TSTP Solution File: LAT008-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT008-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n004.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 06:04:05 EDT 2022
% Result : Unsatisfiable 11.36s 11.46s
% Output : Proof 11.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT008-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n004.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 30 06:19:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 11.36/11.46 % SZS status Unsatisfiable
% 11.36/11.46 % SZS output start Proof
% 11.36/11.46 The input problem is unsatisfiable because
% 11.36/11.46
% 11.36/11.46 [1] the following set of Horn clauses is unsatisfiable:
% 11.36/11.46
% 11.36/11.46 meet(X, join(X, Y)) = X
% 11.36/11.46 meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X))
% 11.36/11.46 join(a, meet(a, b)) = a ==> \bottom
% 11.36/11.46
% 11.36/11.46 This holds because
% 11.36/11.46
% 11.36/11.46 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 11.36/11.46
% 11.36/11.46 E:
% 11.36/11.46 f1(a) = false__
% 11.36/11.46 f1(join(a, meet(a, b))) = true__
% 11.36/11.46 meet(X, join(X, Y)) = X
% 11.36/11.46 meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X))
% 11.36/11.46 G:
% 11.36/11.46 true__ = false__
% 11.36/11.46
% 11.36/11.46 This holds because
% 11.36/11.46
% 11.36/11.46 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 11.36/11.46
% 11.36/11.46 join(Y0, meet(Y2, join(Y0, X1))) = meet(join(Y0, X1), join(Y2, Y0))
% 11.36/11.46 join(Y0, meet(Y2, meet(join(Y0, X1), join(X2, Y0)))) = meet(meet(join(Y0, X1), join(X2, Y0)), join(Y2, Y0))
% 11.36/11.46 join(Y1, Y0) = join(Y0, Y1)
% 11.36/11.46 join(join(X0, X0), meet(Y2, join(X0, X0))) = meet(join(X0, X0), join(Y2, join(X0, X1)))
% 11.36/11.46 join(join(X0, X0), meet(Y2, join(X0, X0))) = meet(join(X0, X0), join(Y2, join(join(X0, X0), X1)))
% 11.36/11.46 join(join(X0, X0), meet(Y2, join(join(X0, X1), X2))) = meet(join(join(X0, X1), X2), join(Y2, join(X0, X0)))
% 11.36/11.46 join(join(meet(X2, Y0), meet(X1, Y0)), meet(Y2, join(X1, X2))) = meet(join(X1, X2), join(Y2, Y0))
% 11.36/11.46 join(join(meet(X2, Y0), meet(X1, Y0)), meet(Y2, join(X1, X2))) = meet(join(X1, X2), join(Y2, meet(Y0, join(X1, X2))))
% 11.36/11.46 join(join(meet(X2, Y0), meet(X1, Y0)), meet(Y2, join(X1, X2))) = meet(join(X1, X2), join(meet(Y2, join(X1, X2)), Y0))
% 11.36/11.46 join(meet(X0, X1), meet(Y1, meet(X1, join(X2, X0)))) = meet(join(meet(X0, X1), meet(X2, X1)), join(Y1, meet(X0, X1)))
% 11.36/11.46 join(meet(X0, X1), meet(Y2, meet(X1, join(X2, X0)))) = meet(meet(X1, join(X2, X0)), join(Y2, meet(X0, X1)))
% 11.36/11.46 join(meet(X0, Y1), meet(Y2, Y1)) = meet(Y1, join(Y2, meet(X0, Y1)))
% 11.36/11.46 join(meet(Y0, Y0), meet(Y2, join(X1, Y0))) = meet(join(X1, Y0), join(Y2, Y0))
% 11.36/11.46 join(meet(Y0, Y1), meet(X0, Y1)) = meet(Y1, join(meet(X0, Y1), Y0))
% 11.36/11.46 join(meet(Y0, Y1), meet(X0, Y1)) = meet(Y1, join(meet(X0, Y1), meet(Y0, Y1)))
% 11.36/11.46 join(meet(Y0, join(X0, X0)), join(X0, X0)) = meet(join(X0, X0), join(join(X0, X1), Y0))
% 11.36/11.46 join(meet(Y0, join(X0, X0)), join(X0, X0)) = meet(join(X0, X0), join(join(X0, X1), meet(Y0, join(X0, X0))))
% 11.36/11.46 join(meet(Y0, join(X1, X2)), join(meet(X2, Y2), meet(X1, Y2))) = meet(join(X1, X2), join(Y2, Y0))
% 11.36/11.46 join(meet(Y0, join(X1, X2)), join(meet(X2, Y2), meet(X1, Y2))) = meet(join(X1, X2), join(Y2, meet(Y0, join(X1, X2))))
% 11.36/11.46 join(meet(Y0, join(X1, X2)), join(meet(X2, Y2), meet(X1, Y2))) = meet(join(X1, X2), join(meet(Y2, join(X1, X2)), Y0))
% 11.36/11.46 join(meet(Y0, join(X1, X2)), meet(Y2, join(X1, meet(X2, Y0)))) = meet(join(X1, meet(X2, Y0)), join(Y2, Y0))
% 11.36/11.46 join(meet(Y0, join(X1, X2)), meet(Y2, join(meet(X1, Y0), X2))) = meet(join(meet(X1, Y0), X2), join(Y2, Y0))
% 11.36/11.46 join(meet(Y0, meet(X1, join(X2, X0))), meet(X0, X1)) = meet(meet(X1, join(X2, X0)), join(meet(X0, X1), Y0))
% 11.36/11.46 join(meet(Y1, Y0), meet(Y2, Y1)) = meet(Y1, join(Y2, Y0))
% 11.36/11.46 meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X))
% 11.36/11.46 meet(Y0, meet(Y0, join(Y2, X0))) = meet(Y0, join(X0, Y2))
% 11.36/11.46 meet(Y1, X0) = meet(X0, Y1)
% 11.36/11.46 meet(join(X0, X0), join(Y1, join(X0, X0))) = meet(join(X0, X0), join(Y1, join(X0, X1)))
% 11.36/11.46 meet(join(X1, X1), join(X0, X0)) = meet(join(X0, X0), join(X1, X1))
% 11.36/11.46 meet(join(X1, X1), join(join(X0, X0), meet(join(X0, X0), join(X1, X1)))) = meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(join(Y1, Y2), Y0) = join(meet(Y2, Y0), meet(Y1, Y0))
% 11.36/11.46 meet(join(Y1, Y2), Y0) = meet(Y0, join(Y2, Y1))
% 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(X1, join(X0, X0))) = meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(X1, join(X0, meet(X0, X1)))) = meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 meet(meet(X0, join(Y1, Y2)), meet(X0, join(Y1, Y2))) = meet(meet(X0, join(Y1, Y2)), join(Y2, Y1))
% 11.36/11.46 meet(meet(X2, X1), meet(X1, join(X2, X0))) = meet(meet(X2, X1), meet(X2, X1))
% 11.36/11.46 f1(a) -> false__
% 11.36/11.46 f1(join(a, meet(a, b))) -> true__
% 11.36/11.46 join(Y0, Y0) -> Y0
% 11.36/11.46 join(Y0, join(X1, Y0)) -> join(X1, Y0)
% 11.36/11.46 join(Y0, join(Y0, Y1)) -> join(Y0, Y1)
% 11.36/11.46 join(Y0, join(meet(Y2, Y1), meet(Y0, Y1))) -> meet(join(Y0, Y2), join(Y1, Y0))
% 11.36/11.46 join(Y0, meet(Y0, Y1)) -> Y0
% 11.36/11.46 join(Y0, meet(Y1, Y0)) -> Y0
% 11.36/11.46 join(Y0, meet(join(Y0, X1), join(X2, Y0))) -> meet(join(Y0, X1), join(X2, Y0))
% 11.36/11.46 join(Y0, meet(join(Y0, X1), join(Y0, join(Y0, X1)))) -> join(Y0, X1)
% 11.36/11.46 join(Y0, meet(join(Y0, Y1), join(Y0, Y1))) -> join(Y0, Y1)
% 11.36/11.46 join(Y1, join(Y1, Y1)) -> join(Y1, Y1)
% 11.36/11.46 join(join(X0, X0), join(join(X0, X1), join(X0, X1))) -> join(join(X0, X1), join(X0, X1))
% 11.36/11.46 join(join(X0, X1), join(X1, X0)) -> join(X1, X0)
% 11.36/11.46 join(join(X0, X1), meet(Y1, join(X1, X0))) -> join(X0, X1)
% 11.36/11.46 join(join(X1, X0), join(X0, X1)) -> join(X1, X0)
% 11.36/11.46 join(join(X1, Y1), Y1) -> join(X1, Y1)
% 11.36/11.46 join(join(Y1, X1), Y1) -> join(Y1, X1)
% 11.36/11.46 join(join(Y1, Y1), join(Y1, Y1)) -> join(Y1, Y1)
% 11.36/11.46 join(meet(X0, X1), meet(X1, join(X0, X0))) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 join(meet(X0, X1), meet(X1, join(X0, meet(X0, X1)))) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 join(meet(X0, X1), meet(join(meet(X0, X1), meet(X2, X1)), meet(X1, join(X2, X0)))) -> join(meet(X0, X1), meet(X2, X1))
% 11.36/11.46 join(meet(X0, X1), meet(meet(X1, join(X2, X0)), join(meet(X0, X1), meet(X2, X1)))) -> join(meet(X0, X1), meet(X2, X1))
% 11.36/11.46 join(meet(X1, join(X0, meet(X0, X1))), meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 join(meet(Y0, Y1), Y1) -> Y1
% 11.36/11.46 join(meet(Y0, join(X0, X0)), join(X0, X0)) -> join(X0, X0)
% 11.36/11.46 join(meet(Y0, join(X1, Y2)), meet(Y2, Y2)) -> meet(join(X1, Y2), join(Y2, Y0))
% 11.36/11.46 join(meet(Y0, join(X1, meet(X2, Y2))), meet(Y2, join(X1, X2))) -> meet(join(X1, meet(X2, Y2)), join(Y2, Y0))
% 11.36/11.46 join(meet(Y0, join(Y2, X1)), Y2) -> meet(join(Y2, X1), join(Y2, Y0))
% 11.36/11.46 join(meet(Y0, join(join(X0, X1), X2)), join(X0, X0)) -> meet(join(join(X0, X1), X2), join(join(X0, X0), Y0))
% 11.36/11.46 join(meet(Y0, meet(X1, join(X0, X0))), meet(X1, join(meet(X0, X1), X0))) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 join(meet(Y0, meet(X1, join(meet(X0, X1), X0))), meet(X1, join(X0, X0))) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 join(meet(Y0, meet(join(Y2, X1), join(X2, Y2))), Y2) -> meet(meet(join(Y2, X1), join(X2, Y2)), join(Y2, Y0))
% 11.36/11.46 join(meet(Y1, Y0), Y1) -> Y1
% 11.36/11.46 join(meet(Y2, Y0), meet(Y1, Y0)) -> meet(Y0, join(Y2, Y1))
% 11.36/11.46 join(meet(Y2, Y2), meet(Y1, Y2)) -> meet(Y2, Y2)
% 11.36/11.46 join(meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))), meet(X1, join(X0, meet(X0, X1)))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 join(meet(join(X1, X1), Y0), meet(meet(X0, join(X1, X1)), Y0)) -> meet(Y0, join(X1, X1))
% 11.36/11.46 join(meet(join(Y1, X1), join(X2, Y1)), Y1) -> meet(join(Y1, X1), join(X2, Y1))
% 11.36/11.46 join(meet(meet(X2, X1), Y0), meet(meet(X0, X1), Y0)) -> meet(Y0, meet(X1, join(X2, X0)))
% 11.36/11.46 meet(X, join(X, Y)) -> X
% 11.36/11.46 meet(X1, join(meet(X0, X1), X0)) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(Y0, Y0) -> Y0
% 11.36/11.46 meet(Y0, join(join(Y1, Y1), Y1)) -> meet(Y0, join(Y1, Y1))
% 11.36/11.46 meet(Y0, meet(X1, join(X2, meet(X0, X1)))) -> meet(Y0, meet(X1, join(X2, X0)))
% 11.36/11.46 meet(Y0, meet(X1, join(meet(X2, X1), X0))) -> meet(Y0, meet(X1, join(X2, X0)))
% 11.36/11.46 meet(Y0, meet(Y0, Y0)) -> Y0
% 11.36/11.46 meet(Y0, meet(Y0, Y2)) -> meet(Y0, Y2)
% 11.36/11.46 meet(Y0, meet(join(Y0, X1), join(Y2, Y0))) -> Y0
% 11.36/11.46 meet(Y0, meet(join(Y0, Y1), Y0)) -> Y0
% 11.36/11.46 meet(Y0, meet(join(Y0, Y1), join(Y0, Y2))) -> Y0
% 11.36/11.46 meet(Y0, meet(join(Y0, Y1), meet(join(Y0, Y1), join(Y0, Y2)))) -> Y0
% 11.36/11.46 meet(Y0, meet(join(Y1, Y0), join(Y2, Y0))) -> Y0
% 11.36/11.46 meet(Y0, meet(join(Y1, Y1), join(Y0, Y1))) -> meet(Y0, join(Y1, Y1))
% 11.36/11.46 meet(Y0, meet(join(Y2, Y0), join(Y0, Y1))) -> Y0
% 11.36/11.46 meet(Y0, meet(meet(join(Y0, X1), join(X2, Y0)), join(Y2, Y0))) -> Y0
% 11.36/11.46 meet(Y1, join(Y2, Y1)) -> meet(Y1, Y1)
% 11.36/11.46 meet(Y1, join(Y2, meet(Y0, Y1))) -> meet(Y1, join(Y2, Y0))
% 11.36/11.46 meet(Y1, join(meet(Y2, Y1), Y0)) -> meet(Y1, join(Y2, Y0))
% 11.36/11.46 meet(Y1, meet(X0, Y1)) -> meet(X0, Y1)
% 11.36/11.46 meet(Y1, meet(Y1, join(Y2, Y1))) -> Y1
% 11.36/11.46 meet(join(X0, X0), join(join(X0, X1), Y0)) -> join(X0, X0)
% 11.36/11.46 meet(join(X0, X0), join(join(X0, X1), meet(Y0, join(X0, X0)))) -> join(X0, X0)
% 11.36/11.46 meet(join(X0, X0), join(join(X1, meet(X1, join(X0, X0))), meet(join(X1, meet(X1, join(X0, X0))), join(X0, X0)))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(join(X0, X0), join(join(join(X0, X0), Y1), Y2)) -> join(X0, X0)
% 11.36/11.46 meet(join(X0, X0), meet(join(X0, X0), join(Y2, join(X0, X1)))) -> join(X0, X0)
% 11.36/11.46 meet(join(X0, X0), meet(join(X0, X0), join(Y2, join(join(X0, X0), X1)))) -> join(X0, X0)
% 11.36/11.46 meet(join(X0, X0), meet(join(join(X0, X1), X2), join(Y2, join(X0, X0)))) -> join(X0, X0)
% 11.36/11.46 meet(join(X0, meet(X2, join(X0, X1))), join(X2, X0)) -> meet(join(X0, X1), join(X2, X0))
% 11.36/11.46 meet(join(X1, X1), join(join(meet(X0, X1), X0), meet(join(meet(X0, X1), X0), join(X1, X1)))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(join(X1, X2), join(Y1, join(meet(X2, Y2), meet(X1, Y2)))) -> meet(join(X1, X2), join(Y1, Y2))
% 11.36/11.46 meet(join(X1, X2), join(join(meet(X2, Y1), meet(X1, Y1)), Y2)) -> meet(join(X1, X2), join(Y1, Y2))
% 11.36/11.46 meet(join(X1, Y0), Y0) -> Y0
% 11.36/11.46 meet(join(Y0, Y1), Y0) -> Y0
% 11.36/11.46 meet(join(Y0, Y2), join(Y0, Y0)) -> join(Y0, Y0)
% 11.36/11.46 meet(join(Y1, Y2), join(Y2, Y1)) -> join(Y1, Y2)
% 11.36/11.46 meet(join(Y2, X1), join(Y2, meet(Y0, join(Y2, X1)))) -> meet(join(Y2, X1), join(Y2, Y0))
% 11.36/11.46 meet(join(Y2, Y2), meet(join(join(Y2, Y2), Y1), join(Y2, Y2))) -> join(Y2, Y2)
% 11.36/11.46 meet(join(join(X0, X0), Y1), join(X0, X0)) -> join(X0, X0)
% 11.36/11.46 meet(join(meet(X0, X1), X0), join(X1, meet(X0, X1))) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(X1, join(X0, X0))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(join(meet(X0, X1), Y1), meet(join(X0, X0), join(X1, X1))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(join(meet(X1, join(X0, X0)), Y1), meet(X1, join(X0, X0))) -> meet(join(X0, X0), join(X1, X1))
% 11.36/11.46 meet(join(meet(X1, join(X0, X0)), Y1), meet(join(X0, X0), join(X1, X1))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), join(X1, X2)) -> meet(Y0, join(X1, X2))
% 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), join(X1, meet(X2, Y0))) -> meet(Y0, join(X1, meet(X2, Y0)))
% 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), join(meet(X1, Y0), X2)) -> meet(Y0, join(meet(X1, Y0), X2))
% 11.36/11.46 meet(join(meet(X2, Y0), meet(X1, Y0)), meet(join(X1, X2), join(Y2, Y0))) -> meet(Y0, join(X1, X2))
% 11.36/11.46 meet(join(meet(join(X0, X0), join(X1, meet(X1, join(X0, X0)))), Y1), meet(X1, join(X0, X0))) -> meet(join(X0, X0), join(X1, meet(X1, join(X0, X0))))
% 11.36/11.46 meet(meet(X0, X1), meet(X1, join(X2, X0))) -> meet(X0, X1)
% 11.36/11.46 meet(meet(X0, X1), meet(meet(X1, join(X2, X0)), join(Y2, meet(X0, X1)))) -> meet(X0, X1)
% 11.36/11.46 meet(meet(X0, X1), meet(meet(X1, join(X2, meet(X0, X1))), join(Y2, meet(X0, X1)))) -> meet(X0, X1)
% 11.36/11.46 meet(meet(X0, Y1), meet(Y1, join(Y2, meet(X0, Y1)))) -> meet(X0, Y1)
% 11.36/11.46 meet(meet(X0, Y1), meet(Y1, meet(X0, Y1))) -> meet(X0, Y1)
% 11.36/11.46 meet(meet(X0, join(Y1, Y2)), join(Y2, Y1)) -> meet(X0, join(Y1, Y2))
% 11.36/11.46 meet(meet(X1, X0), meet(join(meet(X1, X0), Y1), X0)) -> meet(X1, X0)
% 11.36/11.46 meet(meet(X1, join(X0, X0)), join(join(meet(X0, X1), Y1), Y2)) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 meet(meet(X1, join(X2, X0)), meet(X1, join(meet(X0, X1), X0))) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 meet(meet(X1, join(X2, meet(X0, X1))), meet(X1, join(meet(X0, X1), X0))) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 meet(meet(X1, join(meet(X0, X1), X0)), join(meet(X1, join(X2, X0)), Y2)) -> meet(X1, join(meet(X0, X1), X0))
% 11.36/11.46 meet(meet(X2, X1), meet(join(meet(X2, X1), Y1), meet(X1, join(X2, X0)))) -> meet(X2, X1)
% 11.36/11.46 meet(meet(X2, X1), meet(join(meet(X2, X1), Y1), meet(X1, join(meet(X2, X1), X0)))) -> meet(X2, X1)
% 11.36/11.46 meet(meet(Y0, Y0), join(X1, Y0)) -> meet(Y0, Y0)
% 11.36/11.46 meet(meet(Y0, Y2), Y2) -> meet(Y0, Y2)
% 11.36/11.46 meet(meet(Y0, join(X1, X2)), join(X1, meet(X2, Y0))) -> meet(Y0, join(X1, X2))
% 11.36/11.46 meet(meet(Y0, join(X1, X2)), join(meet(X1, Y0), X2)) -> meet(Y0, join(X1, X2))
% 11.36/11.46 meet(meet(Y0, join(X1, X2)), meet(join(X1, meet(X2, Y0)), join(Y2, Y0))) -> meet(Y0, join(X1, X2))
% 11.36/11.46 meet(meet(Y0, join(X2, X1)), meet(Y0, join(X1, X2))) -> meet(Y0, meet(Y0, join(X1, X2)))
% 11.36/11.46 meet(meet(Y0, join(join(Y0, Y0), X1)), join(Y0, Y0)) -> meet(Y0, join(join(Y0, Y0), X1))
% 11.36/11.46 meet(meet(Y0, meet(Y0, join(X2, X1))), join(X1, X2)) -> meet(Y0, join(X1, X2))
% 11.36/11.46 meet(meet(Y1, X1), meet(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1)
% 11.36/11.46 meet(meet(Y2, X1), meet(Y2, join(meet(Y2, X1), Y1))) -> meet(Y2, X1)
% 11.36/11.46 meet(meet(join(X0, X0), join(join(X1, X1), meet(join(X1, X1), join(X0, X0)))), join(join(X1, X1), Y2)) -> meet(join(X0, X0), join(join(X1, X1), meet(join(X1, X1), join(X0, X0))))
% 11.36/11.46 meet(meet(join(X1, X1), join(X0, X0)), join(X1, X1)) -> meet(join(X0, X0), join(X1, X1))
% 11.36/11.46 meet(meet(join(Y0, X2), join(X1, Y0)), join(Y0, Y0)) -> join(Y0, Y0)
% 11.36/11.46 meet(meet(join(Y2, X1), join(X2, Y2)), join(Y2, meet(Y0, meet(join(Y2, X1), join(X2, Y2))))) -> meet(meet(join(Y2, X1), join(X2, Y2)), join(Y2, Y0))
% 11.36/11.46 meet(meet(join(Y2, X1), join(Y2, X1)), meet(join(meet(join(Y2, X1), join(Y2, X1)), Y1), join(Y2, X1))) -> meet(join(Y2, X1), join(Y2, X1))
% 11.36/11.46 meet(meet(join(Y2, Y2), Y1), meet(Y1, join(Y2, Y2))) -> meet(join(Y2, Y2), Y1)
% 11.36/11.46 meet(meet(meet(X2, X1), Y1), meet(Y1, meet(X1, join(X2, X0)))) -> meet(meet(X2, X1), Y1)
% 11.36/11.46 meet(meet(meet(join(Y2, X1), join(Y2, X1)), Y1), meet(Y1, join(Y2, X1))) -> meet(meet(join(Y2, X1), join(Y2, X1)), Y1)
% 11.36/11.46 true__ -> false__
% 11.36/11.46 with the LPO induced by
% 11.36/11.46 b > a > f1 > join > meet > true__ > false__
% 11.36/11.46
% 11.36/11.46 % SZS output end Proof
% 11.36/11.46
%------------------------------------------------------------------------------