TSTP Solution File: LAT028-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:04:12 EDT 2022
% Result : Unsatisfiable 45.32s 45.39s
% Output : Proof 45.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 23:59:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 45.32/45.39 % SZS status Unsatisfiable
% 45.32/45.39 % SZS output start Proof
% 45.32/45.39 The input problem is unsatisfiable because
% 45.32/45.39
% 45.32/45.39 [1] the following set of Horn clauses is unsatisfiable:
% 45.32/45.39
% 45.32/45.39 meet(X, X) = X
% 45.32/45.39 join(X, X) = X
% 45.32/45.39 meet(X, Y) = meet(Y, X)
% 45.32/45.39 join(X, Y) = join(Y, X)
% 45.32/45.39 meet(meet(join(X, Y), join(Z, Y)), Y) = Y
% 45.32/45.39 join(join(meet(X, Y), meet(Z, Y)), Y) = Y
% 45.32/45.39 meet2(X, X) = X
% 45.32/45.39 meet2(X, Y) = meet2(Y, X)
% 45.32/45.39 meet2(meet2(join(X, Y), join(Z, Y)), Y) = Y
% 45.32/45.39 join(join(meet2(X, Y), meet2(Z, Y)), Y) = Y
% 45.32/45.39 meet(a, b) = meet2(a, b) ==> \bottom
% 45.32/45.39
% 45.32/45.39 This holds because
% 45.32/45.39
% 45.32/45.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 45.32/45.39
% 45.32/45.39 E:
% 45.32/45.39 f1(meet(a, b)) = true__
% 45.32/45.39 f1(meet2(a, b)) = false__
% 45.32/45.39 join(X, X) = X
% 45.32/45.39 join(X, Y) = join(Y, X)
% 45.32/45.39 join(join(meet(X, Y), meet(Z, Y)), Y) = Y
% 45.32/45.39 join(join(meet2(X, Y), meet2(Z, Y)), Y) = Y
% 45.32/45.39 meet(X, X) = X
% 45.32/45.39 meet(X, Y) = meet(Y, X)
% 45.32/45.39 meet(meet(join(X, Y), join(Z, Y)), Y) = Y
% 45.32/45.39 meet2(X, X) = X
% 45.32/45.39 meet2(X, Y) = meet2(Y, X)
% 45.32/45.39 meet2(meet2(join(X, Y), join(Z, Y)), Y) = Y
% 45.32/45.39 G:
% 45.32/45.39 true__ = false__
% 45.32/45.39
% 45.32/45.39 This holds because
% 45.32/45.39
% 45.32/45.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 45.32/45.39
% 45.32/45.39 join(X, Y) = join(Y, X)
% 45.32/45.39 join(meet(Y0, Y1), meet2(Y0, Y1)) = meet2(Y1, Y0)
% 45.32/45.39 meet(X, Y) = meet(Y, X)
% 45.32/45.39 meet2(X, Y) = meet2(Y, X)
% 45.32/45.39 meet2(Y0, meet2(Y0, Y1)) = meet2(Y1, Y0)
% 45.32/45.39 f1(meet(a, b)) -> true__
% 45.32/45.39 f1(meet2(a, b)) -> false__
% 45.32/45.39 join(X, X) -> X
% 45.32/45.39 join(Y0, join(Y0, meet(Y0, Y1))) -> Y0
% 45.32/45.39 join(Y0, join(meet(Y0, Y1), meet(Y0, Y2))) -> Y0
% 45.32/45.39 join(Y0, join(meet(Y0, Y1), meet2(Y0, Y2))) -> Y0
% 45.32/45.39 join(Y0, join(meet(Y0, Y1), meet2(Y2, Y0))) -> Y0
% 45.32/45.39 join(Y0, join(meet(Y1, Y0), meet2(X1, Y0))) -> Y0
% 45.32/45.39 join(Y0, join(meet(Y1, Y0), meet2(Y0, Y2))) -> Y0
% 45.32/45.39 join(Y0, join(meet2(X1, Y0), meet(Y2, Y0))) -> Y0
% 45.32/45.39 join(Y0, join(meet2(Y0, Y1), meet(Y0, Y2))) -> Y0
% 45.32/45.39 join(Y0, join(meet2(Y0, Y1), meet(Y2, Y0))) -> Y0
% 45.32/45.39 join(Y0, join(meet2(Y0, Y1), meet2(Y0, Y2))) -> Y0
% 45.32/45.39 join(Y0, join(meet2(Y1, Y0), meet(Y0, Y2))) -> Y0
% 45.32/45.39 join(Y0, meet(Y0, Y1)) -> Y0
% 45.32/45.39 join(Y0, meet2(Y0, Y1)) -> Y0
% 45.32/45.39 join(Y1, join(X1, Y1)) -> join(X1, Y1)
% 45.32/45.39 join(Y1, join(Y1, X1)) -> join(Y1, X1)
% 45.32/45.39 join(Y1, join(Y1, meet(Y2, Y1))) -> Y1
% 45.32/45.39 join(Y1, join(meet(Y0, Y1), meet(Y1, Y2))) -> Y1
% 45.32/45.39 join(Y1, join(meet(Y0, Y1), meet(Y2, Y1))) -> Y1
% 45.32/45.39 join(Y1, join(meet(Y1, Y0), meet(Y2, Y1))) -> Y1
% 45.32/45.39 join(Y1, join(meet2(Y0, Y1), meet2(Y1, Y2))) -> Y1
% 45.32/45.39 join(Y1, join(meet2(Y0, Y1), meet2(Y2, Y1))) -> Y1
% 45.32/45.39 join(Y1, join(meet2(Y1, Y0), meet2(Y2, Y1))) -> Y1
% 45.32/45.39 join(Y1, meet(Y2, Y1)) -> Y1
% 45.32/45.39 join(Y1, meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1))
% 45.32/45.39 join(Y1, meet(join(X1, Y1), join(Y1, X2))) -> meet(join(X1, Y1), join(Y1, X2))
% 45.32/45.39 join(Y1, meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1))
% 45.32/45.39 join(Y1, meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2))
% 45.32/45.39 join(Y1, meet2(Y2, Y1)) -> Y1
% 45.32/45.39 join(Y1, meet2(join(X0, Y1), join(X2, Y1))) -> meet2(join(X0, Y1), join(X2, Y1))
% 45.32/45.39 join(Y1, meet2(join(X1, Y1), join(Y1, X2))) -> meet2(join(X1, Y1), join(Y1, X2))
% 45.32/45.39 join(Y1, meet2(join(Y1, X1), join(X2, Y1))) -> meet2(join(Y1, X1), join(X2, Y1))
% 45.32/45.39 join(Y1, meet2(join(Y1, X1), join(Y1, X2))) -> meet2(join(Y1, X1), join(Y1, X2))
% 45.32/45.39 join(join(X1, Y0), join(Y0, meet(Y2, join(X1, Y0)))) -> join(X1, Y0)
% 45.32/45.39 join(join(X1, Y0), join(Y0, meet2(Y2, join(X1, Y0)))) -> join(X1, Y0)
% 45.32/45.39 join(join(X1, Y2), join(Y2, meet(join(X1, Y2), Y1))) -> join(X1, Y2)
% 45.32/45.39 join(join(X1, Y2), join(Y2, meet2(join(X1, Y2), Y1))) -> join(X1, Y2)
% 45.32/45.39 join(join(Y0, X1), join(Y0, meet(Y2, join(Y0, X1)))) -> join(Y0, X1)
% 45.32/45.39 join(join(Y0, X1), join(Y0, meet2(Y2, join(Y0, X1)))) -> join(Y0, X1)
% 45.32/45.39 join(join(Y2, X1), join(Y2, meet(join(Y2, X1), Y1))) -> join(Y2, X1)
% 45.32/45.39 join(join(Y2, X1), join(Y2, meet2(join(Y2, X1), Y1))) -> join(Y2, X1)
% 45.32/45.39 join(join(meet(X, Y), meet(Z, Y)), Y) -> Y
% 45.32/45.39 join(join(meet2(X, Y), meet2(Z, Y)), Y) -> Y
% 45.32/45.39 join(meet(X0, X1), meet(X0, join(X2, meet(X0, X1)))) -> meet(X0, join(X2, meet(X0, X1)))
% 45.32/45.39 join(meet(X0, X1), meet(X1, join(X2, meet(X0, X1)))) -> meet(X1, join(X2, meet(X0, X1)))
% 45.32/45.39 join(meet(X0, X1), meet(X1, join(meet(X0, X1), X2))) -> meet(X1, join(meet(X0, X1), X2))
% 45.32/45.39 join(meet(X0, X1), meet2(X1, X0)) -> meet2(X1, X0)
% 45.32/45.39 join(meet(X0, X1), meet2(X1, join(X2, meet(X0, X1)))) -> meet2(X1, join(X2, meet(X0, X1)))
% 45.32/45.39 join(meet(X1, X0), meet(X1, join(meet(X1, X0), X2))) -> meet(X1, join(meet(X1, X0), X2))
% 45.32/45.39 join(meet(X1, join(X2, meet(X0, X1))), join(meet(X0, X1), meet(Y2, meet(X1, join(X2, meet(X0, X1)))))) -> meet(X1, join(X2, meet(X0, X1)))
% 45.32/45.39 join(meet(X1, join(X2, meet(X1, X0))), join(meet(X1, X0), meet(Y2, meet(X1, join(X2, meet(X1, X0)))))) -> meet(X1, join(X2, meet(X1, X0)))
% 45.32/45.39 join(meet(Y1, Y0), meet2(Y1, Y0)) -> meet2(Y1, Y0)
% 45.32/45.39 join(meet(join(X0, Y1), join(X2, Y1)), join(Y1, meet(Y2, meet(join(X0, Y1), join(X2, Y1))))) -> meet(join(X0, Y1), join(X2, Y1))
% 45.32/45.39 join(meet(join(X0, Y2), join(X2, Y2)), join(Y2, meet2(Y1, meet(join(X0, Y2), join(X2, Y2))))) -> meet(join(X0, Y2), join(X2, Y2))
% 45.32/45.39 join(meet(join(X1, Y0), join(Y0, X2)), join(Y0, meet(Y2, meet(join(X1, Y0), join(Y0, X2))))) -> meet(join(X1, Y0), join(Y0, X2))
% 45.32/45.39 join(meet(join(X1, Y2), join(X2, Y2)), join(Y2, meet(meet(join(X1, Y2), join(X2, Y2)), Y1))) -> meet(join(X1, Y2), join(X2, Y2))
% 45.32/45.39 join(meet(join(X1, Y2), join(Y2, X2)), join(Y2, meet(meet(join(X1, Y2), join(Y2, X2)), Y1))) -> meet(join(X1, Y2), join(Y2, X2))
% 45.32/45.39 join(meet(join(Y0, X1), join(X2, Y0)), join(Y0, meet(Y2, meet(join(Y0, X1), join(X2, Y0))))) -> meet(join(Y0, X1), join(X2, Y0))
% 45.32/45.39 join(meet(join(Y0, X1), join(Y0, X2)), join(Y0, meet(Y2, meet(join(Y0, X1), join(Y0, X2))))) -> meet(join(Y0, X1), join(Y0, X2))
% 45.32/45.39 join(meet(join(Y2, X1), join(X2, Y2)), join(Y2, meet(meet(join(Y2, X1), join(X2, Y2)), Y1))) -> meet(join(Y2, X1), join(X2, Y2))
% 45.32/45.39 join(meet(join(Y2, X1), join(X2, Y2)), join(Y2, meet2(Y1, meet(join(Y2, X1), join(X2, Y2))))) -> meet(join(Y2, X1), join(X2, Y2))
% 45.32/45.39 join(meet(join(Y2, X1), join(Y2, X2)), join(Y2, meet(meet(join(Y2, X1), join(Y2, X2)), Y1))) -> meet(join(Y2, X1), join(Y2, X2))
% 45.32/45.39 join(meet2(X0, X1), meet(X1, join(X2, meet2(X0, X1)))) -> meet(X1, join(X2, meet2(X0, X1)))
% 45.32/45.39 join(meet2(X0, X1), meet2(X1, join(X2, meet2(X0, X1)))) -> meet2(X1, join(X2, meet2(X0, X1)))
% 45.32/45.39 join(meet2(join(X0, Y1), join(X2, Y1)), join(Y1, meet2(meet2(join(X0, Y1), join(X2, Y1)), Y2))) -> meet2(join(X0, Y1), join(X2, Y1))
% 45.32/45.39 join(meet2(join(X1, Y0), join(X2, Y0)), join(Y0, meet2(Y2, meet2(join(X1, Y0), join(X2, Y0))))) -> meet2(join(X1, Y0), join(X2, Y0))
% 45.32/45.39 join(meet2(join(X1, Y0), join(Y0, X2)), join(Y0, meet2(Y2, meet2(join(X1, Y0), join(Y0, X2))))) -> meet2(join(X1, Y0), join(Y0, X2))
% 45.32/45.39 join(meet2(join(X1, Y2), join(Y2, X2)), join(Y2, meet2(meet2(join(X1, Y2), join(Y2, X2)), Y1))) -> meet2(join(X1, Y2), join(Y2, X2))
% 45.32/45.39 join(meet2(join(Y0, X1), join(X2, Y0)), join(Y0, meet2(Y2, meet2(join(Y0, X1), join(X2, Y0))))) -> meet2(join(Y0, X1), join(X2, Y0))
% 45.32/45.39 join(meet2(join(Y0, X1), join(Y0, X2)), join(Y0, meet2(Y2, meet2(join(Y0, X1), join(Y0, X2))))) -> meet2(join(Y0, X1), join(Y0, X2))
% 45.32/45.39 join(meet2(join(Y2, X1), join(X2, Y2)), join(Y2, meet2(meet2(join(Y2, X1), join(X2, Y2)), Y1))) -> meet2(join(Y2, X1), join(X2, Y2))
% 45.32/45.39 meet(X, X) -> X
% 45.32/45.39 meet(Y0, join(Y0, Y1)) -> Y0
% 45.32/45.39 meet(Y0, meet(join(Y0, Y1), join(Y0, Y2))) -> Y0
% 45.32/45.39 meet(Y0, meet2(join(Y0, Y1), join(Y0, Y2))) -> Y0
% 45.32/45.39 meet(Y1, join(Y2, Y1)) -> Y1
% 45.32/45.39 meet(Y1, join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet(X1, Y1), meet(Y1, X2))) -> join(meet(X1, Y1), meet(Y1, X2))
% 45.32/45.39 meet(Y1, join(meet(X1, Y1), meet2(X2, Y1))) -> join(meet(X1, Y1), meet2(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet(X1, Y1), meet2(Y1, X2))) -> join(meet(X1, Y1), meet2(Y1, X2))
% 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2))
% 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet2(X2, Y1))) -> join(meet(Y1, X1), meet2(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet(Y1, X1), meet2(Y1, X2))) -> join(meet(Y1, X1), meet2(Y1, X2))
% 45.32/45.39 meet(Y1, join(meet2(X0, Y1), meet2(X2, Y1))) -> join(meet2(X0, Y1), meet2(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet2(X1, Y1), meet(X2, Y1))) -> join(meet2(X1, Y1), meet(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet2(X1, Y1), meet(Y1, X2))) -> join(meet2(X1, Y1), meet(Y1, X2))
% 45.32/45.39 meet(Y1, join(meet2(X1, Y1), meet2(Y1, X2))) -> join(meet2(X1, Y1), meet2(Y1, X2))
% 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet(X2, Y1))) -> join(meet2(Y1, X1), meet(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet(Y1, X2))) -> join(meet2(Y1, X1), meet(Y1, X2))
% 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet2(X2, Y1))) -> join(meet2(Y1, X1), meet2(X2, Y1))
% 45.32/45.39 meet(Y1, join(meet2(Y1, X1), meet2(Y1, X2))) -> join(meet2(Y1, X1), meet2(Y1, X2))
% 45.32/45.39 meet(Y1, meet(X1, Y1)) -> meet(X1, Y1)
% 45.32/45.39 meet(Y1, meet(Y1, X1)) -> meet(Y1, X1)
% 45.32/45.39 meet(Y1, meet(Y1, join(Y2, Y1))) -> Y1
% 45.32/45.39 meet(Y1, meet(join(Y0, Y1), join(Y1, Y2))) -> Y1
% 45.32/45.39 meet(Y1, meet(join(Y0, Y1), join(Y2, Y1))) -> Y1
% 45.32/45.39 meet(Y1, meet(join(Y1, Y0), join(Y2, Y1))) -> Y1
% 45.32/45.39 meet(Y1, meet2(X1, Y1)) -> meet2(X1, Y1)
% 45.32/45.39 meet(Y1, meet2(Y1, X1)) -> meet2(Y1, X1)
% 45.32/45.39 meet(Y1, meet2(join(X0, Y1), join(X2, Y1))) -> Y1
% 45.32/45.39 meet(Y1, meet2(join(X1, Y1), join(Y1, X2))) -> Y1
% 45.32/45.39 meet(Y1, meet2(join(Y1, X1), join(X2, Y1))) -> Y1
% 45.32/45.39 meet(join(X0, X1), join(X0, meet(X2, join(X0, X1)))) -> join(X0, meet(X2, join(X0, X1)))
% 45.32/45.39 meet(join(X0, X1), join(X0, meet(join(X0, X1), X2))) -> join(X0, meet(join(X0, X1), X2))
% 45.32/45.39 meet(join(X0, X1), join(X1, meet(X2, join(X0, X1)))) -> join(X1, meet(X2, join(X0, X1)))
% 45.32/45.39 meet(join(X0, X1), join(X1, meet(join(X0, X1), X2))) -> join(X1, meet(join(X0, X1), X2))
% 45.32/45.39 meet(join(X0, X1), join(X1, meet2(X2, join(X0, X1)))) -> join(X1, meet2(X2, join(X0, X1)))
% 45.32/45.39 meet(join(X1, meet(X2, join(X0, X1))), meet(join(X0, X1), join(Y2, join(X1, meet(X2, join(X0, X1)))))) -> join(X1, meet(X2, join(X0, X1)))
% 45.32/45.39 meet(join(meet(X0, Y1), meet(X2, Y1)), meet(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1))))) -> join(meet(X0, Y1), meet(X2, Y1))
% 45.32/45.39 meet(join(meet(X1, Y0), meet(Y0, X2)), meet(Y0, join(Y2, join(meet(X1, Y0), meet(Y0, X2))))) -> join(meet(X1, Y0), meet(Y0, X2))
% 45.32/45.39 meet(join(meet(X1, Y0), meet2(X2, Y0)), meet(Y0, join(Y2, join(meet(X1, Y0), meet2(X2, Y0))))) -> join(meet(X1, Y0), meet2(X2, Y0))
% 45.32/45.39 meet(join(meet(X1, Y2), meet(X2, Y2)), meet(Y2, join(join(meet(X1, Y2), meet(X2, Y2)), Y1))) -> join(meet(X1, Y2), meet(X2, Y2))
% 45.32/45.39 meet(join(meet(X1, Y2), meet(Y2, X2)), meet(Y2, join(join(meet(X1, Y2), meet(Y2, X2)), Y1))) -> join(meet(X1, Y2), meet(Y2, X2))
% 45.32/45.39 meet(join(meet(Y0, X1), meet(X2, Y0)), meet(Y0, join(Y2, join(meet(Y0, X1), meet(X2, Y0))))) -> join(meet(Y0, X1), meet(X2, Y0))
% 45.32/45.39 meet(join(meet(Y0, X1), meet(Y0, X2)), meet(Y0, join(Y2, join(meet(Y0, X1), meet(Y0, X2))))) -> join(meet(Y0, X1), meet(Y0, X2))
% 45.32/45.39 meet(join(meet(Y0, X1), meet2(X2, Y0)), meet(Y0, join(Y2, join(meet(Y0, X1), meet2(X2, Y0))))) -> join(meet(Y0, X1), meet2(X2, Y0))
% 45.32/45.39 meet(join(meet(Y2, X1), meet(X2, Y2)), meet(Y2, join(join(meet(Y2, X1), meet(X2, Y2)), Y1))) -> join(meet(Y2, X1), meet(X2, Y2))
% 45.32/45.39 meet(join(meet(Y2, X1), meet(Y2, X2)), meet(Y2, join(join(meet(Y2, X1), meet(Y2, X2)), Y1))) -> join(meet(Y2, X1), meet(Y2, X2))
% 45.32/45.39 meet(join(meet2(X0, Y1), meet2(X2, Y1)), meet(Y1, join(Y2, join(meet2(X0, Y1), meet2(X2, Y1))))) -> join(meet2(X0, Y1), meet2(X2, Y1))
% 45.32/45.39 meet(join(meet2(X1, Y0), meet(X2, Y0)), meet(Y0, join(Y2, join(meet2(X1, Y0), meet(X2, Y0))))) -> join(meet2(X1, Y0), meet(X2, Y0))
% 45.32/45.39 meet(join(meet2(X1, Y0), meet(Y0, X2)), meet(Y0, join(Y2, join(meet2(X1, Y0), meet(Y0, X2))))) -> join(meet2(X1, Y0), meet(Y0, X2))
% 45.32/45.39 meet(join(meet2(X1, Y0), meet2(Y0, X2)), meet(Y0, join(Y2, join(meet2(X1, Y0), meet2(Y0, X2))))) -> join(meet2(X1, Y0), meet2(Y0, X2))
% 45.32/45.39 meet(join(meet2(X1, Y2), meet(X2, Y2)), meet(Y2, join(join(meet2(X1, Y2), meet(X2, Y2)), Y1))) -> join(meet2(X1, Y2), meet(X2, Y2))
% 45.32/45.39 meet(join(meet2(X1, Y2), meet2(X2, Y2)), meet(Y2, join(join(meet2(X1, Y2), meet2(X2, Y2)), Y1))) -> join(meet2(X1, Y2), meet2(X2, Y2))
% 45.32/45.39 meet(join(meet2(X1, Y2), meet2(Y2, X2)), meet(Y2, join(join(meet2(X1, Y2), meet2(Y2, X2)), Y1))) -> join(meet2(X1, Y2), meet2(Y2, X2))
% 45.32/45.39 meet(join(meet2(Y0, X1), meet(X2, Y0)), meet(Y0, join(Y2, join(meet2(Y0, X1), meet(X2, Y0))))) -> join(meet2(Y0, X1), meet(X2, Y0))
% 45.32/45.39 meet(join(meet2(Y0, X1), meet2(X2, Y0)), meet(Y0, join(Y2, join(meet2(Y0, X1), meet2(X2, Y0))))) -> join(meet2(Y0, X1), meet2(X2, Y0))
% 45.32/45.39 meet(join(meet2(Y0, X1), meet2(Y0, X2)), meet(Y0, join(Y2, join(meet2(Y0, X1), meet2(Y0, X2))))) -> join(meet2(Y0, X1), meet2(Y0, X2))
% 45.32/45.39 meet(join(meet2(Y2, X1), meet2(X2, Y2)), meet(Y2, join(join(meet2(Y2, X1), meet2(X2, Y2)), Y1))) -> join(meet2(Y2, X1), meet2(X2, Y2))
% 45.32/45.39 meet(join(meet2(Y2, X1), meet2(Y2, X2)), meet(Y2, join(join(meet2(Y2, X1), meet2(Y2, X2)), Y1))) -> join(meet2(Y2, X1), meet2(Y2, X2))
% 45.32/45.39 meet(meet(X0, X1), meet(join(Y1, meet(X0, X1)), meet2(X1, X0))) -> meet(X0, X1)
% 45.32/45.39 meet(meet(X0, X1), meet(join(meet(X0, X1), Y1), meet2(X1, X0))) -> meet(X0, X1)
% 45.32/45.39 meet(meet(X0, X1), meet(meet2(X1, X0), join(Y2, meet(X0, X1)))) -> meet(X0, X1)
% 45.32/45.39 meet(meet(X0, X1), meet(meet2(X1, X0), join(meet(X0, X1), Y2))) -> meet(X0, X1)
% 45.32/45.39 meet(meet(X0, X1), meet2(X1, X0)) -> meet(X0, X1)
% 45.32/45.39 meet(meet(X1, Y0), meet(Y0, join(Y2, meet(X1, Y0)))) -> meet(X1, Y0)
% 45.32/45.39 meet(meet(X1, Y1), meet2(Y1, join(Y2, meet(X1, Y1)))) -> meet(X1, Y1)
% 45.32/45.39 meet(meet(X1, Y2), meet(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2)
% 45.32/45.39 meet(meet(X1, Y2), meet2(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2)
% 45.32/45.39 meet(meet(Y0, X1), meet(Y0, join(Y2, meet(Y0, X1)))) -> meet(Y0, X1)
% 45.32/45.39 meet(meet(Y0, Y1), meet2(Y0, Y1)) -> meet(Y0, Y1)
% 45.32/45.39 meet(meet(Y1, X1), meet2(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1)
% 45.32/45.39 meet(meet(Y1, Y0), meet2(Y1, Y0)) -> meet(Y0, Y1)
% 45.32/45.39 meet(meet(Y2, X1), meet(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1)
% 45.32/45.39 meet(meet(Y2, X1), meet2(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1)
% 45.32/45.39 meet(meet(join(X, Y), join(Z, Y)), Y) -> Y
% 45.32/45.39 meet(meet2(X1, Y0), meet(Y0, join(Y2, meet2(X1, Y0)))) -> meet2(X1, Y0)
% 45.32/45.39 meet(meet2(X1, Y1), meet2(Y1, join(Y2, meet2(X1, Y1)))) -> meet2(X1, Y1)
% 45.32/45.39 meet(meet2(X1, Y2), meet(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2)
% 45.32/45.39 meet(meet2(X1, Y2), meet2(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2)
% 45.32/45.39 meet(meet2(Y0, X1), meet(Y0, join(Y2, meet2(Y0, X1)))) -> meet2(Y0, X1)
% 45.32/45.39 meet(meet2(Y0, Y1), meet(Y1, join(Y2, meet2(Y1, Y0)))) -> meet2(Y0, Y1)
% 45.32/45.39 meet(meet2(Y1, X1), meet2(Y1, join(Y2, meet2(Y1, X1)))) -> meet2(Y1, X1)
% 45.32/45.39 meet(meet2(Y1, Y0), meet(Y1, join(Y2, meet2(Y0, Y1)))) -> meet2(Y0, Y1)
% 45.32/45.39 meet(meet2(Y2, X1), meet(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1)
% 45.32/45.39 meet(meet2(Y2, X1), meet2(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1)
% 45.32/45.39 meet2(X, X) -> X
% 45.32/45.39 meet2(Y0, Y1) -> meet(Y1, Y0)
% 45.32/45.39 meet2(Y0, join(Y0, Y1)) -> Y0
% 45.32/45.39 meet2(Y0, meet(join(Y0, Y1), join(Y0, Y2))) -> Y0
% 45.32/45.39 meet2(Y0, meet(join(Y0, Y1), join(Y2, Y0))) -> Y0
% 45.32/45.39 meet2(Y0, meet(join(Y1, Y0), join(Y0, Y2))) -> Y0
% 45.32/45.39 meet2(Y0, meet2(join(Y0, Y1), join(Y0, Y2))) -> Y0
% 45.32/45.39 meet2(Y1, join(Y2, Y1)) -> Y1
% 45.32/45.39 meet2(Y1, join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet(X1, Y1), meet(Y1, X2))) -> join(meet(X1, Y1), meet(Y1, X2))
% 45.32/45.39 meet2(Y1, join(meet(X1, Y1), meet2(X2, Y1))) -> join(meet(X1, Y1), meet2(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet(X1, Y1), meet2(Y1, X2))) -> join(meet(X1, Y1), meet2(Y1, X2))
% 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2))
% 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet2(X2, Y1))) -> join(meet(Y1, X1), meet2(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet(Y1, X1), meet2(Y1, X2))) -> join(meet(Y1, X1), meet2(Y1, X2))
% 45.32/45.39 meet2(Y1, join(meet2(X0, Y1), meet2(X2, Y1))) -> join(meet2(X0, Y1), meet2(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet2(X1, Y1), meet(X2, Y1))) -> join(meet2(X1, Y1), meet(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet2(X1, Y1), meet(Y1, X2))) -> join(meet2(X1, Y1), meet(Y1, X2))
% 45.32/45.39 meet2(Y1, join(meet2(X1, Y1), meet2(Y1, X2))) -> join(meet2(X1, Y1), meet2(Y1, X2))
% 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet(X2, Y1))) -> join(meet2(Y1, X1), meet(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet(Y1, X2))) -> join(meet2(Y1, X1), meet(Y1, X2))
% 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet2(X2, Y1))) -> join(meet2(Y1, X1), meet2(X2, Y1))
% 45.32/45.39 meet2(Y1, join(meet2(Y1, X1), meet2(Y1, X2))) -> join(meet2(Y1, X1), meet2(Y1, X2))
% 45.32/45.39 meet2(Y1, meet(X1, Y1)) -> meet(X1, Y1)
% 45.32/45.39 meet2(Y1, meet(Y1, X1)) -> meet(Y1, X1)
% 45.32/45.39 meet2(Y1, meet(join(X0, Y1), join(X2, Y1))) -> Y1
% 45.32/45.39 meet2(Y1, meet2(X1, Y1)) -> meet2(X1, Y1)
% 45.32/45.39 meet2(Y1, meet2(Y1, X1)) -> meet2(Y1, X1)
% 45.32/45.39 meet2(Y1, meet2(Y1, join(Y2, Y1))) -> Y1
% 45.32/45.40 meet2(Y1, meet2(join(Y0, Y1), join(Y1, Y2))) -> Y1
% 45.32/45.40 meet2(Y1, meet2(join(Y0, Y1), join(Y2, Y1))) -> Y1
% 45.32/45.40 meet2(Y1, meet2(join(Y1, Y0), join(Y2, Y1))) -> Y1
% 45.32/45.40 meet2(join(X0, X1), join(X1, meet(X2, join(X0, X1)))) -> join(X1, meet(X2, join(X0, X1)))
% 45.32/45.40 meet2(join(X0, X1), join(X1, meet(join(X0, X1), X2))) -> join(X1, meet(join(X0, X1), X2))
% 45.32/45.40 meet2(join(meet(X0, Y1), meet(X2, Y1)), meet(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1))))) -> join(meet(X0, Y1), meet(X2, Y1))
% 45.32/45.40 meet2(join(meet(X0, Y1), meet(X2, Y1)), meet2(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1))))) -> join(meet(X0, Y1), meet(X2, Y1))
% 45.32/45.40 meet2(join(meet(X0, Y1), meet(X2, Y1)), meet2(Y1, join(join(meet(X0, Y1), meet(X2, Y1)), Y2))) -> join(meet(X0, Y1), meet(X2, Y1))
% 45.32/45.40 meet2(join(meet(X1, Y0), meet(Y0, X2)), meet2(Y0, join(Y2, join(meet(X1, Y0), meet(Y0, X2))))) -> join(meet(X1, Y0), meet(Y0, X2))
% 45.32/45.40 meet2(join(meet(X1, Y0), meet2(X2, Y0)), meet2(Y0, join(Y2, join(meet(X1, Y0), meet2(X2, Y0))))) -> join(meet(X1, Y0), meet2(X2, Y0))
% 45.32/45.40 meet2(join(meet(X1, Y1), meet(Y1, X2)), meet(Y1, join(Y2, join(meet(X1, Y1), meet(Y1, X2))))) -> join(meet(X1, Y1), meet(Y1, X2))
% 45.32/45.40 meet2(join(meet(X1, Y2), meet(Y2, X2)), meet2(Y2, join(join(meet(X1, Y2), meet(Y2, X2)), Y1))) -> join(meet(X1, Y2), meet(Y2, X2))
% 45.32/45.40 meet2(join(meet(Y0, X1), meet(X2, Y0)), meet2(Y0, join(Y2, join(meet(Y0, X1), meet(X2, Y0))))) -> join(meet(Y0, X1), meet(X2, Y0))
% 45.32/45.40 meet2(join(meet(Y0, X1), meet(Y0, X2)), meet2(Y0, join(Y2, join(meet(Y0, X1), meet(Y0, X2))))) -> join(meet(Y0, X1), meet(Y0, X2))
% 45.32/45.40 meet2(join(meet(Y0, X1), meet2(X2, Y0)), meet2(Y0, join(Y2, join(meet(Y0, X1), meet2(X2, Y0))))) -> join(meet(Y0, X1), meet2(X2, Y0))
% 45.32/45.40 meet2(join(meet(Y1, X1), meet(X2, Y1)), meet(Y1, join(Y2, join(meet(Y1, X1), meet(X2, Y1))))) -> join(meet(Y1, X1), meet(X2, Y1))
% 45.32/45.40 meet2(join(meet(Y2, X1), meet(X2, Y2)), meet2(Y2, join(join(meet(Y2, X1), meet(X2, Y2)), Y1))) -> join(meet(Y2, X1), meet(X2, Y2))
% 45.32/45.40 meet2(join(meet(Y2, X1), meet(Y2, X2)), meet2(Y2, join(join(meet(Y2, X1), meet(Y2, X2)), Y1))) -> join(meet(Y2, X1), meet(Y2, X2))
% 45.32/45.40 meet2(join(meet2(X0, Y1), meet2(X2, Y1)), meet2(Y1, join(Y2, join(meet2(X0, Y1), meet2(X2, Y1))))) -> join(meet2(X0, Y1), meet2(X2, Y1))
% 45.32/45.40 meet2(join(meet2(X0, Y1), meet2(X2, Y1)), meet2(Y1, join(join(meet2(X0, Y1), meet2(X2, Y1)), Y2))) -> join(meet2(X0, Y1), meet2(X2, Y1))
% 45.32/45.40 meet2(join(meet2(X1, Y0), meet(X2, Y0)), meet2(Y0, join(Y2, join(meet2(X1, Y0), meet(X2, Y0))))) -> join(meet2(X1, Y0), meet(X2, Y0))
% 45.32/45.40 meet2(join(meet2(X1, Y0), meet(Y0, X2)), meet2(Y0, join(Y2, join(meet2(X1, Y0), meet(Y0, X2))))) -> join(meet2(X1, Y0), meet(Y0, X2))
% 45.32/45.40 meet2(join(meet2(X1, Y0), meet2(Y0, X2)), meet2(Y0, join(Y2, join(meet2(X1, Y0), meet2(Y0, X2))))) -> join(meet2(X1, Y0), meet2(Y0, X2))
% 45.32/45.40 meet2(join(meet2(X1, Y2), meet2(Y2, X2)), meet2(Y2, join(join(meet2(X1, Y2), meet2(Y2, X2)), Y1))) -> join(meet2(X1, Y2), meet2(Y2, X2))
% 45.32/45.40 meet2(join(meet2(Y0, X1), meet2(X2, Y0)), meet2(Y0, join(Y2, join(meet2(Y0, X1), meet2(X2, Y0))))) -> join(meet2(Y0, X1), meet2(X2, Y0))
% 45.32/45.40 meet2(join(meet2(Y0, X1), meet2(Y0, X2)), meet2(Y0, join(Y2, join(meet2(Y0, X1), meet2(Y0, X2))))) -> join(meet2(Y0, X1), meet2(Y0, X2))
% 45.32/45.40 meet2(join(meet2(Y2, X1), meet2(X2, Y2)), meet2(Y2, join(join(meet2(Y2, X1), meet2(X2, Y2)), Y1))) -> join(meet2(Y2, X1), meet2(X2, Y2))
% 45.32/45.40 meet2(meet(X0, X1), meet(join(Y1, meet(X0, X1)), meet2(X1, X0))) -> meet(X0, X1)
% 45.32/45.40 meet2(meet(X0, X1), meet(meet2(X1, X0), join(Y2, meet(X0, X1)))) -> meet(X0, X1)
% 45.32/45.40 meet2(meet(X0, X1), meet2(join(Y1, meet(X0, X1)), meet2(X1, X0))) -> meet(X0, X1)
% 45.32/45.40 meet2(meet(X0, X1), meet2(join(meet(X0, X1), Y1), meet2(X1, X0))) -> meet(X0, X1)
% 45.32/45.40 meet2(meet(X0, X1), meet2(meet2(X1, X0), join(Y2, meet(X0, X1)))) -> meet(X0, X1)
% 45.32/45.40 meet2(meet(X0, X1), meet2(meet2(X1, X0), join(meet(X0, X1), Y2))) -> meet(X0, X1)
% 45.32/45.40 meet2(meet(X1, Y0), meet2(Y0, join(Y2, meet(X1, Y0)))) -> meet(X1, Y0)
% 45.32/45.40 meet2(meet(X1, Y1), meet(Y1, join(Y2, meet(X1, Y1)))) -> meet(X1, Y1)
% 45.32/45.40 meet2(meet(X1, Y2), meet(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2)
% 45.32/45.40 meet2(meet(X1, Y2), meet2(Y2, join(meet(X1, Y2), Y1))) -> meet(X1, Y2)
% 45.32/45.40 meet2(meet(Y0, X1), meet2(Y0, join(Y2, meet(Y0, X1)))) -> meet(Y0, X1)
% 45.32/45.40 meet2(meet(Y0, Y1), meet2(Y0, Y1)) -> meet(Y0, Y1)
% 45.32/45.40 meet2(meet(Y0, Y1), meet2(Y1, Y0)) -> meet(Y0, Y1)
% 45.32/45.40 meet2(meet(Y0, Y1), meet2(Y1, join(Y2, meet(Y1, Y0)))) -> meet(Y0, Y1)
% 45.32/45.40 meet2(meet(Y1, X1), meet(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1)
% 45.32/45.40 meet2(meet(Y1, Y0), meet2(Y1, Y0)) -> meet(Y0, Y1)
% 45.32/45.40 meet2(meet(Y1, Y0), meet2(Y1, join(Y2, meet(Y0, Y1)))) -> meet(Y0, Y1)
% 45.32/45.40 meet2(meet(Y2, X1), meet(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1)
% 45.32/45.40 meet2(meet(Y2, X1), meet2(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1)
% 45.32/45.40 meet2(meet2(X1, Y0), meet2(Y0, join(Y2, meet2(X1, Y0)))) -> meet2(X1, Y0)
% 45.32/45.40 meet2(meet2(X1, Y1), meet(Y1, join(Y2, meet2(X1, Y1)))) -> meet2(X1, Y1)
% 45.32/45.40 meet2(meet2(X1, Y2), meet(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2)
% 45.32/45.40 meet2(meet2(X1, Y2), meet2(Y2, join(meet2(X1, Y2), Y1))) -> meet2(X1, Y2)
% 45.32/45.40 meet2(meet2(Y0, X1), meet2(Y0, join(Y2, meet2(Y0, X1)))) -> meet2(Y0, X1)
% 45.32/45.40 meet2(meet2(Y1, X1), meet(Y1, join(Y2, meet2(Y1, X1)))) -> meet2(Y1, X1)
% 45.32/45.40 meet2(meet2(Y2, X1), meet(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1)
% 45.32/45.40 meet2(meet2(Y2, X1), meet2(Y2, join(meet2(Y2, X1), Y1))) -> meet2(Y2, X1)
% 45.32/45.40 meet2(meet2(join(X, Y), join(Z, Y)), Y) -> Y
% 45.32/45.40 true__ -> false__
% 45.32/45.40 with the LPO induced by
% 45.32/45.40 b > a > f1 > meet2 > join > meet > true__ > false__
% 45.32/45.40
% 45.32/45.40 % SZS output end Proof
% 45.32/45.40
%------------------------------------------------------------------------------