0, meet(X1, yy)) % 31.05/31.12 join(meet(X0, yy), Y2) = join(meet(X0, xx), join(meet(yy, X0), Y2)) % 31.05/31.12 join(meet(X1, X2), join(meet(X1, meet(X2, Y1)), Y2)) = join(Y2, meet(X1, X2)) % 31.05/31.12 join(meet(X1, X2), join(meet(X1, meet(Y1, X2)), Y2)) = join(Y2, meet(X1, X2)) % 31.05/31.12 join(meet(X1, X2), join(meet(X2, meet(Y1, X1)), Y2)) = join(Y2, meet(X1, X2)) % 31.05/31.12 join(meet(X1, meet(X2, Y0)), meet(Y0, Y2)) = meet(join(meet(X1, X2), Y2), Y0) % 31.05/31.12 join(meet(X1, meet(X2, xx)), meet(X1, meet(yy, X2))) = meet(X1, meet(X2, yy)) % 31.05/31.12 join(meet(X1, meet(X2, xx)), meet(X2, meet(yy, X1))) = meet(X1, meet(X2, yy)) % 31.05/31.12 join(meet(Y0, Y1), meet(X1, meet(X2, Y0))) = meet(join(Y1, X1), meet(join(Y1, X2), Y0)) % 31.05/31.12 join(meet(Y0, Y1), meet(Y2, Y0)) = meet(join(Y1, Y2), Y0) % 31.05/31.12 join(meet(Y0, meet(Y1, xx)), meet(Y0, meet(yy, Y1))) = meet(Y1, meet(Y0, yy)) % 31.05/31.12 join(meet(Y0, meet(Y1, xx)), meet(Y0, meet(yy, Y1))) = meet(Y1, meet(yy, Y0)) % 31.05/31.12 join(meet(Y0, meet(Y1, xx)), meet(Y0, meet(yy, Y1))) = meet(yy, meet(Y0, Y1)) % 31.05/31.12 join(meet(Y0, meet(Y2, X0)), meet(Y0, meet(Y2, X1))) = meet(join(X0, X1), meet(Y2, Y0)) % 31.05/31.12 join(meet(Y0, xx), meet(Y0, meet(X0, yy))) = join(meet(xx, meet(yy, Y0)), meet(yy, meet(Y0, X0))) % 31.05/31.12 join(meet(Y0, xx), meet(Y0, meet(X0, yy))) = meet(join(xx, X0), meet(Y0, yy)) % 31.05/31.12 join(meet(Y0, xx), meet(Y0, meet(X0, yy))) = meet(join(xx, X0), meet(yy, Y0)) % 31.05/31.12 join(meet(Y0, xx), meet(yy, Y0)) = meet(Y0, yy) % 31.05/31.12 join(meet(Y1, X1), Y2) = join(Y2, meet(X1, meet(Y1, X1))) % 31.05/31.12 join(meet(Y1, Y0), meet(Y0, Y2)) = meet(join(Y1, Y2), Y0) % 31.05/31.12 join(meet(Y1, Y2), meet(Y0, Y1)) = meet(join(Y0, Y2), Y1) % 31.05/31.12 join(meet(Y2, Y0), meet(Y0, Y1)) = meet(join(Y1, Y2), Y0) % 31.05/31.12 join(meet(Y3, Y0), meet(Y3, meet(Y1, Y2))) = meet(join(Y0, Y1), meet(join(Y0, Y2), Y3)) % 31.05/31.12 join(meet(Y3, meet(Y0, Y1)), meet(Y3, meet(Y0, Y2))) = meet(Y0, meet(join(Y1, Y2), Y3)) % 31.05/31.12 join(meet(join(Y1, X1), X2), join(meet(X2, Y1), Y2)) = join(Y2, meet(join(Y1, X1), X2)) % 31.05/31.12 join(meet(xx, Y0), meet(yy, Y0)) = meet(Y0, yy) % 31.05/31.12 join(meet(xx, yy), meet(Y0, yy)) = join(xx, meet(yy, Y0)) % 31.05/31.12 join(meet(yy, X0), meet(X0, yy)) = join(meet(X0, xx), meet(yy, X0)) % 31.05/31.12 join(meet(yy, Y0), meet(Y0, xx)) = meet(Y0, yy) % 31.05/31.12 join(xx, join(X1, join(X2, yy))) = join(yy, join(X1, X2)) % 31.05/31.12 join(xx, join(X1, join(yy, X2))) = join(yy, join(X1, X2)) % 31.05/31.12 join(xx, join(X2, join(yy, X1))) = join(yy, join(X1, X2)) % 31.05/31.12 join(xx, join(Y0, join(Y1, yy))) = join(yy, join(Y1, Y0)) % 31.05/31.12 join(xx, join(Y0, yy)) = join(yy, Y0) % 31.05/31.12 join(yy, join(meet(Y1, xx), Y2)) = join(Y2, yy) % 31.05/31.12 meet(X, Y) = meet(Y, X) % 31.05/31.12 meet(X0, meet(xx, meet(X0, meet(yy, Y2)))) = meet(Y2, meet(X0, xx)) % 31.05/31.12 meet(X1, meet(join(Y0, Y1), X2)) = join(meet(X1, meet(X2, Y0)), meet(X1, meet(X2, Y1))) % 31.05/31.12 meet(X2, meet(Y0, Y1)) = meet(Y0, meet(Y1, meet(join(meet(Y0, Y1), X1), X2))) % 31.05/31.12 meet(Y0, Y1) = meet(Y1, meet(join(Y1, X1), Y0)) % 31.05/31.12 meet(Y0, Y2) = join(meet(Y2, Y0), meet(Y2, meet(X1, Y0))) % 31.05/31.12 meet(Y0, Y2) = join(meet(Y2, Y0), meet(Y2, meet(X1, meet(Y0, X2)))) % 31.05/31.12 meet(Y0, meet(X1, meet(join(Y0, Y1), X2))) = meet(X1, meet(X2, Y0)) % 31.05/31.12 meet(Y0, meet(X2, meet(join(Y0, Y1), X1))) = meet(X1, meet(X2, Y0)) % 31.05/31.12 meet(Y0, meet(Y1, xx)) = meet(Y1, meet(xx, meet(yy, Y0))) % 31.05/31.12 meet(Y0, meet(Y1, xx)) = meet(xx, meet(yy, meet(Y0, Y1))) % 31.05/31.12 meet(Y0, meet(join(X1, join(X2, Y0)), Y2)) = meet(Y2, Y0) % 31.05/31.12 meet(Y0, meet(join(X1, join(Y0, X2)), Y2)) = meet(Y2, Y0) % 31.05/31.12 meet(Y0, meet(join(Y0, Y1), Y3)) = meet(Y0, meet(join(Y1, join(Y0, X1)), Y3)) % 31.05/31.12 meet(Y0, meet(join(Y0, Y2), meet(join(meet(Y0, Y2), Y1), Y3))) = meet(Y0, meet(join(Y1, Y2), Y3)) % 31.05/31.12 meet(Y0, meet(join(Y1, Y0), Y2)) = meet(Y2, Y0) % 31.05/31.12 meet(Y1, meet(Y0, Y2)) = meet(Y0, meet(Y1, Y2)) % 31.05/31.12 meet(Y2, meet(Y0, Y1)) = meet(Y0, meet(Y1, Y2)) % 31.05/31.12 meet(join(Y1, Y0), Y2) = join(meet(Y2, Y0), meet(Y2, Y1)) % 31.05/31.12 meet(join(Y1, Y2), Y0) = join(meet(Y0, Y1), meet(Y0, Y2)) % 31.05/31.12 meet(join(meet(Y1, Y2), Y0), Y3) = meet(join(Y0, Y1), meet(join(Y0, Y2), Y3)) % 31.05/31.12 meet(join(yy, X0), Y2) = join(meet(Y2, xx), join(meet(Y2, yy), meet(Y2, X0))) % 31.05/31.12 meet(xx, meet(join(X0, yy), Y2)) = meet(Y2, xx) % 31.05/31.12 meet(xx, meet(join(yy, X0), Y2)) = meet(Y2, xx) % 31.05/31.12 meet(xx, meet(yy, Y0)) = meet(Y0, xx) % 31.05/31.12 meet(yy, Y2) = join(meet(Y2, meet(xx, X0)), meet(Y2, yy)) % 31.05/31.12 meet(yy, Y2) = join(meet(Y2, yy), meet(Y2, meet(xx, X0))) % 31.05/31.12 meet(yy, meet(join(Y1, yy), Y2)) = meet(Y2, yy) % 31.05/31.12 f1(join(meet(xx, yy), meet(yy, zz))) -> false__ % 31.05/31.12 f1(join(xx, meet(yy, zz))) -> true__ % 31.05/31.12 f1(meet(yy, join(xx, zz))) -> false__ % 31.05/31.12 join(X, X) -> X % 31.05/31.12 join(X, meet(X, Y)) -> X % 31.05/31.12 join(X0, join(X1, join(X0, meet(X1, X2)))) -> join(X0, X1) % 31.05/31.12 join(X0, join(X1, join(meet(X1, Y1), meet(join(X0, join(X1, Y1)), Y2)))) -> join(X0, join(X1, meet(Y1, Y2))) % 31.05/31.12 join(X0, join(X1, join(meet(Y1, X0), meet(Y1, meet(X1, X2))))) -> join(X0, X1) % 31.05/31.12 join(X0, join(X1, join(meet(Y1, meet(Y2, X0)), meet(Y1, meet(Y2, X1))))) -> join(X0, X1) % 31.05/31.12 join(X0, join(meet(X0, X1), join(meet(X0, Y1), join(meet(X1, X0), join(X1, join(meet(X1, Y1), meet(join(X0, join(X1, Y1)), Y2))))))) -> join(X0, join(X1, meet(Y1, Y2))) % 31.05/31.12 join(Y0, join(X0, join(X1, join(meet(Y0, X0), meet(Y0, X1))))) -> join(Y0, join(X0, X1)) % 31.05/31.12 join(Y0, join(X1, join(X2, meet(Y0, Y1)))) -> join(Y0, join(X1, X2)) % 31.05/31.12 join(Y0, join(X1, join(X2, meet(Y1, Y0)))) -> join(X1, join(X2, Y0)) % 31.05/31.12 join(Y0, join(X1, join(meet(Y0, Y1), X2))) -> join(Y0, join(X1, X2)) % 31.05/31.12 join(Y0, join(Y1, join(Y0, Y1))) -> join(Y0, Y1) % 31.05/31.12 join(Y0, join(Y1, join(Y0, meet(Y2, Y1)))) -> join(Y0, Y1) % 31.05/31.12 join(Y0, join(Y1, join(meet(X1, Y0), meet(X1, Y1)))) -> join(Y0, Y1) % 31.05/31.12 join(Y0, join(Y1, join(meet(Y2, Y1), meet(join(Y0, join(Y1, Y2)), Y3)))) -> join(Y0, join(Y1, meet(Y2, Y3))) % 31.05/31.12 join(Y0, join(Y1, meet(X1, meet(join(Y0, Y1), X2)))) -> join(Y0, Y1) % 31.05/31.12 join(Y0, join(Y1, meet(join(Y0, Y1), X1))) -> join(Y0, Y1) % 31.05/31.12 join(Y0, join(Y1, meet(join(Y0, join(Y2, Y1)), Y3))) -> join(Y0, join(Y1, meet(Y2, Y3))) % 31.05/31.12 join(Y0, join(Y1, meet(join(Y1, Y0), Y2))) -> join(Y0, Y1) % 31.05/31.12 join(Y0, join(Y1, meet(join(Y1, join(Y2, Y0)), Y3))) -> join(Y0, join(Y1, meet(Y2, Y3))) % 31.05/31.12 join(Y0, join(Y2, meet(Y0, Y1))) -> join(Y0, Y2) % 31.05/31.12 join(Y0, join(meet(X1, X2), meet(X1, meet(Y0, X2)))) -> join(Y0, meet(X1, X2)) % 31.05/31.12 join(Y0, join(meet(X1, X2), meet(X2, meet(Y0, X1)))) -> join(Y0, meet(X1, X2)) % 31.05/31.12 join(Y0, join(meet(X1, Y0), Y2)) -> join(Y0, Y2) % 31.05/31.12 join(Y0, join(meet(X1, meet(X2, Y0)), Y2)) -> join(Y0, Y2) % 31.05/31.12 join(Y0, join(meet(X1, meet(X2, Y0)), meet(Y0, Y2))) -> Y0 % 31.05/31.12 join(Y0, join(meet(X1, meet(Y0, X2)), Y2)) -> join(Y0, Y2) % 31.05/31.12 join(Y0, join(meet(X1, meet(Y0, X2)), meet(Y0, Y2))) -> Y0 % 31.05/31.12 join(Y0, join(meet(Y0, X1), Y2)) -> join(Y0, Y2) % 31.05/31.12 join(Y0, join(meet(Y0, X1), meet(Y0, X2))) -> Y0 % 31.05/31.12 join(Y0, join(meet(Y0, Y1), meet(join(Y0, Y1), Y2))) -> join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(Y0, join(meet(Y1, Y0), join(meet(Y0, Y2), join(Y1, meet(join(Y0, join(Y1, Y2)), Y3))))) -> join(Y0, join(Y1, meet(Y2, Y3))) % 31.05/31.12 join(Y0, join(meet(Y1, Y0), meet(Y0, Y2))) -> Y0 % 31.05/31.12 join(Y0, join(meet(Y1, Y0), meet(Y1, X1))) -> join(Y0, meet(Y1, X1)) % 31.05/31.12 join(Y0, join(meet(Y1, Y0), meet(join(Y0, Y1), Y2))) -> join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(Y0, join(meet(Y1, Y0), meet(join(Y1, Y0), Y2))) -> join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(Y0, join(meet(Y1, Y2), meet(join(Y0, Y1), meet(join(Y0, Y2), X1)))) -> join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(Y0, join(meet(Y2, Y0), join(Y1, meet(join(Y0, join(Y1, Y2)), Y3)))) -> join(Y0, join(Y1, meet(Y2, Y3))) % 31.05/31.12 join(Y0, join(xx, meet(join(Y0, yy), Y3))) -> join(Y0, join(xx, meet(yy, Y3))) % 31.05/31.12 join(Y0, meet(Y1, Y0)) -> Y0 % 31.05/31.12 join(Y0, meet(Y1, meet(X1, meet(X2, Y0)))) -> Y0 % 31.05/31.12 join(Y0, meet(Y1, meet(X1, meet(Y0, X2)))) -> Y0 % 31.05/31.12 join(Y0, meet(Y1, meet(Y0, X1))) -> Y0 % 31.05/31.12 join(Y0, meet(Y1, meet(Y2, Y0))) -> Y0 % 31.05/31.12 join(Y0, meet(join(Y0, X1), Y2)) -> join(Y0, meet(X1, Y2)) % 31.05/31.12 join(Y0, meet(join(Y1, Y0), Y2)) -> join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(Y1, join(Y0, meet(X1, Y1))) -> join(Y0, Y1) % 31.05/31.12 join(Y1, join(Y0, meet(X1, meet(X2, Y1)))) -> join(Y0, Y1) % 31.05/31.12 join(Y1, join(Y0, meet(X1, meet(Y1, X2)))) -> join(Y0, Y1) % 31.05/31.12 join(Y1, join(Y0, meet(Y1, X1))) -> join(Y0, Y1) % 31.05/31.12 join(Y1, join(Y1, Y2)) -> join(Y1, Y2) % 31.05/31.12 join(Y1, join(Y2, join(meet(Y1, Y2), meet(join(Y1, Y2), Y3)))) -> join(Y1, Y2) % 31.05/31.12 join(Y1, join(Y2, meet(Y1, Y2))) -> join(Y1, Y2) % 31.05/31.12 join(Y1, join(yy, Y1)) -> join(yy, Y1) % 31.05/31.12 join(Y3, join(X1, meet(Y1, meet(Y2, Y3)))) -> join(Y3, X1) % 31.05/31.12 join(join(X, Y), Z) -> join(X, join(Y, Z)) % 31.05/31.12 join(meet(X0, X1), join(Y1, meet(X0, meet(X1, Y1)))) -> join(meet(X0, X1), Y1) % 31.05/31.12 join(meet(X0, X1), meet(X0, meet(X1, Y1))) -> meet(X0, X1) % 31.05/31.12 join(meet(X0, X1), meet(Y1, meet(X0, meet(X1, Y2)))) -> meet(X0, X1) % 31.05/31.12 join(meet(X0, Y1), meet(X1, meet(join(X0, X1), Y1))) -> meet(join(X0, X1), Y1) % 31.05/31.12 join(meet(X0, meet(join(X0, X1), Y1)), meet(X1, meet(join(X0, X1), Y1))) -> meet(join(X0, X1), Y1) % 31.05/31.12 join(meet(X0, xx), join(Y0, meet(X0, yy))) -> join(Y0, meet(X0, yy)) % 31.05/31.12 join(meet(X1, X2), join(Y1, meet(X1, meet(X2, Y2)))) -> join(Y1, meet(X1, X2)) % 31.05/31.12 join(meet(X1, X2), join(Y1, meet(X1, meet(Y2, X2)))) -> join(Y1, meet(X1, X2)) % 31.05/31.12 join(meet(X1, X2), meet(X1, meet(Y1, X2))) -> meet(X1, X2) % 31.05/31.12 join(meet(X1, X2), meet(X2, meet(Y1, X1))) -> meet(X1, X2) % 31.05/31.12 join(meet(X1, X2), meet(Y1, meet(X1, meet(Y2, X2)))) -> meet(X1, X2) % 31.05/31.12 join(meet(X1, X2), meet(Y1, meet(X2, meet(Y2, X1)))) -> meet(X1, X2) % 31.05/31.12 join(meet(X1, X2), meet(Y1, meet(Y2, meet(X1, meet(X2, Y3))))) -> meet(X1, X2) % 31.05/31.12 join(meet(X1, X2), meet(Y1, meet(Y2, meet(X1, meet(Y3, X2))))) -> meet(X1, X2) % 31.05/31.12 join(meet(X1, meet(X0, X1)), meet(X0, meet(X1, X2))) -> meet(X0, X1) % 31.05/31.12 join(meet(X1, meet(X2, xx)), meet(X1, meet(X2, yy))) -> meet(X1, meet(X2, yy)) % 31.05/31.12 join(meet(Y0, Y1), join(Y0, meet(join(Y1, Y0), Y2))) -> join(Y0, meet(Y1, Y2)) % 31.05/31.12 join(meet(Y0, Y1), meet(Y0, meet(X1, meet(Y1, X2)))) -> meet(Y0, Y1) % 31.05/31.12 join(meet(Y0, meet(X1, meet(X2, Y0))), meet(Y0, meet(X1, meet(X2, Y1)))) -> meet(X1, meet(X2, Y0)) % 31.05/31.12 join(meet(Y0, meet(X1, meet(X2, Y0))), meet(Y0, meet(X1, meet(X2, Y1)))) -> meet(Y0, meet(X1, X2)) % 31.05/31.12 join(meet(Y0, meet(Y1, meet(join(Y1, Y2), Y0))), join(meet(Y0, meet(Y2, meet(join(Y1, Y2), Y0))), meet(Y0, meet(join(Y1, Y2), X1)))) -> join(meet(Y0, Y1), meet(Y0, Y2)) % 31.05/31.12 join(meet(Y0, meet(Y1, meet(join(Y1, Y2), Y0))), meet(Y0, meet(Y2, meet(join(Y1, Y2), Y0)))) -> join(meet(Y0, Y1), meet(Y0, Y2)) % 31.05/31.12 join(meet(Y0, xx), join(meet(Y0, yy), meet(Y0, X0))) -> join(meet(Y0, yy), meet(Y0, X0)) % 31.05/31.12 join(meet(Y0, xx), meet(Y0, meet(yy, Y0))) -> meet(Y0, yy) % 31.05/31.12 join(meet(Y0, xx), meet(Y0, yy)) -> meet(Y0, yy) % 31.05/31.12 join(meet(Y0, xx), meet(yy, Y0)) -> meet(yy, Y0) % 31.05/31.12 join(meet(Y0, yy), meet(xx, Y0)) -> meet(Y0, yy) % 31.05/31.12 join(meet(Y1, X2), meet(join(Y1, X1), X2)) -> meet(join(Y1, X1), X2) % 31.05/31.12 join(meet(Y1, meet(Y0, Y1)), meet(Y1, meet(Y0, X1))) -> meet(Y0, Y1) % 31.05/31.12 join(meet(Y1, meet(Y2, xx)), yy) -> yy % 31.05/31.12 join(meet(Y1, xx), yy) -> yy % 31.05/31.12 join(meet(Y2, X1), join(Y1, meet(Y2, X1))) -> join(Y1, meet(Y2, X1)) % 31.05/31.12 join(meet(join(Y1, X1), X2), meet(X2, Y1)) -> meet(join(Y1, X1), X2) % 31.05/31.12 join(meet(join(Y2, X1), X2), meet(Y1, meet(X2, Y2))) -> meet(join(Y2, X1), X2) % 31.05/31.12 join(meet(join(Y2, X1), X2), meet(Y1, meet(Y2, X2))) -> meet(join(Y2, X1), X2) % 31.05/31.12 join(meet(xx, X0), join(Y0, yy)) -> join(Y0, yy) % 31.05/31.12 join(meet(xx, Y0), meet(Y0, yy)) -> meet(Y0, yy) % 31.05/31.12 join(meet(xx, Y0), yy) -> yy % 31.05/31.12 join(meet(xx, yy), join(meet(xx, X0), meet(join(yy, X0), Y2))) -> join(xx, meet(join(yy, X0), Y2)) % 31.05/31.12 join(meet(xx, yy), meet(xx, X0)) -> xx % 31.05/31.12 join(meet(xx, yy), meet(yy, Y2)) -> join(xx, meet(yy, Y2)) % 31.05/31.12 join(xx, join(X0, join(meet(Y1, xx), meet(Y1, meet(X0, yy))))) -> join(xx, X0) % 31.05/31.12 join(xx, join(Y0, join(X0, yy))) -> join(Y0, join(X0, yy)) % 31.05/31.12 join(xx, join(Y0, join(yy, X0))) -> join(Y0, join(yy, X0)) % 31.05/31.12 join(xx, join(Y0, yy)) -> join(Y0, yy) % 31.05/31.12 join(xx, join(Y1, xx)) -> join(Y1, xx) % 31.05/31.12 join(xx, join(Y1, xx)) -> join(xx, Y1) % 31.05/31.12 join(xx, join(meet(Y1, yy), meet(join(xx, Y1), X0))) -> join(xx, join(meet(Y1, yy), meet(Y1, X0))) % 31.05/31.12 join(xx, join(yy, Y2)) -> join(yy, Y2) % 31.05/31.12 join(xx, yy) -> yy % 31.05/31.12 join(yy, join(Y0, yy)) -> join(Y0, yy) % 31.05/31.12 join(yy, join(Y1, yy)) -> join(yy, Y1) % 31.05/31.12 join(yy, join(meet(Y1, xx), meet(Y1, meet(X0, yy)))) -> yy % 31.05/31.12 join(yy, join(meet(xx, X0), Y2)) -> join(yy, Y2) % 31.05/31.12 join(yy, join(meet(xx, X0), yy)) -> yy % 31.05/31.12 join(yy, meet(X1, meet(X2, xx))) -> yy % 31.05/31.12 join(yy, meet(X1, meet(xx, X2))) -> yy % 31.05/31.12 join(yy, meet(Y0, xx)) -> yy % 31.05/31.12 join(yy, meet(xx, Y2)) -> yy % 31.05/31.12 meet(X, X) -> X % 31.05/31.12 meet(X, join(X, Y)) -> X % 31.05/31.12 meet(X, join(Y, Z)) -> join(meet(X, Y), meet(X, Z)) % 31.05/31.12 meet(X0, meet(xx, meet(X0, yy))) -> meet(xx, X0) % 31.05/31.12 meet(X0, meet(xx, yy)) -> meet(X0, xx) % 31.05/31.12 meet(Y0, meet(X1, meet(join(Y0, Y1), X2))) -> meet(Y0, meet(X1, X2)) % 31.05/31.12 meet(Y0, meet(X2, meet(join(Y0, X1), X2))) -> meet(Y0, X2) % 31.05/31.12 meet(Y0, meet(Y1, meet(Y0, Y1))) -> meet(Y0, Y1) % 31.05/31.12 meet(Y0, meet(join(X1, join(X2, Y0)), Y2)) -> meet(Y0, Y2) % 31.05/31.12 meet(Y0, meet(join(Y0, X1), Y2)) -> meet(Y0, Y2) % 31.05/31.12 meet(Y0, meet(join(Y0, Y1), meet(join(meet(Y0, Y1), Y2), Y3))) -> meet(Y0, meet(join(Y1, Y2), Y3)) % 31.05/31.12 meet(Y0, meet(join(Y0, Y1), meet(join(meet(Y1, Y0), Y2), Y3))) -> meet(Y0, meet(join(Y1, Y2), Y3)) % 31.05/31.12 meet(Y0, meet(join(Y0, join(X1, Y2)), Y3)) -> meet(Y0, meet(join(Y0, Y2), Y3)) % 31.05/31.12 meet(Y0, meet(join(Y1, Y0), Y2)) -> meet(Y0, Y2) % 31.05/31.12 meet(Y0, meet(xx, meet(yy, Y0))) -> meet(Y0, xx) % 31.05/31.12 meet(Y0, meet(xx, meet(yy, Y2))) -> meet(Y0, meet(xx, Y2)) % 31.05/31.12 meet(Y0, meet(yy, Y0)) -> meet(Y0, yy) % 31.05/31.12 meet(Y1, meet(Y0, meet(join(Y1, X1), X2))) -> meet(Y0, meet(Y1, X2)) % 31.05/31.12 meet(Y1, meet(Y1, Y2)) -> meet(Y1, Y2) % 31.05/31.12 meet(Y1, meet(Y2, meet(join(Y1, Y2), meet(join(Y2, Y1), Y3)))) -> meet(Y1, meet(Y2, Y3)) % 31.05/31.12 meet(join(X, Y), join(X, Z)) -> join(X, meet(Y, Z)) % 31.05/31.12 meet(join(X0, meet(X1, X2)), Y2) -> meet(join(X0, X1), meet(join(X0, X2), Y2)) % 31.05/31.12 meet(join(X1, join(X2, xx)), yy) -> join(xx, meet(join(X1, X2), yy)) % 31.05/31.12 meet(join(X1, join(xx, X2)), yy) -> join(xx, meet(join(X1, X2), yy)) % 31.05/31.12 meet(join(Y0, Y1), meet(join(Y0, join(Y1, X1)), Y3)) -> meet(join(Y0, Y1), Y3) % 31.05/31.12 meet(join(Y0, Y2), Y1) -> join(meet(Y0, Y1), meet(Y2, Y1)) % 31.05/31.12 meet(join(Y0, xx), yy) -> join(xx, meet(Y0, yy)) % 31.05/31.12 meet(join(meet(Y0, X1), meet(Y0, X2)), Y2) -> meet(Y0, meet(join(X1, X2), Y2)) % 31.05/31.12 meet(join(xx, Y1), yy) -> join(xx, meet(Y1, yy)) % 31.05/31.12 meet(meet(X, Y), Z) -> meet(X, meet(Y, Z)) % 31.05/31.12 meet(xx, meet(X1, yy)) -> meet(xx, X1) % 31.05/31.12 meet(xx, meet(Y0, yy)) -> meet(Y0, xx) % 31.05/31.12 meet(xx, meet(join(X0, yy), Y2)) -> meet(xx, Y2) % 31.05/31.12 meet(xx, meet(join(yy, X0), Y2)) -> meet(xx, Y2) % 31.05/31.12 meet(xx, meet(yy, Y2)) -> meet(xx, Y2) % 31.05/31.12 meet(xx, yy) -> xx % 31.05/31.12 meet(yy, meet(join(Y1, yy), Y2)) -> meet(yy, Y2) % 31.05/31.12 true__ -> false__ % 31.05/31.12 with the LPO induced by % 31.05/31.12 zz > f1 > yy > xx > meet > join > true__ > false__ % 31.05/31.12 % 31.05/31.12 % SZS output end Proof % 31.05/31.12 %------------------------------------------------------------------------------