TSTP Solution File: LAT089-1 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LAT089-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n008.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 06:04:34 EDT 2022
% Result : Unsatisfiable 18.51s 18.63s
% Output : Proof 18.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : LAT089-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.07 % Command : moca.sh %s
% 0.06/0.26 % Computer : n008.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Thu Jun 30 01:53:38 EDT 2022
% 0.06/0.26 % CPUTime :
% 18.51/18.63 % SZS status Unsatisfiable
% 18.51/18.63 % SZS output start Proof
% 18.51/18.63 The input problem is unsatisfiable because
% 18.51/18.63
% 18.51/18.63 [1] the following set of Horn clauses is unsatisfiable:
% 18.51/18.63
% 18.51/18.63 join(meet(A, B), meet(A, join(A, B))) = A
% 18.51/18.63 join(meet(A, A), meet(B, join(A, A))) = A
% 18.51/18.63 join(meet(A, B), meet(B, join(A, B))) = B
% 18.51/18.63 meet(meet(join(A, B), join(C, A)), A) = A
% 18.51/18.63 join(join(meet(A, B), meet(C, A)), A) = A
% 18.51/18.63 meet(b, a) = meet(a, b) ==> \bottom
% 18.51/18.63
% 18.51/18.63 This holds because
% 18.51/18.63
% 18.51/18.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 18.51/18.63
% 18.51/18.63 E:
% 18.51/18.63 f1(meet(a, b)) = false__
% 18.51/18.63 f1(meet(b, a)) = true__
% 18.51/18.63 join(join(meet(A, B), meet(C, A)), A) = A
% 18.51/18.63 join(meet(A, A), meet(B, join(A, A))) = A
% 18.51/18.63 join(meet(A, B), meet(A, join(A, B))) = A
% 18.51/18.63 join(meet(A, B), meet(B, join(A, B))) = B
% 18.51/18.63 meet(meet(join(A, B), join(C, A)), A) = A
% 18.51/18.63 G:
% 18.51/18.63 true__ = false__
% 18.51/18.63
% 18.51/18.63 This holds because
% 18.51/18.63
% 18.51/18.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 18.51/18.63
% 18.51/18.63 meet(X0, X1) = meet(X1, X0)
% 18.51/18.63 f1(meet(a, b)) -> false__
% 18.51/18.63 f1(meet(b, a)) -> true__
% 18.51/18.63 join(X0, meet(X0, join(X0, X1))) -> X0
% 18.51/18.63 join(Y0, join(X1, Y0)) -> join(X1, Y0)
% 18.51/18.63 join(Y0, join(Y0, Y0)) -> Y0
% 18.51/18.63 join(Y0, join(join(Y0, X1), Y0)) -> join(join(Y0, X1), Y0)
% 18.51/18.63 join(Y0, join(meet(X1, Y0), meet(Y2, Y0))) -> Y0
% 18.51/18.63 join(Y0, join(meet(Y0, Y1), meet(Y0, X1))) -> Y0
% 18.51/18.63 join(Y0, join(meet(Y1, Y0), meet(Y0, X1))) -> Y0
% 18.51/18.63 join(Y0, meet(Y0, X1)) -> Y0
% 18.51/18.63 join(Y0, meet(Y0, meet(X1, Y0))) -> Y0
% 18.51/18.63 join(Y0, meet(Y1, Y0)) -> Y0
% 18.51/18.63 join(Y0, meet(Y1, join(Y0, Y0))) -> Y0
% 18.51/18.63 join(Y1, Y1) -> Y1
% 18.51/18.63 join(Y1, join(Y1, X1)) -> join(Y1, X1)
% 18.51/18.63 join(Y1, join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.63 join(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> Y1
% 18.51/18.63 join(Y1, meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1))
% 18.51/18.63 join(Y1, meet(Y1, join(Y1, Y1))) -> Y1
% 18.51/18.63 join(Y1, meet(Y1, join(join(Y1, X1), Y1))) -> Y1
% 18.51/18.63 join(Y1, meet(Y1, join(meet(Y1, join(X1, Y1)), Y1))) -> Y1
% 18.51/18.63 join(Y1, meet(Y1, join(meet(join(Y1, X1), Y1), Y1))) -> Y1
% 18.51/18.63 join(Y1, meet(Y1, join(meet(join(Y1, X1), join(X2, Y1)), Y1))) -> Y1
% 18.51/18.63 join(Y1, meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1))
% 18.51/18.63 join(Y1, meet(join(X0, Y1), join(Y1, X2))) -> meet(join(X0, Y1), join(Y1, X2))
% 18.51/18.63 join(Y1, meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(Y1, meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2))
% 18.51/18.63 join(Y1, meet(join(Y1, X1), join(join(Y1, X1), Y1))) -> join(Y1, X1)
% 18.51/18.63 join(Y1, meet(meet(Y1, join(X1, Y1)), join(meet(Y1, join(X1, Y1)), Y1))) -> meet(Y1, join(X1, Y1))
% 18.51/18.63 join(Y1, meet(meet(join(Y1, X1), Y1), join(meet(join(Y1, X1), Y1), Y1))) -> meet(join(Y1, X1), Y1)
% 18.51/18.63 join(Y1, meet(meet(join(Y1, X1), join(X2, Y1)), join(meet(join(Y1, X1), join(X2, Y1)), Y1))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(join(X0, X0), meet(join(X0, X0), join(meet(join(join(X0, X0), Y1), X0), join(X0, X0)))) -> join(X0, X0)
% 18.51/18.63 join(join(X0, Y1), join(Y1, meet(Y2, join(X0, Y1)))) -> join(X0, Y1)
% 18.51/18.63 join(join(X0, meet(X0, X1)), meet(X0, X1)) -> join(X0, meet(X0, X1))
% 18.51/18.63 join(join(X1, Y1), Y1) -> join(X1, Y1)
% 18.51/18.63 join(join(X1, Y1), join(Y1, meet(join(X1, Y1), Y2))) -> join(X1, Y1)
% 18.51/18.63 join(join(X1, Y1), meet(join(X1, Y1), Y1)) -> join(X1, Y1)
% 18.51/18.63 join(join(X1, Y2), join(meet(Y1, join(X1, Y2)), Y2)) -> join(X1, Y2)
% 18.51/18.63 join(join(X1, Y2), join(meet(join(X1, Y2), Y1), Y2)) -> join(X1, Y2)
% 18.51/18.63 join(join(Y0, join(X1, Y0)), join(X1, Y0)) -> join(X1, Y0)
% 18.51/18.63 join(join(Y0, meet(Y0, X1)), Y0) -> Y0
% 18.51/18.63 join(join(Y1, X1), Y1) -> join(Y1, X1)
% 18.51/18.63 join(join(Y1, X1), join(Y1, meet(Y2, join(Y1, X1)))) -> join(Y1, X1)
% 18.51/18.63 join(join(Y1, X1), join(Y1, meet(join(Y1, X1), Y2))) -> join(Y1, X1)
% 18.51/18.63 join(join(Y1, Y1), Y1) -> Y1
% 18.51/18.63 join(join(Y1, join(Y1, X1)), join(Y1, X1)) -> join(Y1, X1)
% 18.51/18.63 join(join(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(Y1, join(meet(Y1, X1), Y1))
% 18.51/18.63 join(join(Y1, meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1))
% 18.51/18.63 join(join(Y1, meet(Y2, Y1)), Y1) -> Y1
% 18.51/18.63 join(join(Y1, meet(Y2, join(X0, Y1))), join(X0, Y1)) -> join(X0, Y1)
% 18.51/18.63 join(join(Y1, meet(Y2, join(Y1, X1))), join(Y1, X1)) -> join(Y1, X1)
% 18.51/18.63 join(join(Y1, meet(Y2, join(join(Y1, X1), Y1))), join(join(Y1, X1), Y1)) -> join(join(Y1, X1), Y1)
% 18.51/18.63 join(join(Y1, meet(Y2, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.63 join(join(Y1, meet(Y2, meet(Y1, join(X1, Y1)))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1))
% 18.51/18.63 join(join(Y1, meet(Y2, meet(join(X0, Y1), join(X2, Y1)))), meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1))
% 18.51/18.63 join(join(Y1, meet(Y2, meet(join(X0, Y1), join(Y1, X2)))), meet(join(X0, Y1), join(Y1, X2))) -> meet(join(X0, Y1), join(Y1, X2))
% 18.51/18.63 join(join(Y1, meet(Y2, meet(join(Y1, X1), Y1))), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1)
% 18.51/18.63 join(join(Y1, meet(Y2, meet(join(Y1, X1), join(X2, Y1)))), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(join(Y1, meet(Y2, meet(join(Y1, X1), join(Y1, X2)))), meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2))
% 18.51/18.63 join(join(Y1, meet(join(X0, Y1), Y2)), join(X0, Y1)) -> join(X0, Y1)
% 18.51/18.63 join(join(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1)
% 18.51/18.63 join(join(Y1, meet(join(Y1, X1), Y2)), join(Y1, X1)) -> join(Y1, X1)
% 18.51/18.63 join(join(Y1, meet(join(Y1, X1), join(X2, Y1))), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(join(Y1, meet(meet(join(X0, Y1), join(X2, Y1)), Y2)), meet(join(X0, Y1), join(X2, Y1))) -> meet(join(X0, Y1), join(X2, Y1))
% 18.51/18.63 join(join(Y1, meet(meet(join(X0, Y1), join(Y1, X2)), Y2)), meet(join(X0, Y1), join(Y1, X2))) -> meet(join(X0, Y1), join(Y1, X2))
% 18.51/18.63 join(join(Y1, meet(meet(join(Y1, X1), join(X2, Y1)), Y2)), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(join(Y1, meet(meet(join(Y1, X1), join(Y1, X2)), Y2)), meet(join(Y1, X1), join(Y1, X2))) -> meet(join(Y1, X1), join(Y1, X2))
% 18.51/18.63 join(join(Y2, X1), join(meet(Y1, join(Y2, X1)), Y2)) -> join(Y2, X1)
% 18.51/18.63 join(join(Y2, X1), join(meet(join(Y2, X1), Y1), Y2)) -> join(Y2, X1)
% 18.51/18.63 join(join(join(X1, Y1), Y1), join(X1, Y1)) -> join(X1, Y1)
% 18.51/18.63 join(join(join(Y1, X1), Y1), Y1) -> join(join(Y1, X1), Y1)
% 18.51/18.63 join(join(join(Y1, X1), Y1), join(Y1, X1)) -> join(Y1, X1)
% 18.51/18.63 join(join(join(Y1, X1), Y1), meet(join(join(Y1, X1), Y1), Y1)) -> join(join(Y1, X1), Y1)
% 18.51/18.63 join(join(join(join(Y1, X1), Y1), Y1), join(join(Y1, X1), Y1)) -> join(join(Y1, X1), Y1)
% 18.51/18.63 join(join(meet(A, B), meet(C, A)), A) -> A
% 18.51/18.63 join(join(meet(X0, X0), meet(X0, meet(X0, X0))), meet(X0, meet(X0, X0))) -> meet(X0, meet(X0, X0))
% 18.51/18.63 join(join(meet(X0, X1), meet(X0, meet(X0, X1))), meet(X0, meet(X0, X1))) -> meet(X0, meet(X0, X1))
% 18.51/18.63 join(join(meet(X0, X1), meet(meet(X0, X1), X1)), meet(meet(X0, X1), X1)) -> meet(meet(X0, X1), X1)
% 18.51/18.63 join(join(meet(X0, X2), meet(X0, join(X1, meet(X0, X2)))), meet(X0, join(X1, meet(X0, X2)))) -> meet(X0, join(X1, meet(X0, X2)))
% 18.51/18.63 join(join(meet(X1, X0), meet(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.63 join(join(meet(X1, Y0), Y0), Y0) -> Y0
% 18.51/18.63 join(join(meet(X1, Y0), meet(Y0, Y2)), Y0) -> Y0
% 18.51/18.63 join(join(meet(X1, Y0), meet(Y2, Y0)), Y0) -> Y0
% 18.51/18.63 join(join(meet(X2, X0), meet(X0, join(X1, meet(X2, X0)))), meet(X0, join(X1, meet(X2, X0)))) -> meet(X0, join(X1, meet(X2, X0)))
% 18.51/18.63 join(join(meet(Y0, Y1), Y0), Y0) -> Y0
% 18.51/18.63 join(join(meet(Y0, Y1), meet(Y0, X1)), Y0) -> Y0
% 18.51/18.63 join(join(meet(Y0, join(X1, Y2)), Y2), join(X1, Y2)) -> join(X1, Y2)
% 18.51/18.63 join(join(meet(Y0, join(Y2, X1)), Y2), join(Y2, X1)) -> join(Y2, X1)
% 18.51/18.63 join(join(meet(Y0, join(join(Y2, X1), Y2)), Y2), join(join(Y2, X1), Y2)) -> join(join(Y2, X1), Y2)
% 18.51/18.63 join(join(meet(Y0, meet(join(X0, Y2), join(X2, Y2))), Y2), meet(join(X0, Y2), join(X2, Y2))) -> meet(join(X0, Y2), join(X2, Y2))
% 18.51/18.63 join(join(meet(Y0, meet(join(X1, Y2), join(Y2, X2))), Y2), meet(join(X1, Y2), join(Y2, X2))) -> meet(join(X1, Y2), join(Y2, X2))
% 18.51/18.63 join(join(meet(Y0, meet(join(Y2, X1), join(X2, Y2))), Y2), meet(join(Y2, X1), join(X2, Y2))) -> meet(join(Y2, X1), join(X2, Y2))
% 18.51/18.63 join(join(meet(Y0, meet(join(Y2, X1), join(Y2, X2))), Y2), meet(join(Y2, X1), join(Y2, X2))) -> meet(join(Y2, X1), join(Y2, X2))
% 18.51/18.63 join(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1))) -> join(Y1, join(meet(Y1, X1), Y1))
% 18.51/18.63 join(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1)))) -> join(meet(Y1, X1), Y1)
% 18.51/18.63 join(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), join(meet(Y1, join(Y2, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)))) -> join(meet(Y1, X1), Y1)
% 18.51/18.63 join(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), join(meet(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)))) -> join(meet(Y1, X1), Y1)
% 18.51/18.63 join(join(meet(Y1, X1), meet(X2, Y1)), meet(join(meet(Y1, X1), meet(X2, Y1)), join(Y1, join(meet(Y1, X1), meet(X2, Y1))))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.63 join(join(meet(join(X1, Y2), Y1), Y2), join(X1, Y2)) -> join(X1, Y2)
% 18.51/18.63 join(join(meet(join(Y2, X1), Y1), Y2), join(Y2, X1)) -> join(Y2, X1)
% 18.51/18.63 join(join(meet(join(join(Y2, X1), Y2), Y1), Y2), join(join(Y2, X1), Y2)) -> join(join(Y2, X1), Y2)
% 18.51/18.63 join(join(meet(meet(join(X1, Y2), join(X2, Y2)), Y1), Y2), meet(join(X1, Y2), join(X2, Y2))) -> meet(join(X1, Y2), join(X2, Y2))
% 18.51/18.63 join(join(meet(meet(join(X1, Y2), join(Y2, X2)), Y1), Y2), meet(join(X1, Y2), join(Y2, X2))) -> meet(join(X1, Y2), join(Y2, X2))
% 18.51/18.63 join(join(meet(meet(join(Y2, X1), join(X2, Y2)), Y1), Y2), meet(join(Y2, X1), join(X2, Y2))) -> meet(join(Y2, X1), join(X2, Y2))
% 18.51/18.63 join(join(meet(meet(join(Y2, X1), join(Y2, X2)), Y1), Y2), meet(join(Y2, X1), join(Y2, X2))) -> meet(join(Y2, X1), join(Y2, X2))
% 18.51/18.63 join(meet(A, A), meet(B, join(A, A))) -> A
% 18.51/18.63 join(meet(A, B), meet(A, join(A, B))) -> A
% 18.51/18.63 join(meet(A, B), meet(B, join(A, B))) -> B
% 18.51/18.63 join(meet(X0, X0), meet(meet(X0, X0), join(meet(X0, join(Y2, meet(X0, X0))), meet(X0, X0)))) -> meet(X0, X0)
% 18.51/18.63 join(meet(X0, X0), meet(meet(X0, X0), join(meet(X0, meet(X0, X0)), meet(X0, X0)))) -> meet(X0, X0)
% 18.51/18.63 join(meet(X0, X0), meet(meet(X0, meet(X0, X0)), join(meet(X0, meet(X0, X0)), meet(X0, X0)))) -> meet(X0, meet(X0, X0))
% 18.51/18.63 join(meet(X0, X1), join(X0, meet(X0, X1))) -> join(X0, meet(X0, X1))
% 18.51/18.63 join(meet(X0, X1), meet(X1, X0)) -> meet(X0, X1)
% 18.51/18.63 join(meet(X0, X1), meet(meet(X0, meet(X0, X1)), join(meet(X0, meet(X0, X1)), meet(X0, X1)))) -> meet(X0, meet(X0, X1))
% 18.51/18.63 join(meet(X0, X2), meet(X0, join(X1, meet(X0, X2)))) -> meet(X0, join(X1, meet(X0, X2)))
% 18.51/18.63 join(meet(X0, X2), meet(meet(X0, X2), join(meet(X0, join(X1, meet(X0, X2))), meet(X0, X2)))) -> meet(X0, X2)
% 18.51/18.63 join(meet(X0, X2), meet(meet(X0, join(X1, meet(X0, X2))), join(meet(X0, join(X1, meet(X0, X2))), meet(X0, X2)))) -> meet(X0, join(X1, meet(X0, X2)))
% 18.51/18.63 join(meet(X0, Y1), meet(meet(X0, Y1), join(meet(Y1, join(Y2, meet(X0, Y1))), meet(X0, Y1)))) -> meet(X0, Y1)
% 18.51/18.63 join(meet(X0, join(X0, X1)), join(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1)))) -> meet(X0, join(X0, X1))
% 18.51/18.63 join(meet(X0, join(X0, X1)), meet(meet(X0, X0), join(meet(X0, X0), meet(X0, join(X0, X1))))) -> meet(X0, X0)
% 18.51/18.63 join(meet(X0, join(X1, meet(X0, X2))), meet(X0, X2)) -> meet(X0, join(X1, meet(X0, X2)))
% 18.51/18.63 join(meet(X0, join(X1, meet(X2, X0))), meet(X2, X0)) -> meet(X0, join(X1, meet(X2, X0)))
% 18.51/18.63 join(meet(X1, X0), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.63 join(meet(X1, Y0), Y0) -> Y0
% 18.51/18.63 join(meet(X1, Y0), meet(meet(X1, Y0), Y0)) -> meet(X1, Y0)
% 18.51/18.63 join(meet(X1, Y1), meet(meet(X1, Y1), join(meet(meet(X1, Y1), Y1), meet(X1, Y1)))) -> meet(X1, Y1)
% 18.51/18.63 join(meet(X1, Y2), meet(meet(X1, Y2), join(meet(join(meet(X1, Y2), Y1), Y2), meet(X1, Y2)))) -> meet(X1, Y2)
% 18.51/18.63 join(meet(X2, X0), meet(X0, join(X1, meet(X2, X0)))) -> meet(X0, join(X1, meet(X2, X0)))
% 18.51/18.63 join(meet(X2, X0), meet(meet(X0, join(X1, meet(X2, X0))), join(meet(X0, join(X1, meet(X2, X0))), meet(X2, X0)))) -> meet(X0, join(X1, meet(X2, X0)))
% 18.51/18.63 join(meet(Y0, X1), Y0) -> Y0
% 18.51/18.63 join(meet(Y0, X1), meet(Y0, join(Y0, meet(Y0, X1)))) -> Y0
% 18.51/18.63 join(meet(Y0, X1), meet(meet(Y0, X1), join(Y0, meet(Y0, X1)))) -> meet(Y0, X1)
% 18.51/18.63 join(meet(Y0, Y0), join(Y0, Y0)) -> Y0
% 18.51/18.63 join(meet(Y0, join(Y0, Y0)), Y0) -> Y0
% 18.51/18.63 join(meet(Y0, join(Y0, Y0)), Y0) -> join(Y0, Y0)
% 18.51/18.63 join(meet(Y0, join(join(Y0, X1), Y0)), Y0) -> Y0
% 18.51/18.63 join(meet(Y0, join(join(Y0, X1), Y0)), Y0) -> meet(Y0, join(join(Y0, X1), Y0))
% 18.51/18.63 join(meet(Y0, meet(X1, Y0)), Y0) -> Y0
% 18.51/18.63 join(meet(Y0, meet(X1, Y0)), meet(meet(X1, Y0), Y0)) -> meet(X1, Y0)
% 18.51/18.63 join(meet(Y1, join(X1, Y1)), Y1) -> Y1
% 18.51/18.63 join(meet(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1)
% 18.51/18.63 join(meet(join(X0, Y1), join(X2, Y1)), Y1) -> meet(join(X0, Y1), join(X2, Y1))
% 18.51/18.63 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))
% 18.51/18.63 join(meet(join(X0, Y1), join(X2, Y1)), join(Y1, meet(meet(join(X0, Y1), join(X2, Y1)), Y2))) -> meet(join(X0, Y1), join(X2, Y1))
% 18.51/18.63 join(meet(join(X0, Y1), join(Y1, X2)), Y1) -> meet(join(X0, Y1), join(Y1, X2))
% 18.51/18.63 join(meet(join(X0, Y2), join(X2, Y2)), join(meet(Y1, meet(join(X0, Y2), join(X2, Y2))), Y2)) -> meet(join(X0, Y2), join(X2, Y2))
% 18.51/18.63 join(meet(join(X0, Y2), join(X2, Y2)), join(meet(meet(join(X0, Y2), join(X2, Y2)), Y1), Y2)) -> meet(join(X0, Y2), join(X2, Y2))
% 18.51/18.63 join(meet(join(Y1, X1), join(X2, Y1)), Y1) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(meet(join(Y1, X1), join(X2, Y1)), join(Y1, meet(Y2, meet(join(Y1, X1), join(X2, Y1))))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(meet(join(Y1, X1), join(X2, Y1)), join(Y1, meet(meet(join(Y1, X1), join(X2, Y1)), Y2))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.63 join(meet(join(Y1, X1), join(Y1, X2)), Y1) -> meet(join(Y1, X1), join(Y1, X2))
% 18.51/18.63 join(meet(join(Y1, X1), join(Y1, X2)), join(Y1, meet(Y2, meet(join(Y1, X1), join(Y1, X2))))) -> meet(join(Y1, X1), join(Y1, X2))
% 18.51/18.63 join(meet(join(Y1, Y1), Y1), Y1) -> Y1
% 18.51/18.63 join(meet(join(Y1, meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))), meet(Y1, join(X1, Y1))) -> meet(Y1, join(X1, Y1))
% 18.51/18.63 join(meet(join(Y1, meet(join(Y1, X1), Y1)), meet(join(Y1, X1), Y1)), meet(meet(join(Y1, X1), Y1), meet(join(Y1, X1), Y1))) -> meet(join(Y1, X1), Y1)
% 18.51/18.63 join(meet(join(Y2, X1), join(X2, Y2)), join(meet(Y1, meet(join(Y2, X1), join(X2, Y2))), Y2)) -> meet(join(Y2, X1), join(X2, Y2))
% 18.51/18.63 join(meet(join(Y2, X1), join(X2, Y2)), join(meet(meet(join(Y2, X1), join(X2, Y2)), Y1), Y2)) -> meet(join(Y2, X1), join(X2, Y2))
% 18.51/18.63 join(meet(join(join(Y1, X1), Y1), Y1), join(join(Y1, X1), Y1)) -> join(join(Y1, X1), Y1)
% 18.51/18.63 join(meet(join(meet(X1, Y0), Y0), Y0), Y0) -> Y0
% 18.51/18.63 join(meet(join(meet(Y0, Y1), Y0), Y0), Y0) -> Y0
% 18.51/18.63 join(meet(join(meet(Y1, X1), Y1), Y1), meet(Y1, Y1)) -> Y1
% 18.51/18.63 join(meet(join(meet(Y1, X1), Y1), Y1), meet(join(meet(Y1, X1), Y1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.63 join(meet(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.63 join(meet(join(meet(Y1, X1), meet(X2, Y1)), Y1), meet(Y1, Y1)) -> Y1
% 18.51/18.63 join(meet(join(meet(Y1, X1), meet(X2, Y1)), Y1), meet(join(meet(Y1, X1), meet(X2, Y1)), Y1)) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.63 join(meet(join(meet(Y1, X1), meet(X2, Y1)), join(Y1, join(meet(Y1, X1), meet(X2, Y1)))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.63 join(meet(meet(X0, X0), join(X0, X0)), meet(join(X0, X0), X0)) -> join(X0, X0)
% 18.51/18.63 join(meet(meet(X0, X0), join(X0, X0)), meet(meet(X0, X0), X0)) -> meet(X0, X0)
% 18.51/18.63 join(meet(meet(X0, X0), meet(X1, join(X0, X0))), meet(meet(X0, X0), X0)) -> meet(X0, X0)
% 18.51/18.63 join(meet(meet(X0, X0), meet(X1, join(X0, X0))), meet(meet(X1, join(X0, X0)), X0)) -> meet(X1, join(X0, X0))
% 18.51/18.63 join(meet(meet(X0, X1), join(X0, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.63 join(meet(meet(X0, X1), meet(X0, join(X0, X1))), meet(meet(X0, X1), X0)) -> meet(X0, X1)
% 18.51/18.63 join(meet(meet(X0, X1), meet(X0, join(X0, X1))), meet(meet(X0, join(X0, X1)), X0)) -> meet(X0, join(X0, X1))
% 18.51/18.63 join(meet(meet(X0, X1), meet(X1, join(X0, X1))), meet(meet(X0, X1), X1)) -> meet(X0, X1)
% 18.51/18.63 join(meet(meet(X0, X1), meet(X1, join(X0, X1))), meet(meet(X1, join(X0, X1)), X1)) -> meet(X1, join(X0, X1))
% 18.51/18.63 join(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1))
% 18.51/18.63 meet(X0, meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.63 meet(X0, meet(X1, X0)) -> meet(X1, X0)
% 18.51/18.63 meet(X1, meet(X1, join(X0, X1))) -> meet(X1, join(X0, X1))
% 18.51/18.63 meet(Y0, join(join(Y0, X1), Y0)) -> Y0
% 18.51/18.63 meet(Y0, meet(Y0, join(Y0, Y1))) -> meet(Y0, join(Y0, Y1))
% 18.51/18.63 meet(Y0, meet(join(X1, Y0), join(Y0, Y2))) -> Y0
% 18.51/18.63 meet(Y0, meet(join(X1, Y0), join(Y2, Y0))) -> Y0
% 18.51/18.63 meet(Y0, meet(join(Y0, Y1), join(Y0, X1))) -> Y0
% 18.51/18.63 meet(Y1, Y1) -> Y1
% 18.51/18.64 meet(Y1, join(X1, Y1)) -> Y1
% 18.51/18.64 meet(Y1, join(Y1, X1)) -> Y1
% 18.51/18.64 meet(Y1, join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 meet(Y1, join(meet(X0, Y1), meet(Y1, X2))) -> join(meet(X0, Y1), meet(Y1, X2))
% 18.51/18.64 meet(Y1, join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.64 meet(Y1, join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(Y1, join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2))
% 18.51/18.64 meet(Y1, meet(join(Y1, X1), Y1)) -> meet(join(Y1, X1), Y1)
% 18.51/18.64 meet(Y1, meet(join(Y1, X1), join(X2, Y1))) -> Y1
% 18.51/18.64 meet(join(X0, X1), join(X0, join(X0, X1))) -> join(X0, join(X0, X1))
% 18.51/18.64 meet(join(X0, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.64 meet(join(X1, Y1), Y1) -> Y1
% 18.51/18.64 meet(join(Y1, X1), Y1) -> Y1
% 18.51/18.64 meet(join(Y1, X1), join(join(Y1, X1), Y1)) -> join(Y1, X1)
% 18.51/18.64 meet(join(Y1, join(Y1, X1)), join(Y1, X1)) -> join(Y1, X1)
% 18.51/18.64 meet(join(Y1, join(meet(X0, Y1), meet(X2, Y1))), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 meet(join(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.64 meet(join(Y1, join(meet(Y1, X1), meet(X2, Y1))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(join(Y1, meet(X1, Y1)), Y1) -> join(Y1, meet(X1, Y1))
% 18.51/18.64 meet(join(Y1, meet(join(Y1, X1), join(X2, Y1))), meet(join(Y1, X1), join(X2, Y1))) -> meet(join(Y1, X1), join(X2, Y1))
% 18.51/18.64 meet(join(Y2, Y2), Y2) -> Y2
% 18.51/18.64 meet(join(join(Y1, X1), Y1), Y1) -> Y1
% 18.51/18.64 meet(join(meet(X0, Y1), meet(X2, Y1)), Y1) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 meet(join(meet(X0, Y1), meet(X2, Y1)), join(Y1, join(meet(X0, Y1), meet(X2, Y1)))) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 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))
% 18.51/18.64 meet(join(meet(X0, Y1), meet(X2, Y1)), meet(Y1, join(join(meet(X0, Y1), meet(X2, Y1)), Y2))) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 meet(join(meet(X0, Y1), meet(Y1, X2)), Y1) -> join(meet(X0, Y1), meet(Y1, X2))
% 18.51/18.64 meet(join(meet(X0, Y1), meet(Y1, X2)), meet(Y1, join(Y2, join(meet(X0, Y1), meet(Y1, X2))))) -> join(meet(X0, Y1), meet(Y1, X2))
% 18.51/18.64 meet(join(meet(X0, Y2), meet(X2, Y2)), meet(join(Y1, join(meet(X0, Y2), meet(X2, Y2))), Y2)) -> join(meet(X0, Y2), meet(X2, Y2))
% 18.51/18.64 meet(join(meet(X0, Y2), meet(X2, Y2)), meet(join(join(meet(X0, Y2), meet(X2, Y2)), Y1), Y2)) -> join(meet(X0, Y2), meet(X2, Y2))
% 18.51/18.64 meet(join(meet(Y0, X1), Y0), Y0) -> Y0
% 18.51/18.64 meet(join(meet(Y1, X1), Y1), Y1) -> join(meet(Y1, X1), Y1)
% 18.51/18.64 meet(join(meet(Y1, X1), Y1), join(Y1, join(meet(Y1, X1), Y1))) -> join(meet(Y1, X1), Y1)
% 18.51/18.64 meet(join(meet(Y1, X1), Y1), meet(join(meet(Y1, X1), Y1), Y1)) -> meet(join(meet(Y1, X1), Y1), Y1)
% 18.51/18.64 meet(join(meet(Y1, X1), meet(X2, Y1)), Y1) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(join(meet(Y1, X1), meet(X2, Y1)), join(Y1, join(meet(Y1, X1), meet(X2, Y1)))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(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))
% 18.51/18.64 meet(join(meet(Y1, X1), meet(X2, Y1)), meet(Y1, join(join(meet(Y1, X1), meet(X2, Y1)), Y2))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(join(meet(Y1, X1), meet(Y1, X2)), Y1) -> join(meet(Y1, X1), meet(Y1, X2))
% 18.51/18.64 meet(join(meet(Y1, X1), meet(Y1, X2)), meet(Y1, join(Y2, join(meet(Y1, X1), meet(Y1, X2))))) -> join(meet(Y1, X1), meet(Y1, X2))
% 18.51/18.64 meet(join(meet(Y2, X1), meet(X2, Y2)), meet(join(Y1, join(meet(Y2, X1), meet(X2, Y2))), Y2)) -> join(meet(Y2, X1), meet(X2, Y2))
% 18.51/18.64 meet(join(meet(Y2, X1), meet(X2, Y2)), meet(join(join(meet(Y2, X1), meet(X2, Y2)), Y1), Y2)) -> join(meet(Y2, X1), meet(X2, Y2))
% 18.51/18.64 meet(meet(X0, X1), join(X0, meet(X0, X1))) -> meet(X0, X1)
% 18.51/18.64 meet(meet(X0, Y1), Y1) -> meet(X0, Y1)
% 18.51/18.64 meet(meet(X0, Y1), meet(Y1, join(Y2, meet(X0, Y1)))) -> meet(X0, Y1)
% 18.51/18.64 meet(meet(X0, Y1), meet(Y1, join(meet(X0, Y1), Y2))) -> meet(X0, Y1)
% 18.51/18.64 meet(meet(X0, join(X0, X1)), X0) -> meet(X0, join(X0, X1))
% 18.51/18.64 meet(meet(X0, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.64 meet(meet(X0, meet(X0, X0)), meet(X0, X0)) -> meet(X0, X0)
% 18.51/18.64 meet(meet(X0, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.64 meet(meet(X1, Y1), meet(meet(X1, Y1), Y1)) -> meet(meet(X1, Y1), Y1)
% 18.51/18.64 meet(meet(X1, Y2), meet(join(Y1, meet(X1, Y2)), Y2)) -> meet(X1, Y2)
% 18.51/18.64 meet(meet(X1, Y2), meet(join(meet(X1, Y2), Y1), Y2)) -> meet(X1, Y2)
% 18.51/18.64 meet(meet(X1, join(Y2, meet(X0, X1))), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.64 meet(meet(X1, meet(X0, X1)), meet(X0, X1)) -> meet(X0, X1)
% 18.51/18.64 meet(meet(Y0, X0), meet(Y0, join(X0, X0))) -> meet(Y0, join(X0, X0))
% 18.51/18.64 meet(meet(Y0, Y0), meet(Y0, join(X0, Y0))) -> meet(Y0, join(X0, Y0))
% 18.51/18.64 meet(meet(Y0, Y0), meet(Y0, join(Y0, X1))) -> meet(Y0, join(Y0, X1))
% 18.51/18.64 meet(meet(Y0, Y2), meet(Y2, Y0)) -> meet(Y2, Y0)
% 18.51/18.64 meet(meet(Y0, join(Y2, Y0)), Y0) -> Y0
% 18.51/18.64 meet(meet(Y1, X1), Y1) -> meet(Y1, X1)
% 18.51/18.64 meet(meet(Y1, X1), meet(Y1, join(Y2, meet(Y1, X1)))) -> meet(Y1, X1)
% 18.51/18.64 meet(meet(Y1, X1), meet(Y1, join(meet(Y1, X1), Y2))) -> meet(Y1, X1)
% 18.51/18.64 meet(meet(Y1, join(Y1, Y1)), join(Y1, Y1)) -> join(Y1, Y1)
% 18.51/18.64 meet(meet(Y1, join(Y1, meet(X1, Y1))), join(Y1, meet(X1, Y1))) -> join(Y1, meet(X1, Y1))
% 18.51/18.64 meet(meet(Y1, join(Y2, join(meet(X0, Y1), meet(X2, Y1)))), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 meet(meet(Y1, join(Y2, join(meet(X0, Y1), meet(Y1, X2)))), join(meet(X0, Y1), meet(Y1, X2))) -> join(meet(X0, Y1), meet(Y1, X2))
% 18.51/18.64 meet(meet(Y1, join(Y2, join(meet(Y1, X1), Y1))), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.64 meet(meet(Y1, join(Y2, join(meet(Y1, X1), meet(X2, Y1)))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(meet(Y1, join(Y2, join(meet(Y1, X1), meet(Y1, X2)))), join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2))
% 18.51/18.64 meet(meet(Y1, join(join(meet(X0, Y1), meet(X2, Y1)), Y2)), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 meet(meet(Y1, join(join(meet(X0, Y1), meet(Y1, X2)), Y2)), join(meet(X0, Y1), meet(Y1, X2))) -> join(meet(X0, Y1), meet(Y1, X2))
% 18.51/18.64 meet(meet(Y1, join(join(meet(Y1, X1), meet(X2, Y1)), Y2)), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(meet(Y1, join(join(meet(Y1, X1), meet(Y1, X2)), Y2)), join(meet(Y1, X1), meet(Y1, X2))) -> join(meet(Y1, X1), meet(Y1, X2))
% 18.51/18.64 meet(meet(Y1, join(meet(X0, Y1), Y2)), meet(X0, Y1)) -> meet(X0, Y1)
% 18.51/18.64 meet(meet(Y1, join(meet(X0, Y1), meet(X2, Y1))), join(meet(X0, Y1), meet(X2, Y1))) -> join(meet(X0, Y1), meet(X2, Y1))
% 18.51/18.64 meet(meet(Y1, join(meet(Y1, X1), Y1)), join(meet(Y1, X1), Y1)) -> join(meet(Y1, X1), Y1)
% 18.51/18.64 meet(meet(Y1, join(meet(Y1, X1), Y2)), meet(Y1, X1)) -> meet(Y1, X1)
% 18.51/18.64 meet(meet(Y1, join(meet(Y1, X1), meet(X2, Y1))), join(meet(Y1, X1), meet(X2, Y1))) -> join(meet(Y1, X1), meet(X2, Y1))
% 18.51/18.64 meet(meet(Y1, meet(X1, Y1)), Y1) -> meet(Y1, meet(X1, Y1))
% 18.51/18.64 meet(meet(Y2, X1), meet(join(Y1, meet(Y2, X1)), Y2)) -> meet(Y2, X1)
% 18.51/18.64 meet(meet(Y2, X1), meet(join(meet(Y2, X1), Y1), Y2)) -> meet(Y2, X1)
% 18.51/18.64 meet(meet(join(A, B), join(C, A)), A) -> A
% 18.51/18.64 meet(meet(join(X1, Y0), join(Y0, Y2)), Y0) -> Y0
% 18.51/18.64 meet(meet(join(X1, Y0), join(Y2, Y0)), Y0) -> Y0
% 18.51/18.64 meet(meet(join(Y0, Y1), Y0), Y0) -> Y0
% 18.51/18.64 meet(meet(join(Y0, Y1), join(Y0, X1)), Y0) -> Y0
% 18.51/18.64 meet(meet(join(Y0, join(meet(X0, Y2), meet(X2, Y2))), Y2), join(meet(X0, Y2), meet(X2, Y2))) -> join(meet(X0, Y2), meet(X2, Y2))
% 18.51/18.64 meet(meet(join(Y0, join(meet(Y2, X1), meet(X2, Y2))), Y2), join(meet(Y2, X1), meet(X2, Y2))) -> join(meet(Y2, X1), meet(X2, Y2))
% 18.51/18.64 meet(meet(join(Y0, meet(X1, Y2)), Y2), meet(X1, Y2)) -> meet(X1, Y2)
% 18.51/18.64 meet(meet(join(Y0, meet(Y2, X1)), Y2), meet(Y2, X1)) -> meet(Y2, X1)
% 18.51/18.64 meet(meet(join(Y2, X1), Y2), meet(Y2, join(Y2, X1))) -> meet(Y2, join(Y2, X1))
% 18.51/18.64 meet(meet(join(join(X0, X0), Y1), X0), join(X0, X0)) -> join(X0, X0)
% 18.51/18.64 meet(meet(join(join(meet(X1, Y2), meet(X2, Y2)), Y1), Y2), join(meet(X1, Y2), meet(X2, Y2))) -> join(meet(X1, Y2), meet(X2, Y2))
% 18.51/18.64 meet(meet(join(join(meet(X1, Y2), meet(Y2, X2)), Y1), Y2), join(meet(X1, Y2), meet(Y2, X2))) -> join(meet(X1, Y2), meet(Y2, X2))
% 18.51/18.64 meet(meet(join(join(meet(Y2, X1), meet(X2, Y2)), Y1), Y2), join(meet(Y2, X1), meet(X2, Y2))) -> join(meet(Y2, X1), meet(X2, Y2))
% 18.51/18.64 meet(meet(join(join(meet(Y2, X1), meet(Y2, X2)), Y1), Y2), join(meet(Y2, X1), meet(Y2, X2))) -> join(meet(Y2, X1), meet(Y2, X2))
% 18.51/18.64 meet(meet(join(meet(X0, join(X0, X1)), Y1), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1))
% 18.51/18.64 meet(meet(join(meet(X1, Y2), Y1), Y2), meet(X1, Y2)) -> meet(X1, Y2)
% 18.51/18.64 meet(meet(join(meet(X1, join(X0, X0)), Y1), X0), meet(X1, join(X0, X0))) -> meet(X1, join(X0, X0))
% 18.51/18.64 meet(meet(join(meet(X1, join(X0, X1)), Y1), X1), meet(X1, join(X0, X1))) -> meet(X1, join(X0, X1))
% 18.51/18.64 meet(meet(join(meet(Y1, X1), Y1), Y1), Y1) -> meet(join(meet(Y1, X1), Y1), Y1)
% 18.51/18.64 meet(meet(join(meet(Y2, X1), Y1), Y2), meet(Y2, X1)) -> meet(Y2, X1)
% 18.51/18.64 meet(meet(meet(X0, X0), meet(X0, X0)), meet(meet(X0, X0), X0)) -> meet(meet(X0, X0), X0)
% 18.51/18.64 meet(meet(meet(X0, X1), meet(X0, X1)), meet(meet(X0, X1), X0)) -> meet(meet(X0, X1), X0)
% 18.51/18.64 meet(meet(meet(X0, join(X0, X1)), X0), meet(X0, join(X0, X1))) -> meet(X0, join(X0, X1))
% 18.51/18.64 meet(meet(meet(X1, Y1), Y1), meet(X1, Y1)) -> meet(X1, Y1)
% 18.51/18.64 true__ -> false__
% 18.51/18.64 with the LPO induced by
% 18.51/18.64 b > a > f1 > meet > join > true__ > false__
% 18.51/18.64
% 18.51/18.64 % SZS output end Proof
% 18.51/18.64
%------------------------------------------------------------------------------