TSTP Solution File: LAT039-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------