%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT399-2 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:45:46 AM UTC 2026
% Result : Unsatisfiable 35.47s 4.97s
% Output : CNFRefutation 40.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 12
% Syntax : Number of clauses : 957 ( 957 unt; 0 nHn; 4 RR)
% Number of literals : 957 ( 956 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 3044 ( 118 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
upme(meet(a,z1),z2,z3) != lome(meet(a,z1),z2,z3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
cnf(c2,axiom,
lojo(X,Y,X1) = join(X,meet(Y,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_lojo) ).
cnf(c3,plain,
lojo(lome(X5,X4,X3),X2,X5) = join(lome(X5,X4,X3),meet(X2,X5)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
upme(X2,Y2,Z) = meet(X2,join(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_upme) ).
cnf(c5,plain,
upme(X5,X4,lome(X4,X3,X2)) = meet(X5,join(X4,lome(X4,X3,X2))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
lojo(meet(X4,X3),X4,X2) = join(meet(X4,X3),meet(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,axiom,
lome(X2,Y2,Z2) = join(meet(X2,Y2),meet(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_lome) ).
cnf(c8,plain,
lome(X4,X3,X2) = join(meet(X4,X3),meet(X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
join(meet(X4,X3),meet(X4,X2)) = lome(X4,X3,X2),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
lojo(meet(X4,X3),X4,X2) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c6,c9]) ).
cnf(c11,plain,
lome(X4,X3,X2) = lojo(meet(X4,X3),X4,X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
join(X4,lome(X4,X3,X2)) = join(X4,lojo(meet(X4,X3),X4,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
join(X2,Y2) = join(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_001) ).
cnf(c14,plain,
join(X2,meet(X4,X3)) = join(meet(X4,X3),X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
join(meet(X4,X3),X2) = join(X2,meet(X4,X3)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
lojo(X2,X4,X3) = join(X2,meet(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
join(X2,meet(X4,X3)) = lojo(X2,X4,X3),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
join(meet(X4,X3),X2) = lojo(X2,X4,X3),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
join(meet(X4,X2),X3) = lojo(X3,X4,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
lojo(X3,X4,X2) = join(meet(X4,X2),X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
join(X4,lojo(X3,X4,X2)) = join(X4,join(meet(X4,X2),X3)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
join(X2,join(Y2,Z2)) = join(join(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_002) ).
cnf(c23,plain,
join(X4,join(meet(X4,X2),X3)) = join(join(X4,meet(X4,X2)),X3),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,axiom,
join(X2,meet(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption) ).
cnf(c25,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
join(join(X4,meet(X4,X2)),X3) = join(X4,X3),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
join(X4,join(meet(X4,X2),X3)) = join(X4,X3),
inference(transitivity,[status(thm)],[c23,c26]) ).
cnf(c28,plain,
join(X4,lojo(X3,X4,X2)) = join(X4,X3),
inference(transitivity,[status(thm)],[c21,c27]) ).
cnf(c29,plain,
join(X4,lojo(meet(X4,X3),X4,X2)) = join(X4,meet(X4,X3)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c31,plain,
join(X4,lojo(meet(X4,X3),X4,X2)) = X4,
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
join(X4,lome(X4,X3,X2)) = X4,
inference(transitivity,[status(thm)],[c12,c31]) ).
cnf(c33,plain,
meet(X5,join(X4,lome(X4,X3,X2))) = meet(X5,X4),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
upme(X5,X4,lome(X4,X3,X2)) = meet(X5,X4),
inference(transitivity,[status(thm)],[c5,c33]) ).
cnf(c35,plain,
upme(X2,X5,lome(X5,X4,X3)) = meet(X2,X5),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(X2,X5) = upme(X2,X5,lome(X5,X4,X3)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
join(lome(X5,X4,X3),meet(X2,X5)) = join(lome(X5,X4,X3),upme(X2,X5,lome(X5,X4,X3))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).
cnf(c39,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
lojo(meet(X4,X3),X3,X2) = lojo(meet(X3,X4),X3,X2),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
lojo(meet(X3,X4),X3,X2) = lome(X3,X4,X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c43,plain,
lojo(meet(X4,X3),X3,X2) = lome(X3,X4,X2),
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
lojo(meet(X3,join(X4,X3)),join(X4,X3),X2) = lome(join(X4,X3),X3,X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
lome(join(X4,X3),X3,X2) = lojo(meet(X3,join(X4,X3)),join(X4,X3),X2),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c47,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,axiom,
meet(X2,join(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption_003) ).
cnf(c50,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
meet(X3,join(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c48,c50]) ).
cnf(c52,plain,
meet(X2,join(X3,X2)) = X2,
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
lojo(meet(X3,join(X4,X3)),join(X4,X3),X2) = lojo(X3,join(X4,X3),X2),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
lojo(X4,X2,X3) = join(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c56,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
join(X4,meet(X2,X3)) = join(X4,meet(X3,X2)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
lojo(X4,X3,X2) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
join(X4,meet(X3,X2)) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
join(X4,meet(X2,X3)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c57,c59]) ).
cnf(c61,plain,
lojo(X4,X2,X3) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c54,c60]) ).
cnf(c62,plain,
lojo(X3,X2,join(X4,X3)) = lojo(X3,join(X4,X3),X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
lojo(X3,join(X4,X3),X2) = lojo(X3,X2,join(X4,X3)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c65,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
lojo(X5,X4,join(X3,X2)) = lojo(X5,X4,join(X2,X3)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
lojo(X5,X4,join(X2,X3)) = join(X5,meet(X4,join(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c68,plain,
upme(X4,X2,X3) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c69,plain,
meet(X4,join(X2,X3)) = upme(X4,X2,X3),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
join(X5,meet(X4,join(X2,X3))) = join(X5,upme(X4,X2,X3)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
upme(X4,X2,X3) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c72,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c73,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
meet(X4,join(X2,X3)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
upme(X4,X3,X2) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c76,plain,
meet(X4,join(X3,X2)) = upme(X4,X3,X2),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
meet(X4,join(X2,X3)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c74,c76]) ).
cnf(c78,plain,
upme(X4,X2,X3) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c71,c77]) ).
cnf(c79,plain,
upme(X4,X3,X2) = upme(X4,X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
upme(X4,X2,X3) = upme(X4,X3,X2),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
join(X5,upme(X4,X2,X3)) = join(X5,upme(X4,X3,X2)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
join(X5,meet(X4,join(X2,X3))) = join(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c70,c81]) ).
cnf(c83,plain,
lojo(X5,X4,join(X2,X3)) = join(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c67,c82]) ).
cnf(c84,plain,
lojo(X5,X4,join(X3,X2)) = join(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c66,c83]) ).
cnf(c85,plain,
lojo(X3,X2,join(X4,X3)) = join(X3,upme(X2,X4,X3)),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
lojo(X3,join(X4,X3),X2) = join(X3,upme(X2,X4,X3)),
inference(transitivity,[status(thm)],[c63,c85]) ).
cnf(c87,plain,
lojo(meet(X3,join(X4,X3)),join(X4,X3),X2) = join(X3,upme(X2,X4,X3)),
inference(transitivity,[status(thm)],[c53,c86]) ).
cnf(c88,plain,
lome(join(X4,X3),X3,X2) = join(X3,upme(X2,X4,X3)),
inference(transitivity,[status(thm)],[c45,c87]) ).
cnf(c89,plain,
lome(join(X5,lome(X5,X4,X3)),lome(X5,X4,X3),X2) = join(lome(X5,X4,X3),upme(X2,X5,lome(X5,X4,X3))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
join(lome(X5,X4,X3),upme(X2,X5,lome(X5,X4,X3))) = lome(join(X5,lome(X5,X4,X3)),lome(X5,X4,X3),X2),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
lome(join(X5,lome(X5,X4,X3)),lome(X5,X4,X3),X2) = lome(X5,lome(X5,X4,X3),X2),
inference(congruence,[status(thm)],[c32]) ).
cnf(c92,plain,
lojo(meet(X4,X2),X4,X3) = lome(X4,X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c93,plain,
lome(X4,X2,X3) = lojo(meet(X4,X2),X4,X3),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c95,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
lojo(meet(X3,X2),X5,X4) = lojo(meet(X2,X3),X5,X4),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
lojo(meet(X2,X3),X5,X4) = lojo(meet(X2,X3),X4,X5),
inference(substitution,[status(thm)],[c61]) ).
cnf(c98,plain,
lojo(meet(X2,X3),X4,X5) = join(meet(X2,X3),meet(X4,X5)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c99,plain,
join(meet(X2,X3),meet(X4,X5)) = lojo(meet(X4,X5),X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c100,plain,
lojo(meet(X4,X5),X3,X2) = lojo(meet(X4,X5),X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c101,plain,
lojo(meet(X4,X5),X2,X3) = lojo(meet(X4,X5),X3,X2),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c103,plain,
lojo(meet(X4,X5),X3,X2) = lojo(meet(X5,X4),X3,X2),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
lojo(meet(X4,X5),X2,X3) = lojo(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c101,c103]) ).
cnf(c105,plain,
join(meet(X2,X3),meet(X4,X5)) = lojo(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c99,c104]) ).
cnf(c106,plain,
lojo(meet(X2,X3),X4,X5) = lojo(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c98,c105]) ).
cnf(c107,plain,
lojo(meet(X2,X3),X5,X4) = lojo(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c97,c106]) ).
cnf(c108,plain,
lojo(meet(X3,X2),X5,X4) = lojo(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c96,c107]) ).
cnf(c109,plain,
lojo(meet(X4,X2),X4,X3) = lojo(meet(X4,X3),X4,X2),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
lojo(meet(X4,X2),X4,X3) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c109,c10]) ).
cnf(c111,plain,
lome(X4,X2,X3) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c93,c110]) ).
cnf(c112,plain,
lome(X5,X2,lome(X5,X4,X3)) = lome(X5,lome(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
lome(X5,lome(X5,X4,X3),X2) = lome(X5,X2,lome(X5,X4,X3)),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
lome(join(X5,lome(X5,X4,X3)),lome(X5,X4,X3),X2) = lome(X5,X2,lome(X5,X4,X3)),
inference(transitivity,[status(thm)],[c91,c113]) ).
cnf(c115,plain,
join(lome(X5,X4,X3),upme(X2,X5,lome(X5,X4,X3))) = lome(X5,X2,lome(X5,X4,X3)),
inference(transitivity,[status(thm)],[c90,c114]) ).
cnf(c116,plain,
join(lome(X5,X4,X3),meet(X2,X5)) = lome(X5,X2,lome(X5,X4,X3)),
inference(transitivity,[status(thm)],[c37,c115]) ).
cnf(c117,plain,
lojo(lome(X5,X4,X3),X2,X5) = lome(X5,X2,lome(X5,X4,X3)),
inference(transitivity,[status(thm)],[c3,c116]) ).
cnf(c118,plain,
lojo(lome(X4,X3,X2),X3,X4) = lome(X4,X3,lome(X4,X3,X2)),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
lome(X4,X3,lome(X4,X3,X2)) = lojo(lome(X4,X3,X2),X3,X4),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
lojo(lome(X4,X3,X2),X3,X4) = join(lome(X4,X3,X2),meet(X3,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c121,plain,
meet(lome(X4,X3,X2),X4) = meet(X4,lome(X4,X3,X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c122,plain,
meet(X4,lome(X4,X3,X2)) = meet(lome(X4,X3,X2),X4),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
X4 = join(X4,lome(X4,X3,X2)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c124,plain,
meet(lome(X4,X3,X2),X4) = meet(lome(X4,X3,X2),join(X4,lome(X4,X3,X2))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
meet(lome(X4,X3,X2),join(X4,lome(X4,X3,X2))) = lome(X4,X3,X2),
inference(substitution,[status(thm)],[c51]) ).
cnf(c126,plain,
meet(lome(X4,X3,X2),X4) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
meet(X4,lome(X4,X3,X2)) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c122,c126]) ).
cnf(c128,plain,
meet(X3,lome(X3,X4,X2)) = lome(X3,X4,X2),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
lome(X3,X4,X2) = meet(X3,lome(X3,X4,X2)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
meet(X4,lome(X3,X4,X2)) = meet(X4,meet(X3,lome(X3,X4,X2))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
meet(meet(X3,X2),X4) = meet(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c132,plain,
meet(X4,meet(X3,X2)) = meet(meet(X3,X2),X4),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,axiom,
meet(X2,meet(Y2,Z2)) = meet(meet(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c134,plain,
meet(X3,meet(X2,X4)) = meet(meet(X3,X2),X4),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X2,X4)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c137,plain,
meet(X3,meet(X2,X4)) = meet(X3,meet(X4,X2)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c135,c137]) ).
cnf(c139,plain,
meet(X4,meet(X3,X2)) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c132,c138]) ).
cnf(c140,plain,
meet(X3,meet(X4,lome(X3,X4,X2))) = meet(X4,meet(X3,lome(X3,X4,X2))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
meet(X4,meet(X3,lome(X3,X4,X2))) = meet(X3,meet(X4,lome(X3,X4,X2))),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
meet(X4,meet(X3,lome(X4,X3,X2))) = meet(meet(X4,X3),lome(X4,X3,X2)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c143,plain,
lome(X4,X3,X2) = lojo(meet(X4,X3),X4,X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c144,plain,
meet(meet(X4,X3),lome(X4,X3,X2)) = meet(meet(X4,X3),lojo(meet(X4,X3),X4,X2)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
lojo(X4,X3,X2) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c146,plain,
meet(X4,lojo(X4,X3,X2)) = meet(X4,join(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
meet(X4,join(X4,meet(X3,X2))) = X4,
inference(substitution,[status(thm)],[c49]) ).
cnf(c148,plain,
meet(X4,lojo(X4,X3,X2)) = X4,
inference(transitivity,[status(thm)],[c146,c147]) ).
cnf(c149,plain,
meet(meet(X4,X3),lojo(meet(X4,X3),X4,X2)) = meet(X4,X3),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
meet(meet(X4,X3),lome(X4,X3,X2)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c144,c149]) ).
cnf(c151,plain,
meet(X4,meet(X3,lome(X4,X3,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c142,c150]) ).
cnf(c152,plain,
meet(X3,meet(X4,lome(X3,X4,X2))) = meet(X3,X4),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c154,plain,
meet(X3,meet(X4,lome(X3,X4,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
meet(X4,meet(X3,lome(X3,X4,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c141,c154]) ).
cnf(c156,plain,
meet(X4,lome(X3,X4,X2)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c130,c155]) ).
cnf(c157,plain,
meet(X3,lome(X4,X3,X2)) = meet(X3,X4),
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
meet(X3,X4) = meet(X3,lome(X4,X3,X2)),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
join(lome(X4,X3,X2),meet(X3,X4)) = join(lome(X4,X3,X2),meet(X3,lome(X4,X3,X2))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c38]) ).
cnf(c161,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c164,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c162,c163]) ).
cnf(c165,plain,
join(lome(X4,X3,X2),meet(X3,lome(X4,X3,X2))) = lome(X4,X3,X2),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
join(lome(X4,X3,X2),meet(X3,X4)) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c159,c165]) ).
cnf(c167,plain,
lojo(lome(X4,X3,X2),X3,X4) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c120,c166]) ).
cnf(c168,plain,
lome(X4,X3,lome(X4,X3,X2)) = lome(X4,X3,X2),
inference(transitivity,[status(thm)],[c119,c167]) ).
cnf(c169,plain,
lome(meet(a,X4),X3,lome(meet(a,X4),X3,X2)) = lome(meet(a,X4),X3,X2),
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
lome(meet(a,X4),X3,X2) = lome(meet(a,X4),X3,lome(meet(a,X4),X3,X2)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
lome(meet(a,X5),X4,lome(meet(a,X5),X3,X2)) = lome(meet(a,X5),lome(meet(a,X5),X3,X2),X4),
inference(substitution,[status(thm)],[c111]) ).
cnf(c172,plain,
meet(X4,meet(X3,X2)) = meet(meet(X4,X3),X2),
inference(substitution,[status(thm)],[c133]) ).
cnf(c173,plain,
lojo(meet(X5,meet(X4,X3)),X3,X2) = lojo(meet(meet(X5,X4),X3),X3,X2),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
lojo(meet(meet(X5,X4),X3),X3,X2) = lome(X3,meet(X5,X4),X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c175,plain,
lome(X3,X2,meet(X5,X4)) = lome(X3,meet(X5,X4),X2),
inference(substitution,[status(thm)],[c111]) ).
cnf(c176,plain,
lome(X3,meet(X5,X4),X2) = lome(X3,X2,meet(X5,X4)),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
lojo(meet(meet(X5,X4),X3),X3,X2) = lome(X3,X2,meet(X5,X4)),
inference(transitivity,[status(thm)],[c174,c176]) ).
cnf(c178,plain,
lojo(meet(X5,meet(X4,X3)),X3,X2) = lome(X3,X2,meet(X5,X4)),
inference(transitivity,[status(thm)],[c173,c177]) ).
cnf(c179,plain,
lojo(meet(X2,meet(X5,meet(X5,X4))),meet(X5,X4),X3) = lome(meet(X5,X4),X3,meet(X2,X5)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
lome(meet(X5,X4),X3,meet(X2,X5)) = lojo(meet(X2,meet(X5,meet(X5,X4))),meet(X5,X4),X3),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
meet(meet(X3,X2),X3) = meet(X3,meet(X3,X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c182,plain,
meet(X3,meet(X3,X2)) = meet(meet(X3,X2),X3),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c184,plain,
X3 = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
meet(meet(X3,X2),X3) = meet(meet(X3,X2),join(X3,meet(X3,X2))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
meet(meet(X3,X2),join(X3,meet(X3,X2))) = meet(X3,X2),
inference(substitution,[status(thm)],[c51]) ).
cnf(c187,plain,
meet(meet(X3,X2),X3) = meet(X3,X2),
inference(transitivity,[status(thm)],[c185,c186]) ).
cnf(c188,plain,
meet(X3,meet(X3,X2)) = meet(X3,X2),
inference(transitivity,[status(thm)],[c182,c187]) ).
cnf(c189,plain,
meet(X2,meet(X4,meet(X4,X3))) = meet(X2,meet(X4,X3)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
lojo(meet(X2,meet(X5,meet(X5,X4))),meet(X5,X4),X3) = lojo(meet(X2,meet(X5,X4)),meet(X5,X4),X3),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
lojo(meet(X2,meet(X5,X4)),meet(X5,X4),X3) = lome(meet(X5,X4),X2,X3),
inference(substitution,[status(thm)],[c43]) ).
cnf(c192,plain,
lome(meet(X5,X4),X3,X2) = lome(meet(X5,X4),X2,X3),
inference(substitution,[status(thm)],[c111]) ).
cnf(c193,plain,
lome(meet(X5,X4),X2,X3) = lome(meet(X5,X4),X3,X2),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
lojo(meet(X2,meet(X5,X4)),meet(X5,X4),X3) = lome(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c191,c193]) ).
cnf(c195,plain,
lojo(meet(X2,meet(X5,meet(X5,X4))),meet(X5,X4),X3) = lome(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c190,c194]) ).
cnf(c196,plain,
lome(meet(X5,X4),X3,meet(X2,X5)) = lome(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c180,c195]) ).
cnf(c197,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(X4,a)) = lome(meet(a,X5),lome(meet(a,X5),X3,X2),X4),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),X4) = lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(X4,a)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
upme(X5,meet(X4,X3),X2) = upme(X5,X2,meet(X4,X3)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c200,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c201,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
upme(X5,X4,meet(X3,X2)) = upme(X5,X4,meet(X2,X3)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
upme(X5,X4,meet(X2,X3)) = meet(X5,join(X4,meet(X2,X3))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c204,plain,
lojo(X4,X2,X3) = join(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c205,plain,
join(X4,meet(X2,X3)) = lojo(X4,X2,X3),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
meet(X5,join(X4,meet(X2,X3))) = meet(X5,lojo(X4,X2,X3)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c208,plain,
lojo(X4,X2,X3) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
meet(X5,lojo(X4,X2,X3)) = meet(X5,lojo(X4,X3,X2)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
meet(X5,join(X4,meet(X2,X3))) = meet(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c206,c209]) ).
cnf(c211,plain,
upme(X5,X4,meet(X2,X3)) = meet(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c203,c210]) ).
cnf(c212,plain,
upme(X5,X4,meet(X3,X2)) = meet(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c202,c211]) ).
cnf(c213,plain,
upme(X5,X2,meet(X4,X3)) = meet(X5,lojo(X2,X4,X3)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
upme(X5,meet(X4,X3),X2) = meet(X5,lojo(X2,X4,X3)),
inference(transitivity,[status(thm)],[c199,c213]) ).
cnf(c215,plain,
upme(a,meet(X4,X3),X2) = meet(a,lojo(X2,X4,X3)),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
meet(a,lojo(X2,X4,X3)) = upme(a,meet(X4,X3),X2),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
lome(X4,X3,meet(a,lojo(X2,X4,X3))) = lome(X4,X3,upme(a,meet(X4,X3),X2)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
lojo(meet(X4,X3),X4,upme(a,meet(X4,X3),X2)) = lome(X4,X3,upme(a,meet(X4,X3),X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c219,plain,
lome(X4,X3,upme(a,meet(X4,X3),X2)) = lojo(meet(X4,X3),X4,upme(a,meet(X4,X3),X2)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
upme(a,X3,X2) = upme(a,X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c221,plain,
lojo(X4,X3,upme(a,X4,X2)) = lojo(X4,X3,upme(a,X2,X4)),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
upme(X3,X2,X4) = upme(X3,X4,X2),
inference(substitution,[status(thm)],[c78]) ).
cnf(c223,plain,
lojo(X6,X4,upme(X5,X3,X2)) = lojo(X6,X4,upme(X5,X2,X3)),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
upme(X4,X2,X3) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c225,plain,
lojo(X6,X4,upme(X5,X2,X3)) = lojo(X6,X4,meet(X5,join(X2,X3))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c227,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
lojo(X5,X2,meet(X4,X3)) = lojo(X5,X2,meet(X3,X4)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
lojo(X5,X2,meet(X3,X4)) = join(X5,meet(X2,meet(X3,X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c230,plain,
meet(X2,meet(X3,X4)) = meet(meet(X2,X3),X4),
inference(substitution,[status(thm)],[c133]) ).
cnf(c231,plain,
join(X5,meet(X2,meet(X3,X4))) = join(X5,meet(meet(X2,X3),X4)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
lojo(X5,meet(X2,X3),X4) = join(X5,meet(meet(X2,X3),X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c233,plain,
join(X5,meet(meet(X2,X3),X4)) = lojo(X5,meet(X2,X3),X4),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
lojo(X5,X4,meet(X2,X3)) = lojo(X5,meet(X2,X3),X4),
inference(substitution,[status(thm)],[c61]) ).
cnf(c235,plain,
lojo(X5,meet(X2,X3),X4) = lojo(X5,X4,meet(X2,X3)),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c237,plain,
lojo(X5,X4,meet(X2,X3)) = lojo(X5,X4,meet(X3,X2)),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
lojo(X5,meet(X2,X3),X4) = lojo(X5,X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c235,c237]) ).
cnf(c239,plain,
join(X5,meet(meet(X2,X3),X4)) = lojo(X5,X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c233,c238]) ).
cnf(c240,plain,
join(X5,meet(X2,meet(X3,X4))) = lojo(X5,X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c231,c239]) ).
cnf(c241,plain,
lojo(X5,X2,meet(X3,X4)) = lojo(X5,X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c229,c240]) ).
cnf(c242,plain,
lojo(X5,X2,meet(X4,X3)) = lojo(X5,X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c228,c241]) ).
cnf(c243,plain,
lojo(X6,X4,meet(X5,join(X2,X3))) = lojo(X6,X5,meet(join(X2,X3),X4)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c244,plain,
meet(X2,join(X4,X3)) = meet(join(X4,X3),X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c245,plain,
meet(join(X4,X3),X2) = meet(X2,join(X4,X3)),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
upme(X2,X4,X3) = meet(X2,join(X4,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c247,plain,
meet(X2,join(X4,X3)) = upme(X2,X4,X3),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
meet(join(X4,X3),X2) = upme(X2,X4,X3),
inference(transitivity,[status(thm)],[c245,c247]) ).
cnf(c249,plain,
meet(join(X2,X3),X4) = upme(X4,X2,X3),
inference(substitution,[status(thm)],[c248]) ).
cnf(c250,plain,
lojo(X6,X5,meet(join(X2,X3),X4)) = lojo(X6,X5,upme(X4,X2,X3)),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
upme(X4,X3,X2) = upme(X4,X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c252,plain,
upme(X4,X2,X3) = upme(X4,X3,X2),
inference(symmetry,[status(thm)],[c251]) ).
cnf(c253,plain,
lojo(X6,X5,upme(X4,X2,X3)) = lojo(X6,X5,upme(X4,X3,X2)),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
lojo(X6,X5,meet(join(X2,X3),X4)) = lojo(X6,X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c250,c253]) ).
cnf(c255,plain,
lojo(X6,X4,meet(X5,join(X2,X3))) = lojo(X6,X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c243,c254]) ).
cnf(c256,plain,
lojo(X6,X4,upme(X5,X2,X3)) = lojo(X6,X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c225,c255]) ).
cnf(c257,plain,
lojo(X6,X4,upme(X5,X3,X2)) = lojo(X6,X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c223,c256]) ).
cnf(c258,plain,
lojo(X4,X3,upme(a,X2,X4)) = lojo(X4,a,upme(X3,X2,X4)),
inference(substitution,[status(thm)],[c257]) ).
cnf(c259,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c260,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
lome(X4,X3,join(X2,X3)) = lome(X4,X3,join(X3,X2)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c263,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
lome(X4,X3,join(X3,X2)) = lome(X4,X3,join(X2,X3)),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
lome(X4,X3,join(X2,X3)) = lome(X4,join(X2,X3),X3),
inference(substitution,[status(thm)],[c111]) ).
cnf(c266,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c267,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
lome(X4,join(X2,X3),X3) = lome(X4,join(X3,X2),X3),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
upme(X4,X3,X2) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c270,plain,
lojo(upme(X5,X4,X3),X5,X2) = lojo(meet(X5,join(X4,X3)),X5,X2),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
lojo(meet(X5,join(X4,X3)),X5,X2) = lome(X5,join(X4,X3),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c272,plain,
lojo(upme(X5,X4,X3),X5,X2) = lome(X5,join(X4,X3),X2),
inference(transitivity,[status(thm)],[c270,c271]) ).
cnf(c273,plain,
lojo(upme(X4,X3,X2),X4,X3) = lome(X4,join(X3,X2),X3),
inference(substitution,[status(thm)],[c272]) ).
cnf(c274,plain,
lome(X4,join(X3,X2),X3) = lojo(upme(X4,X3,X2),X4,X3),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
lojo(upme(X4,X3,X2),X4,X3) = lojo(upme(X4,X3,X2),X3,X4),
inference(substitution,[status(thm)],[c61]) ).
cnf(c276,plain,
lojo(upme(X4,X3,X2),X3,X4) = join(upme(X4,X3,X2),meet(X3,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c277,plain,
meet(join(X4,X2),X3) = upme(X3,X4,X2),
inference(substitution,[status(thm)],[c248]) ).
cnf(c278,plain,
upme(X3,X4,X2) = meet(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
meet(X4,upme(X3,X4,X2)) = meet(X4,meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(meet(X4,join(X4,X2)),X3),
inference(substitution,[status(thm)],[c133]) ).
cnf(c281,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c49]) ).
cnf(c282,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,X3),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c280,c282]) ).
cnf(c284,plain,
meet(X4,upme(X3,X4,X2)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c279,c283]) ).
cnf(c285,plain,
meet(X3,upme(X4,X3,X2)) = meet(X3,X4),
inference(substitution,[status(thm)],[c284]) ).
cnf(c286,plain,
meet(X3,X4) = meet(X3,upme(X4,X3,X2)),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
join(upme(X4,X3,X2),meet(X3,X4)) = join(upme(X4,X3,X2),meet(X3,upme(X4,X3,X2))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
join(upme(X4,X3,X2),meet(X3,upme(X4,X3,X2))) = upme(X4,X3,X2),
inference(substitution,[status(thm)],[c164]) ).
cnf(c289,plain,
join(upme(X4,X3,X2),meet(X3,X4)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c287,c288]) ).
cnf(c290,plain,
lojo(upme(X4,X3,X2),X3,X4) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c276,c289]) ).
cnf(c291,plain,
lojo(upme(X4,X3,X2),X4,X3) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c275,c290]) ).
cnf(c292,plain,
lome(X4,join(X3,X2),X3) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c274,c291]) ).
cnf(c293,plain,
lome(X4,join(X2,X3),X3) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c268,c292]) ).
cnf(c294,plain,
lome(X4,X3,join(X2,X3)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c265,c293]) ).
cnf(c295,plain,
lome(X4,X3,join(X3,X2)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c264,c294]) ).
cnf(c296,plain,
lome(X4,X3,join(X2,X3)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c261,c295]) ).
cnf(c297,plain,
lome(X3,X2,join(X4,X2)) = upme(X3,X2,X4),
inference(substitution,[status(thm)],[c296]) ).
cnf(c298,plain,
upme(X3,X2,X4) = lome(X3,X2,join(X4,X2)),
inference(symmetry,[status(thm)],[c297]) ).
cnf(c299,plain,
lojo(X4,a,upme(X3,X2,X4)) = lojo(X4,a,lome(X3,X2,join(X4,X2))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
lojo(upme(X5,X4,X3),X5,X2) = lojo(upme(X5,X4,X3),X2,X5),
inference(substitution,[status(thm)],[c61]) ).
cnf(c301,plain,
lojo(upme(X5,X4,X3),X2,X5) = lojo(upme(X5,X4,X3),X5,X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c302,plain,
lome(X5,X2,join(X4,X3)) = lome(X5,join(X4,X3),X2),
inference(substitution,[status(thm)],[c111]) ).
cnf(c303,plain,
lome(X5,join(X4,X3),X2) = lome(X5,X2,join(X4,X3)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
lojo(upme(X5,X4,X3),X5,X2) = lome(X5,X2,join(X4,X3)),
inference(transitivity,[status(thm)],[c272,c303]) ).
cnf(c305,plain,
lojo(upme(X5,X4,X3),X2,X5) = lome(X5,X2,join(X4,X3)),
inference(transitivity,[status(thm)],[c301,c304]) ).
cnf(c306,plain,
lojo(upme(X5,X4,X3),X5,X2) = lome(X5,X2,join(X4,X3)),
inference(transitivity,[status(thm)],[c300,c305]) ).
cnf(c307,plain,
lojo(upme(X3,X4,X2),X3,X2) = lome(X3,X2,join(X4,X2)),
inference(substitution,[status(thm)],[c306]) ).
cnf(c308,plain,
lome(X3,X2,join(X4,X2)) = lojo(upme(X3,X4,X2),X3,X2),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
lojo(X4,a,lome(X3,X2,join(X4,X2))) = lojo(X4,a,lojo(upme(X3,X4,X2),X3,X2)),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
lojo(X4,a,lojo(upme(X3,X4,X2),X3,X2)) = join(X4,meet(a,lojo(upme(X3,X4,X2),X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c311,plain,
upme(a,meet(X3,X2),upme(X3,X4,X2)) = meet(a,lojo(upme(X3,X4,X2),X3,X2)),
inference(substitution,[status(thm)],[c214]) ).
cnf(c312,plain,
meet(a,lojo(upme(X3,X4,X2),X3,X2)) = upme(a,meet(X3,X2),upme(X3,X4,X2)),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
join(X4,meet(a,lojo(upme(X3,X4,X2),X3,X2))) = join(X4,upme(a,meet(X3,X2),upme(X3,X4,X2))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
lome(a,X3,X2) = lome(a,X2,X3),
inference(substitution,[status(thm)],[c111]) ).
cnf(c315,plain,
lojo(X3,X2,a) = lojo(X3,a,X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c316,plain,
meet(a,lojo(X3,X2,a)) = meet(a,lojo(X3,a,X2)),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
lojo(X4,X3,meet(X2,X3)) = lojo(X4,X2,meet(X3,X3)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c318,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c319,plain,
X3 = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
meet(X3,X3) = meet(X3,join(X3,meet(X3,X2))),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
meet(X3,join(X3,meet(X3,X2))) = X3,
inference(substitution,[status(thm)],[c49]) ).
cnf(c322,plain,
meet(X2,X2) = X2,
inference(transitivity,[status(thm)],[c320,c321]) ).
cnf(c323,plain,
lojo(X4,X2,meet(X3,X3)) = lojo(X4,X2,X3),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c325,plain,
lojo(X4,X2,X3) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
lojo(X4,X2,meet(X3,X3)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c323,c325]) ).
cnf(c327,plain,
lojo(X4,X3,meet(X2,X3)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c317,c326]) ).
cnf(c328,plain,
lojo(X3,a,meet(X2,a)) = lojo(X3,a,X2),
inference(substitution,[status(thm)],[c327]) ).
cnf(c329,plain,
lojo(X3,a,X2) = lojo(X3,a,meet(X2,a)),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
meet(a,lojo(X3,a,X2)) = meet(a,lojo(X3,a,meet(X2,a))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
lojo(X3,X3,X2) = join(X3,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c332,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c333,plain,
lojo(X3,X3,X2) = X3,
inference(transitivity,[status(thm)],[c331,c332]) ).
cnf(c334,plain,
lojo(a,a,meet(X2,X3)) = a,
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
a = lojo(a,a,meet(X2,X3)),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
meet(a,lojo(X3,a,meet(X2,a))) = meet(lojo(a,a,meet(X2,X3)),lojo(X3,a,meet(X2,a))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
upme(lojo(X4,a,meet(X3,X2)),meet(a,meet(X3,X4)),X2) = meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c338,plain,
meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4))) = upme(lojo(X4,a,meet(X3,X2)),meet(a,meet(X3,X4)),X2),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
meet(join(meet(a,meet(X3,X4)),X2),lojo(X4,a,meet(X3,X2))) = upme(lojo(X4,a,meet(X3,X2)),meet(a,meet(X3,X4)),X2),
inference(substitution,[status(thm)],[c248]) ).
cnf(c340,plain,
upme(lojo(X4,a,meet(X3,X2)),meet(a,meet(X3,X4)),X2) = meet(join(meet(a,meet(X3,X4)),X2),lojo(X4,a,meet(X3,X2))),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
upme(join(meet(a,meet(X3,X4)),X2),meet(a,meet(X3,X2)),X4) = meet(join(meet(a,meet(X3,X4)),X2),lojo(X4,a,meet(X3,X2))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c342,plain,
meet(join(meet(a,meet(X3,X4)),X2),lojo(X4,a,meet(X3,X2))) = upme(join(meet(a,meet(X3,X4)),X2),meet(a,meet(X3,X2)),X4),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
meet(a,meet(X3,X2)) = meet(meet(a,X3),X2),
inference(substitution,[status(thm)],[c133]) ).
cnf(c344,plain,
upme(join(meet(a,meet(X3,X4)),X2),meet(a,meet(X3,X2)),X4) = upme(join(meet(a,meet(X3,X4)),X2),meet(meet(a,X3),X2),X4),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
meet(a,meet(X2,X3)) = meet(meet(a,X2),X3),
inference(substitution,[status(thm)],[c133]) ).
cnf(c346,plain,
join(meet(a,meet(X3,X4)),X2) = join(meet(meet(a,X3),X4),X2),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
upme(join(meet(a,meet(X3,X4)),X2),meet(meet(a,X3),X2),X4) = upme(join(meet(meet(a,X3),X4),X2),meet(meet(a,X3),X2),X4),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
upme(join(meet(meet(a,X3),X4),X2),meet(meet(a,X3),X2),X4) = meet(join(meet(meet(a,X3),X4),X2),join(meet(meet(a,X3),X2),X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c349,negated_conjecture,
join(upme(meet(a,X1_2),Y1,W),meet(Y1,W)) = meet(join(meet(meet(a,X1_2),Y1),W),join(meet(meet(a,X1_2),W),Y1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture) ).
cnf(c350,plain,
join(upme(meet(a,X3),X4,X2),meet(X4,X2)) = meet(join(meet(meet(a,X3),X4),X2),join(meet(meet(a,X3),X2),X4)),
inference(substitution,[status(thm)],[c349]) ).
cnf(c351,plain,
meet(join(meet(meet(a,X3),X4),X2),join(meet(meet(a,X3),X2),X4)) = join(upme(meet(a,X3),X4,X2),meet(X4,X2)),
inference(symmetry,[status(thm)],[c350]) ).
cnf(c352,plain,
lojo(upme(meet(a,X3),X4,X2),X4,X2) = join(upme(meet(a,X3),X4,X2),meet(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c353,plain,
join(upme(meet(a,X3),X4,X2),meet(X4,X2)) = lojo(upme(meet(a,X3),X4,X2),X4,X2),
inference(symmetry,[status(thm)],[c352]) ).
cnf(c354,plain,
upme(meet(X5,X4),X3,X2) = meet(meet(X5,X4),join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c355,plain,
meet(X5,meet(X4,join(X3,X2))) = meet(meet(X5,X4),join(X3,X2)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c356,plain,
meet(meet(X5,X4),join(X3,X2)) = meet(X5,meet(X4,join(X3,X2))),
inference(symmetry,[status(thm)],[c355]) ).
cnf(c357,plain,
upme(X4,X3,X2) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c358,plain,
meet(X4,join(X3,X2)) = upme(X4,X3,X2),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
meet(X5,meet(X4,join(X3,X2))) = meet(X5,upme(X4,X3,X2)),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
meet(meet(X5,X4),join(X3,X2)) = meet(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c356,c359]) ).
cnf(c361,plain,
upme(meet(X5,X4),X3,X2) = meet(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c354,c360]) ).
cnf(c362,plain,
upme(meet(a,X3),X4,X2) = meet(a,upme(X3,X4,X2)),
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
lojo(upme(meet(a,X3),X4,X2),X4,X2) = lojo(meet(a,upme(X3,X4,X2)),X4,X2),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
lojo(meet(X4,X2),a,upme(X3,X4,X2)) = lojo(meet(a,upme(X3,X4,X2)),X4,X2),
inference(substitution,[status(thm)],[c108]) ).
cnf(c365,plain,
lojo(meet(a,upme(X3,X4,X2)),X4,X2) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
lojo(upme(meet(a,X3),X4,X2),X4,X2) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c363,c365]) ).
cnf(c367,plain,
join(upme(meet(a,X3),X4,X2),meet(X4,X2)) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c353,c366]) ).
cnf(c368,plain,
meet(join(meet(meet(a,X3),X4),X2),join(meet(meet(a,X3),X2),X4)) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c351,c367]) ).
cnf(c369,plain,
upme(join(meet(meet(a,X3),X4),X2),meet(meet(a,X3),X2),X4) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c348,c368]) ).
cnf(c370,plain,
upme(join(meet(a,meet(X3,X4)),X2),meet(meet(a,X3),X2),X4) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c347,c369]) ).
cnf(c371,plain,
upme(join(meet(a,meet(X3,X4)),X2),meet(a,meet(X3,X2)),X4) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c344,c370]) ).
cnf(c372,plain,
meet(join(meet(a,meet(X3,X4)),X2),lojo(X4,a,meet(X3,X2))) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c342,c371]) ).
cnf(c373,plain,
upme(lojo(X4,a,meet(X3,X2)),meet(a,meet(X3,X4)),X2) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c340,c372]) ).
cnf(c374,plain,
meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4))) = lojo(meet(X4,X2),a,upme(X3,X4,X2)),
inference(transitivity,[status(thm)],[c338,c373]) ).
cnf(c375,plain,
meet(lojo(a,a,meet(X2,X3)),lojo(X3,a,meet(X2,a))) = lojo(meet(a,X3),a,upme(X2,a,X3)),
inference(substitution,[status(thm)],[c374]) ).
cnf(c376,plain,
lojo(meet(a,X3),a,upme(X2,a,X3)) = lome(a,X3,upme(X2,a,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c377,plain,
upme(X3,X4,X2) = upme(X3,X2,X4),
inference(substitution,[status(thm)],[c78]) ).
cnf(c378,plain,
lome(X5,X4,upme(X3,X5,X2)) = lome(X5,X4,upme(X3,X2,X5)),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
lome(X5,X4,upme(X3,X2,X5)) = lome(X5,upme(X3,X2,X5),X4),
inference(substitution,[status(thm)],[c111]) ).
cnf(c380,plain,
lojo(meet(X5,upme(X3,X2,X5)),X5,X4) = lome(X5,upme(X3,X2,X5),X4),
inference(substitution,[status(thm)],[c10]) ).
cnf(c381,plain,
lome(X5,upme(X3,X2,X5),X4) = lojo(meet(X5,upme(X3,X2,X5)),X5,X4),
inference(symmetry,[status(thm)],[c380]) ).
cnf(c382,plain,
upme(X3,X2,X4) = upme(X3,X4,X2),
inference(substitution,[status(thm)],[c78]) ).
cnf(c383,plain,
meet(X4,upme(X3,X2,X4)) = meet(X4,upme(X3,X4,X2)),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
meet(X4,upme(X3,X2,X4)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c383,c284]) ).
cnf(c385,plain,
lojo(meet(X5,upme(X3,X2,X5)),X5,X4) = lojo(meet(X5,X3),X5,X4),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
lojo(meet(X4,X2),X4,X3) = lome(X4,X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c387,plain,
lojo(meet(X5,upme(X3,X2,X5)),X5,X4) = lome(X5,X3,X4),
inference(transitivity,[status(thm)],[c385,c386]) ).
cnf(c388,plain,
lome(X5,upme(X3,X2,X5),X4) = lome(X5,X3,X4),
inference(transitivity,[status(thm)],[c381,c387]) ).
cnf(c389,plain,
lome(X5,X4,upme(X3,X2,X5)) = lome(X5,X3,X4),
inference(transitivity,[status(thm)],[c379,c388]) ).
cnf(c390,plain,
lome(X5,X4,upme(X3,X5,X2)) = lome(X5,X3,X4),
inference(transitivity,[status(thm)],[c378,c389]) ).
cnf(c391,plain,
lome(a,X3,upme(X2,a,X3)) = lome(a,X2,X3),
inference(substitution,[status(thm)],[c390]) ).
cnf(c392,plain,
lome(a,X3,X2) = lome(a,X2,X3),
inference(substitution,[status(thm)],[c111]) ).
cnf(c393,plain,
lome(a,X2,X3) = lome(a,X3,X2),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
lome(a,X3,upme(X2,a,X3)) = lome(a,X3,X2),
inference(transitivity,[status(thm)],[c391,c393]) ).
cnf(c395,plain,
lojo(meet(a,X3),a,upme(X2,a,X3)) = lome(a,X3,X2),
inference(transitivity,[status(thm)],[c376,c394]) ).
cnf(c396,plain,
meet(lojo(a,a,meet(X2,X3)),lojo(X3,a,meet(X2,a))) = lome(a,X3,X2),
inference(transitivity,[status(thm)],[c375,c395]) ).
cnf(c397,plain,
meet(a,lojo(X3,a,meet(X2,a))) = lome(a,X3,X2),
inference(transitivity,[status(thm)],[c336,c396]) ).
cnf(c398,plain,
meet(a,lojo(X3,a,X2)) = lome(a,X3,X2),
inference(transitivity,[status(thm)],[c330,c397]) ).
cnf(c399,plain,
meet(a,lojo(X3,X2,a)) = lome(a,X3,X2),
inference(transitivity,[status(thm)],[c316,c398]) ).
cnf(c400,plain,
meet(a,lojo(X2,X3,a)) = lome(a,X2,X3),
inference(substitution,[status(thm)],[c399]) ).
cnf(c401,plain,
lome(a,X2,X3) = meet(a,lojo(X2,X3,a)),
inference(symmetry,[status(thm)],[c400]) ).
cnf(c402,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c403,plain,
X3 = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
upjo(X4,X3,meet(X3,X2)) = upjo(X4,join(X3,meet(X3,X2)),meet(X3,X2)),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c406,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
upjo(X4,join(X3,X2),X2) = upjo(X4,join(X2,X3),X2),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
upme(join(X4,X3),X4,X2) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c409,axiom,
upjo(X2,Y2,Z2) = meet(join(X2,Y2),join(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_upjo) ).
cnf(c410,plain,
upjo(X4,X3,X2) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c409]) ).
cnf(c411,plain,
meet(join(X4,X3),join(X4,X2)) = upjo(X4,X3,X2),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c412,plain,
upme(join(X4,X3),X4,X2) = upjo(X4,X3,X2),
inference(transitivity,[status(thm)],[c408,c411]) ).
cnf(c413,plain,
upme(join(X4,join(X3,X2)),X4,X3) = upjo(X4,join(X3,X2),X3),
inference(substitution,[status(thm)],[c412]) ).
cnf(c414,plain,
upjo(X4,join(X3,X2),X3) = upme(join(X4,join(X3,X2)),X4,X3),
inference(symmetry,[status(thm)],[c413]) ).
cnf(c415,plain,
meet(join(X4,X3),join(X4,join(X3,X2))) = upme(join(X4,join(X3,X2)),X4,X3),
inference(substitution,[status(thm)],[c248]) ).
cnf(c416,plain,
upme(join(X4,join(X3,X2)),X4,X3) = meet(join(X4,X3),join(X4,join(X3,X2))),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
join(X4,join(X3,X2)) = join(join(X4,X3),X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c418,plain,
meet(join(X4,X3),join(X4,join(X3,X2))) = meet(join(X4,X3),join(join(X4,X3),X2)),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
meet(join(X4,X3),join(join(X4,X3),X2)) = join(X4,X3),
inference(substitution,[status(thm)],[c49]) ).
cnf(c420,plain,
meet(join(X4,X3),join(X4,join(X3,X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c418,c419]) ).
cnf(c421,plain,
upme(join(X4,join(X3,X2)),X4,X3) = join(X4,X3),
inference(transitivity,[status(thm)],[c416,c420]) ).
cnf(c422,plain,
upjo(X4,join(X3,X2),X3) = join(X4,X3),
inference(transitivity,[status(thm)],[c414,c421]) ).
cnf(c423,plain,
upjo(X4,join(X2,X3),X2) = join(X4,X2),
inference(substitution,[status(thm)],[c422]) ).
cnf(c424,plain,
upjo(X4,join(X3,X2),X2) = join(X4,X2),
inference(transitivity,[status(thm)],[c407,c423]) ).
cnf(c425,plain,
upjo(X4,join(X3,meet(X3,X2)),meet(X3,X2)) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c424]) ).
cnf(c426,plain,
lojo(X4,X3,X2) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c427,plain,
join(X4,meet(X3,X2)) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c426]) ).
cnf(c428,plain,
upjo(X4,join(X3,meet(X3,X2)),meet(X3,X2)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c425,c427]) ).
cnf(c429,plain,
upjo(X4,X3,meet(X3,X2)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c404,c428]) ).
cnf(c430,plain,
upjo(X2,X3,meet(X3,a)) = lojo(X2,X3,a),
inference(substitution,[status(thm)],[c429]) ).
cnf(c431,plain,
lojo(X2,X3,a) = upjo(X2,X3,meet(X3,a)),
inference(symmetry,[status(thm)],[c430]) ).
cnf(c432,plain,
meet(a,lojo(X2,X3,a)) = meet(a,upjo(X2,X3,meet(X3,a))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
upme(lojo(X5,X4,X3),X5,X2) = upme(lojo(X5,X4,X3),X2,X5),
inference(substitution,[status(thm)],[c78]) ).
cnf(c434,plain,
upme(lojo(X5,X4,X3),X2,X5) = upme(lojo(X5,X4,X3),X5,X2),
inference(substitution,[status(thm)],[c78]) ).
cnf(c435,plain,
lojo(X4,X3,X2) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c436,plain,
upme(lojo(X5,X4,X3),X5,X2) = upme(join(X5,meet(X4,X3)),X5,X2),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
upme(join(X5,meet(X4,X3)),X5,X2) = upjo(X5,meet(X4,X3),X2),
inference(substitution,[status(thm)],[c412]) ).
cnf(c438,plain,
upme(lojo(X5,X4,X3),X5,X2) = upjo(X5,meet(X4,X3),X2),
inference(transitivity,[status(thm)],[c436,c437]) ).
cnf(c439,plain,
upme(join(X4,X2),X4,X3) = upjo(X4,X2,X3),
inference(substitution,[status(thm)],[c412]) ).
cnf(c440,plain,
upjo(X4,X2,X3) = upme(join(X4,X2),X4,X3),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c442,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
upme(join(X3,X2),X5,X4) = upme(join(X2,X3),X5,X4),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
upme(join(X2,X3),X5,X4) = upme(join(X2,X3),X4,X5),
inference(substitution,[status(thm)],[c78]) ).
cnf(c445,plain,
upme(join(X2,X3),X4,X5) = meet(join(X2,X3),join(X4,X5)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c446,plain,
meet(join(X2,X3),join(X4,X5)) = upme(join(X4,X5),X2,X3),
inference(substitution,[status(thm)],[c248]) ).
cnf(c447,plain,
upme(join(X4,X5),X3,X2) = upme(join(X4,X5),X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c448,plain,
upme(join(X4,X5),X2,X3) = upme(join(X4,X5),X3,X2),
inference(symmetry,[status(thm)],[c447]) ).
cnf(c449,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c450,plain,
upme(join(X4,X5),X3,X2) = upme(join(X5,X4),X3,X2),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
upme(join(X4,X5),X2,X3) = upme(join(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c448,c450]) ).
cnf(c452,plain,
meet(join(X2,X3),join(X4,X5)) = upme(join(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c446,c451]) ).
cnf(c453,plain,
upme(join(X2,X3),X4,X5) = upme(join(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c445,c452]) ).
cnf(c454,plain,
upme(join(X2,X3),X5,X4) = upme(join(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c444,c453]) ).
cnf(c455,plain,
upme(join(X3,X2),X5,X4) = upme(join(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c443,c454]) ).
cnf(c456,plain,
upme(join(X4,X2),X4,X3) = upme(join(X4,X3),X4,X2),
inference(substitution,[status(thm)],[c455]) ).
cnf(c457,plain,
upme(join(X4,X2),X4,X3) = upjo(X4,X3,X2),
inference(transitivity,[status(thm)],[c456,c412]) ).
cnf(c458,plain,
upjo(X4,X2,X3) = upjo(X4,X3,X2),
inference(transitivity,[status(thm)],[c440,c457]) ).
cnf(c459,plain,
upjo(X5,X2,meet(X4,X3)) = upjo(X5,meet(X4,X3),X2),
inference(substitution,[status(thm)],[c458]) ).
cnf(c460,plain,
upjo(X5,meet(X4,X3),X2) = upjo(X5,X2,meet(X4,X3)),
inference(symmetry,[status(thm)],[c459]) ).
cnf(c461,plain,
upme(lojo(X5,X4,X3),X5,X2) = upjo(X5,X2,meet(X4,X3)),
inference(transitivity,[status(thm)],[c438,c460]) ).
cnf(c462,plain,
upme(lojo(X5,X4,X3),X2,X5) = upjo(X5,X2,meet(X4,X3)),
inference(transitivity,[status(thm)],[c434,c461]) ).
cnf(c463,plain,
upme(lojo(X5,X4,X3),X5,X2) = upjo(X5,X2,meet(X4,X3)),
inference(transitivity,[status(thm)],[c433,c462]) ).
cnf(c464,plain,
upme(lojo(X2,X3,a),X2,X3) = upjo(X2,X3,meet(X3,a)),
inference(substitution,[status(thm)],[c463]) ).
cnf(c465,plain,
upjo(X2,X3,meet(X3,a)) = upme(lojo(X2,X3,a),X2,X3),
inference(symmetry,[status(thm)],[c464]) ).
cnf(c466,plain,
meet(a,upjo(X2,X3,meet(X3,a))) = meet(a,upme(lojo(X2,X3,a),X2,X3)),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
meet(X2,upme(X5,X4,X3)) = meet(upme(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c468,plain,
meet(upme(X5,X4,X3),X2) = meet(X2,upme(X5,X4,X3)),
inference(symmetry,[status(thm)],[c467]) ).
cnf(c469,plain,
upme(X4,X3,X2) = upme(X4,X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c470,plain,
meet(X4,upme(X5,X3,X2)) = meet(X4,upme(X5,X2,X3)),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
meet(upme(X5,X2,X3),X4) = meet(X4,upme(X5,X2,X3)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c472,plain,
meet(X4,upme(X5,X2,X3)) = meet(upme(X5,X2,X3),X4),
inference(symmetry,[status(thm)],[c471]) ).
cnf(c473,plain,
upme(X4,X2,X3) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c474,plain,
meet(upme(X5,X2,X3),X4) = meet(meet(X5,join(X2,X3)),X4),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
meet(X5,meet(join(X2,X3),X4)) = meet(meet(X5,join(X2,X3)),X4),
inference(substitution,[status(thm)],[c133]) ).
cnf(c476,plain,
meet(meet(X5,join(X2,X3)),X4) = meet(X5,meet(join(X2,X3),X4)),
inference(symmetry,[status(thm)],[c475]) ).
cnf(c477,plain,
meet(join(X2,X3),X4) = upme(X4,X2,X3),
inference(substitution,[status(thm)],[c248]) ).
cnf(c478,plain,
meet(X5,meet(join(X2,X3),X4)) = meet(X5,upme(X4,X2,X3)),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
upme(X4,X3,X2) = upme(X4,X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c480,plain,
upme(X4,X2,X3) = upme(X4,X3,X2),
inference(symmetry,[status(thm)],[c479]) ).
cnf(c481,plain,
meet(X5,upme(X4,X2,X3)) = meet(X5,upme(X4,X3,X2)),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
meet(X5,meet(join(X2,X3),X4)) = meet(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c478,c481]) ).
cnf(c483,plain,
meet(meet(X5,join(X2,X3)),X4) = meet(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c476,c482]) ).
cnf(c484,plain,
meet(upme(X5,X2,X3),X4) = meet(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c474,c483]) ).
cnf(c485,plain,
meet(X4,upme(X5,X2,X3)) = meet(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c472,c484]) ).
cnf(c486,plain,
meet(X4,upme(X5,X3,X2)) = meet(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c470,c485]) ).
cnf(c487,plain,
meet(X5,upme(X2,X4,X3)) = meet(X2,upme(X5,X4,X3)),
inference(substitution,[status(thm)],[c486]) ).
cnf(c488,plain,
meet(X2,upme(X5,X4,X3)) = meet(X5,upme(X2,X4,X3)),
inference(symmetry,[status(thm)],[c487]) ).
cnf(c489,plain,
meet(upme(X5,X4,X3),X2) = meet(X5,upme(X2,X4,X3)),
inference(transitivity,[status(thm)],[c468,c488]) ).
cnf(c490,plain,
meet(upme(a,X2,X3),lojo(X2,X3,a)) = meet(a,upme(lojo(X2,X3,a),X2,X3)),
inference(substitution,[status(thm)],[c489]) ).
cnf(c491,plain,
meet(a,upme(lojo(X2,X3,a),X2,X3)) = meet(upme(a,X2,X3),lojo(X2,X3,a)),
inference(symmetry,[status(thm)],[c490]) ).
cnf(c492,plain,
lojo(X3,a,join(X3,X2)) = join(X3,upme(a,X3,X2)),
inference(substitution,[status(thm)],[c84]) ).
cnf(c493,plain,
join(X3,upme(a,X3,X2)) = lojo(X3,a,join(X3,X2)),
inference(symmetry,[status(thm)],[c492]) ).
cnf(c494,plain,
lojo(X3,a,join(X3,X2)) = join(X3,meet(a,join(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c495,plain,
lojo(meet(X4,meet(X3,X2)),X4,X3) = lome(X4,meet(X3,X2),X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c496,plain,
lome(X4,meet(X3,X2),X3) = lojo(meet(X4,meet(X3,X2)),X4,X3),
inference(symmetry,[status(thm)],[c495]) ).
cnf(c497,plain,
meet(X4,meet(X3,X2)) = meet(meet(X4,X3),X2),
inference(substitution,[status(thm)],[c133]) ).
cnf(c498,plain,
lojo(meet(X4,meet(X3,X2)),X4,X3) = lojo(meet(meet(X4,X3),X2),X4,X3),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
join(meet(X4,X3),meet(meet(X4,X3),X2)) = lojo(meet(meet(X4,X3),X2),X4,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c500,plain,
lojo(meet(meet(X4,X3),X2),X4,X3) = join(meet(X4,X3),meet(meet(X4,X3),X2)),
inference(symmetry,[status(thm)],[c499]) ).
cnf(c501,plain,
join(meet(X4,X3),meet(meet(X4,X3),X2)) = meet(X4,X3),
inference(substitution,[status(thm)],[c24]) ).
cnf(c502,plain,
lojo(meet(meet(X4,X3),X2),X4,X3) = meet(X4,X3),
inference(transitivity,[status(thm)],[c500,c501]) ).
cnf(c503,plain,
lojo(meet(X4,meet(X3,X2)),X4,X3) = meet(X4,X3),
inference(transitivity,[status(thm)],[c498,c502]) ).
cnf(c504,plain,
lome(X4,meet(X3,X2),X3) = meet(X4,X3),
inference(transitivity,[status(thm)],[c496,c503]) ).
cnf(c505,plain,
lome(a,meet(join(X3,X2),X2),join(X3,X2)) = meet(a,join(X3,X2)),
inference(substitution,[status(thm)],[c504]) ).
cnf(c506,plain,
meet(a,join(X3,X2)) = lome(a,meet(join(X3,X2),X2),join(X3,X2)),
inference(symmetry,[status(thm)],[c505]) ).
cnf(c507,plain,
join(X3,meet(a,join(X3,X2))) = join(X3,lome(a,meet(join(X3,X2),X2),join(X3,X2))),
inference(congruence,[status(thm)],[c506]) ).
cnf(c508,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c509,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c508]) ).
cnf(c510,plain,
upme(join(X3,X2),X3,X2) = upme(join(X2,X3),X3,X2),
inference(congruence,[status(thm)],[c509]) ).
cnf(c511,plain,
upme(join(X2,X3),X3,X2) = upme(join(X2,X3),X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c512,plain,
upme(join(X2,X3),X2,X3) = meet(join(X2,X3),join(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c513,plain,
meet(join(X2,X3),join(X2,X3)) = join(X2,X3),
inference(substitution,[status(thm)],[c322]) ).
cnf(c514,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c515,plain,
meet(join(X2,X3),join(X2,X3)) = join(X3,X2),
inference(transitivity,[status(thm)],[c513,c514]) ).
cnf(c516,plain,
upme(join(X2,X3),X2,X3) = join(X3,X2),
inference(transitivity,[status(thm)],[c512,c515]) ).
cnf(c517,plain,
upme(join(X2,X3),X3,X2) = join(X3,X2),
inference(transitivity,[status(thm)],[c511,c516]) ).
cnf(c518,plain,
upme(join(X3,X2),X3,X2) = join(X3,X2),
inference(transitivity,[status(thm)],[c510,c517]) ).
cnf(c519,plain,
join(X3,X2) = upme(join(X3,X2),X3,X2),
inference(symmetry,[status(thm)],[c518]) ).
cnf(c520,plain,
lome(a,meet(join(X3,X2),X2),join(X3,X2)) = lome(a,meet(join(X3,X2),X2),upme(join(X3,X2),X3,X2)),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
join(X3,lome(a,meet(join(X3,X2),X2),join(X3,X2))) = join(X3,lome(a,meet(join(X3,X2),X2),upme(join(X3,X2),X3,X2))),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
lome(a,meet(X3,X2),upme(X3,X4,X2)) = lome(a,upme(X3,X4,X2),meet(X3,X2)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c523,plain,
join(X4,lome(a,meet(X3,X2),upme(X3,X4,X2))) = join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)) = join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c525,plain,
join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))) = join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c526,plain,
join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))) = lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c527,plain,
lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2) = join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(symmetry,[status(thm)],[c526]) ).
cnf(c528,plain,
join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)) = join(X4,join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2)))),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c530,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
lojo(meet(X5,X4),X3,X2) = lojo(meet(X4,X5),X3,X2),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
join(X6,lojo(meet(X5,X4),X3,X2)) = join(X6,lojo(meet(X4,X5),X3,X2)),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
lojo(meet(X4,X5),X3,X2) = lojo(meet(X4,X5),X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c534,plain,
join(X6,lojo(meet(X4,X5),X3,X2)) = join(X6,lojo(meet(X4,X5),X2,X3)),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
lojo(meet(X4,X5),X2,X3) = lojo(meet(X2,X3),X4,X5),
inference(substitution,[status(thm)],[c108]) ).
cnf(c536,plain,
join(X6,lojo(meet(X4,X5),X2,X3)) = join(X6,lojo(meet(X2,X3),X4,X5)),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
lojo(join(X5,X4),X3,X2) = join(join(X5,X4),meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c538,plain,
join(X5,join(X4,meet(X3,X2))) = join(join(X5,X4),meet(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c539,plain,
join(join(X5,X4),meet(X3,X2)) = join(X5,join(X4,meet(X3,X2))),
inference(symmetry,[status(thm)],[c538]) ).
cnf(c540,plain,
lojo(X4,X3,X2) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c541,plain,
join(X4,meet(X3,X2)) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c540]) ).
cnf(c542,plain,
join(X5,join(X4,meet(X3,X2))) = join(X5,lojo(X4,X3,X2)),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
join(join(X5,X4),meet(X3,X2)) = join(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c539,c542]) ).
cnf(c544,plain,
lojo(join(X5,X4),X3,X2) = join(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c537,c543]) ).
cnf(c545,plain,
lojo(join(X6,meet(X2,X3)),X4,X5) = join(X6,lojo(meet(X2,X3),X4,X5)),
inference(substitution,[status(thm)],[c544]) ).
cnf(c546,plain,
join(X6,lojo(meet(X2,X3),X4,X5)) = lojo(join(X6,meet(X2,X3)),X4,X5),
inference(symmetry,[status(thm)],[c545]) ).
cnf(c547,plain,
lojo(X4,X2,X3) = join(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c548,plain,
join(X4,meet(X2,X3)) = lojo(X4,X2,X3),
inference(symmetry,[status(thm)],[c547]) ).
cnf(c549,plain,
lojo(join(X6,meet(X2,X3)),X4,X5) = lojo(lojo(X6,X2,X3),X4,X5),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c551,plain,
lojo(lojo(X6,X3,X2),X5,X4) = lojo(lojo(X6,X2,X3),X5,X4),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
lojo(lojo(X6,X2,X3),X5,X4) = lojo(lojo(X6,X2,X3),X4,X5),
inference(substitution,[status(thm)],[c61]) ).
cnf(c553,plain,
join(meet(X2,X3),X4) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c554,plain,
lojo(X4,X2,X3) = join(meet(X2,X3),X4),
inference(symmetry,[status(thm)],[c553]) ).
cnf(c555,plain,
lojo(lojo(X6,X2,X3),X4,X5) = lojo(join(meet(X2,X3),X6),X4,X5),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
lojo(join(meet(X2,X3),X6),X4,X5) = join(meet(X2,X3),lojo(X6,X4,X5)),
inference(substitution,[status(thm)],[c544]) ).
cnf(c557,plain,
join(meet(X2,X3),lojo(X6,X4,X5)) = lojo(lojo(X6,X4,X5),X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c558,plain,
lojo(lojo(X6,X4,X5),X3,X2) = lojo(lojo(X6,X4,X5),X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c559,plain,
lojo(lojo(X6,X4,X5),X2,X3) = lojo(lojo(X6,X4,X5),X3,X2),
inference(symmetry,[status(thm)],[c558]) ).
cnf(c560,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c561,plain,
lojo(X4,X2,X3) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
lojo(lojo(X6,X4,X5),X3,X2) = lojo(lojo(X6,X5,X4),X3,X2),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
lojo(lojo(X6,X4,X5),X2,X3) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c559,c562]) ).
cnf(c564,plain,
join(meet(X2,X3),lojo(X6,X4,X5)) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c557,c563]) ).
cnf(c565,plain,
lojo(join(meet(X2,X3),X6),X4,X5) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c556,c564]) ).
cnf(c566,plain,
lojo(lojo(X6,X2,X3),X4,X5) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c555,c565]) ).
cnf(c567,plain,
lojo(lojo(X6,X2,X3),X5,X4) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c552,c566]) ).
cnf(c568,plain,
lojo(lojo(X6,X3,X2),X5,X4) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c551,c567]) ).
cnf(c569,plain,
lojo(lojo(X6,X4,X5),X2,X3) = lojo(lojo(X6,X2,X3),X4,X5),
inference(substitution,[status(thm)],[c568]) ).
cnf(c570,plain,
lojo(lojo(X6,X2,X3),X4,X5) = lojo(lojo(X6,X4,X5),X2,X3),
inference(symmetry,[status(thm)],[c569]) ).
cnf(c571,plain,
lojo(lojo(X6,X4,X5),X3,X2) = lojo(lojo(X6,X4,X5),X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c572,plain,
lojo(lojo(X6,X4,X5),X2,X3) = lojo(lojo(X6,X4,X5),X3,X2),
inference(symmetry,[status(thm)],[c571]) ).
cnf(c573,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c574,plain,
lojo(X4,X2,X3) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
lojo(lojo(X6,X4,X5),X3,X2) = lojo(lojo(X6,X5,X4),X3,X2),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
lojo(lojo(X6,X4,X5),X2,X3) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c572,c575]) ).
cnf(c577,plain,
lojo(lojo(X6,X2,X3),X4,X5) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c570,c576]) ).
cnf(c578,plain,
lojo(join(X6,meet(X2,X3)),X4,X5) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c549,c577]) ).
cnf(c579,plain,
join(X6,lojo(meet(X2,X3),X4,X5)) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c546,c578]) ).
cnf(c580,plain,
join(X6,lojo(meet(X4,X5),X2,X3)) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c536,c579]) ).
cnf(c581,plain,
join(X6,lojo(meet(X4,X5),X3,X2)) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c534,c580]) ).
cnf(c582,plain,
join(X6,lojo(meet(X5,X4),X3,X2)) = lojo(lojo(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c532,c581]) ).
cnf(c583,plain,
join(X5,lojo(meet(X4,X3),X4,X2)) = lojo(lojo(X5,X4,X3),X4,X2),
inference(substitution,[status(thm)],[c582]) ).
cnf(c584,plain,
lojo(lojo(X5,X4,X3),X4,X2) = join(X5,lojo(meet(X4,X3),X4,X2)),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c585,plain,
join(X5,lojo(meet(X4,X3),X4,X2)) = join(X5,lome(X4,X3,X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c586,plain,
lojo(lojo(X5,X4,X3),X4,X2) = join(X5,lome(X4,X3,X2)),
inference(transitivity,[status(thm)],[c584,c585]) ).
cnf(c587,plain,
lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2)) = join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(substitution,[status(thm)],[c586]) ).
cnf(c588,plain,
join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))) = lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2)),
inference(symmetry,[status(thm)],[c587]) ).
cnf(c589,plain,
join(X4,join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2)))) = join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))),
inference(congruence,[status(thm)],[c588]) ).
cnf(c590,plain,
join(X2,lojo(X5,X4,X3)) = join(lojo(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c591,plain,
join(lojo(X5,X4,X3),X2) = join(X2,lojo(X5,X4,X3)),
inference(symmetry,[status(thm)],[c590]) ).
cnf(c592,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c593,plain,
join(X4,lojo(X5,X3,X2)) = join(X4,lojo(X5,X2,X3)),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
join(lojo(X5,X2,X3),X4) = join(X4,lojo(X5,X2,X3)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c595,plain,
join(X4,lojo(X5,X2,X3)) = join(lojo(X5,X2,X3),X4),
inference(symmetry,[status(thm)],[c594]) ).
cnf(c596,plain,
lojo(X4,X2,X3) = join(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c597,plain,
join(lojo(X5,X2,X3),X4) = join(join(X5,meet(X2,X3)),X4),
inference(congruence,[status(thm)],[c596]) ).
cnf(c598,plain,
join(X5,join(meet(X2,X3),X4)) = join(join(X5,meet(X2,X3)),X4),
inference(substitution,[status(thm)],[c22]) ).
cnf(c599,plain,
join(join(X5,meet(X2,X3)),X4) = join(X5,join(meet(X2,X3),X4)),
inference(symmetry,[status(thm)],[c598]) ).
cnf(c600,plain,
join(meet(X2,X3),X4) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c601,plain,
join(X5,join(meet(X2,X3),X4)) = join(X5,lojo(X4,X2,X3)),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c603,plain,
lojo(X4,X2,X3) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c602]) ).
cnf(c604,plain,
join(X5,lojo(X4,X2,X3)) = join(X5,lojo(X4,X3,X2)),
inference(congruence,[status(thm)],[c603]) ).
cnf(c605,plain,
join(X5,join(meet(X2,X3),X4)) = join(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c601,c604]) ).
cnf(c606,plain,
join(join(X5,meet(X2,X3)),X4) = join(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c599,c605]) ).
cnf(c607,plain,
join(lojo(X5,X2,X3),X4) = join(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c597,c606]) ).
cnf(c608,plain,
join(X4,lojo(X5,X2,X3)) = join(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c595,c607]) ).
cnf(c609,plain,
join(X4,lojo(X5,X3,X2)) = join(X5,lojo(X4,X3,X2)),
inference(transitivity,[status(thm)],[c593,c608]) ).
cnf(c610,plain,
join(X5,lojo(X2,X4,X3)) = join(X2,lojo(X5,X4,X3)),
inference(substitution,[status(thm)],[c609]) ).
cnf(c611,plain,
join(X2,lojo(X5,X4,X3)) = join(X5,lojo(X2,X4,X3)),
inference(symmetry,[status(thm)],[c610]) ).
cnf(c612,plain,
join(lojo(X5,X4,X3),X2) = join(X5,lojo(X2,X4,X3)),
inference(transitivity,[status(thm)],[c591,c611]) ).
cnf(c613,plain,
join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))) = join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))),
inference(substitution,[status(thm)],[c612]) ).
cnf(c614,plain,
join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))) = join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))),
inference(symmetry,[status(thm)],[c613]) ).
cnf(c615,plain,
lojo(meet(X4,X2),a,upme(X3,X4,X2)) = meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4))),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c616,plain,
join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))) = join(lojo(X4,a,meet(X3,X2)),meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4)))),
inference(congruence,[status(thm)],[c615]) ).
cnf(c617,plain,
join(lojo(X4,a,meet(X3,X2)),meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4)))) = lojo(X4,a,meet(X3,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c618,plain,
lojo(X4,a,meet(X3,X2)) = lojo(X4,X3,meet(X2,a)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c619,plain,
join(lojo(X4,a,meet(X3,X2)),meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4)))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c617,c618]) ).
cnf(c620,plain,
join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c616,c619]) ).
cnf(c621,plain,
join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c614,c620]) ).
cnf(c622,plain,
join(X4,join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2)))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c589,c621]) ).
cnf(c623,plain,
join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c528,c622]) ).
cnf(c624,plain,
join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c525,c623]) ).
cnf(c625,plain,
join(X4,lome(a,meet(X3,X2),upme(X3,X4,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c523,c624]) ).
cnf(c626,plain,
join(X3,lome(a,meet(join(X3,X2),X2),upme(join(X3,X2),X3,X2))) = lojo(X3,join(X3,X2),meet(X2,a)),
inference(substitution,[status(thm)],[c625]) ).
cnf(c627,plain,
lojo(X5,join(X4,X3),X2) = lojo(X5,X2,join(X4,X3)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c628,plain,
lojo(X5,X2,join(X4,X3)) = join(X5,upme(X2,X4,X3)),
inference(substitution,[status(thm)],[c84]) ).
cnf(c629,plain,
lojo(X5,join(X4,X3),X2) = join(X5,upme(X2,X4,X3)),
inference(transitivity,[status(thm)],[c627,c628]) ).
cnf(c630,plain,
lojo(X3,join(X3,X2),meet(X2,a)) = join(X3,upme(meet(X2,a),X3,X2)),
inference(substitution,[status(thm)],[c629]) ).
cnf(c631,plain,
upme(meet(X2,a),X3,X2) = meet(X2,upme(a,X3,X2)),
inference(substitution,[status(thm)],[c361]) ).
cnf(c632,plain,
join(X3,upme(meet(X2,a),X3,X2)) = join(X3,meet(X2,upme(a,X3,X2))),
inference(congruence,[status(thm)],[c631]) ).
cnf(c633,plain,
lojo(X3,X2,upme(a,X3,X2)) = join(X3,meet(X2,upme(a,X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c634,plain,
join(X3,meet(X2,upme(a,X3,X2))) = lojo(X3,X2,upme(a,X3,X2)),
inference(symmetry,[status(thm)],[c633]) ).
cnf(c635,plain,
upme(X3,X2,X4) = upme(X3,X4,X2),
inference(substitution,[status(thm)],[c78]) ).
cnf(c636,plain,
lojo(X5,X4,upme(X3,X2,X4)) = lojo(X5,X4,upme(X3,X4,X2)),
inference(congruence,[status(thm)],[c635]) ).
cnf(c637,plain,
lojo(X5,X4,upme(X3,X4,X2)) = join(X5,meet(X4,upme(X3,X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c638,plain,
join(X5,meet(X4,upme(X3,X4,X2))) = join(X5,meet(X4,X3)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c639,plain,
lojo(X4,X3,X2) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c640,plain,
join(X4,meet(X3,X2)) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c639]) ).
cnf(c641,plain,
join(X5,meet(X4,upme(X3,X4,X2))) = lojo(X5,X4,X3),
inference(transitivity,[status(thm)],[c638,c640]) ).
cnf(c642,plain,
lojo(X5,X4,upme(X3,X4,X2)) = lojo(X5,X4,X3),
inference(transitivity,[status(thm)],[c637,c641]) ).
cnf(c643,plain,
lojo(X5,X4,upme(X3,X2,X4)) = lojo(X5,X4,X3),
inference(transitivity,[status(thm)],[c636,c642]) ).
cnf(c644,plain,
lojo(X3,X2,upme(a,X3,X2)) = lojo(X3,X2,a),
inference(substitution,[status(thm)],[c643]) ).
cnf(c645,plain,
join(X3,meet(X2,upme(a,X3,X2))) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c634,c644]) ).
cnf(c646,plain,
join(X3,upme(meet(X2,a),X3,X2)) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c632,c645]) ).
cnf(c647,plain,
lojo(X3,join(X3,X2),meet(X2,a)) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c630,c646]) ).
cnf(c648,plain,
join(X3,lome(a,meet(join(X3,X2),X2),upme(join(X3,X2),X3,X2))) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c626,c647]) ).
cnf(c649,plain,
join(X3,lome(a,meet(join(X3,X2),X2),join(X3,X2))) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c521,c648]) ).
cnf(c650,plain,
join(X3,meet(a,join(X3,X2))) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c507,c649]) ).
cnf(c651,plain,
lojo(X3,a,join(X3,X2)) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c494,c650]) ).
cnf(c652,plain,
join(X3,upme(a,X3,X2)) = lojo(X3,X2,a),
inference(transitivity,[status(thm)],[c493,c651]) ).
cnf(c653,plain,
join(X2,upme(a,X2,X3)) = lojo(X2,X3,a),
inference(substitution,[status(thm)],[c652]) ).
cnf(c654,plain,
lojo(X2,X3,a) = join(X2,upme(a,X2,X3)),
inference(symmetry,[status(thm)],[c653]) ).
cnf(c655,plain,
meet(upme(a,X2,X3),lojo(X2,X3,a)) = meet(upme(a,X2,X3),join(X2,upme(a,X2,X3))),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
meet(upme(a,X2,X3),join(X2,upme(a,X2,X3))) = upme(a,X2,X3),
inference(substitution,[status(thm)],[c51]) ).
cnf(c657,plain,
upme(a,X3,X2) = upme(a,X2,X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c658,plain,
upme(a,X2,X3) = upme(a,X3,X2),
inference(symmetry,[status(thm)],[c657]) ).
cnf(c659,plain,
meet(upme(a,X2,X3),join(X2,upme(a,X2,X3))) = upme(a,X3,X2),
inference(transitivity,[status(thm)],[c656,c658]) ).
cnf(c660,plain,
meet(upme(a,X2,X3),lojo(X2,X3,a)) = upme(a,X3,X2),
inference(transitivity,[status(thm)],[c655,c659]) ).
cnf(c661,plain,
meet(a,upme(lojo(X2,X3,a),X2,X3)) = upme(a,X3,X2),
inference(transitivity,[status(thm)],[c491,c660]) ).
cnf(c662,plain,
meet(a,upjo(X2,X3,meet(X3,a))) = upme(a,X3,X2),
inference(transitivity,[status(thm)],[c466,c661]) ).
cnf(c663,plain,
meet(a,lojo(X2,X3,a)) = upme(a,X3,X2),
inference(transitivity,[status(thm)],[c432,c662]) ).
cnf(c664,plain,
lome(a,X2,X3) = upme(a,X3,X2),
inference(transitivity,[status(thm)],[c401,c663]) ).
cnf(c665,plain,
lome(a,X3,X2) = upme(a,X3,X2),
inference(transitivity,[status(thm)],[c314,c664]) ).
cnf(c666,plain,
lome(a,meet(X3,X2),upme(X3,X4,X2)) = upme(a,meet(X3,X2),upme(X3,X4,X2)),
inference(substitution,[status(thm)],[c665]) ).
cnf(c667,plain,
upme(a,meet(X3,X2),upme(X3,X4,X2)) = lome(a,meet(X3,X2),upme(X3,X4,X2)),
inference(symmetry,[status(thm)],[c666]) ).
cnf(c668,plain,
join(X4,upme(a,meet(X3,X2),upme(X3,X4,X2))) = join(X4,lome(a,meet(X3,X2),upme(X3,X4,X2))),
inference(congruence,[status(thm)],[c667]) ).
cnf(c669,plain,
lome(a,meet(X3,X2),upme(X3,X4,X2)) = lome(a,upme(X3,X4,X2),meet(X3,X2)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c670,plain,
join(X4,lome(a,meet(X3,X2),upme(X3,X4,X2))) = join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)) = join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c672,plain,
join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))) = join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)),
inference(symmetry,[status(thm)],[c671]) ).
cnf(c673,plain,
join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))) = lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c674,plain,
lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2) = join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(symmetry,[status(thm)],[c673]) ).
cnf(c675,plain,
join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)) = join(X4,join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2)))),
inference(congruence,[status(thm)],[c674]) ).
cnf(c676,plain,
lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2)) = join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))),
inference(substitution,[status(thm)],[c586]) ).
cnf(c677,plain,
join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2))) = lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2)),
inference(symmetry,[status(thm)],[c676]) ).
cnf(c678,plain,
join(X4,join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2)))) = join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))),
inference(congruence,[status(thm)],[c677]) ).
cnf(c679,plain,
join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))) = join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))),
inference(substitution,[status(thm)],[c612]) ).
cnf(c680,plain,
join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))) = join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))),
inference(symmetry,[status(thm)],[c679]) ).
cnf(c681,plain,
lojo(meet(X4,X2),a,upme(X3,X4,X2)) = meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4))),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c682,plain,
join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))) = join(lojo(X4,a,meet(X3,X2)),meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4)))),
inference(congruence,[status(thm)],[c681]) ).
cnf(c683,plain,
join(lojo(X4,a,meet(X3,X2)),meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4)))) = lojo(X4,a,meet(X3,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c684,plain,
lojo(X4,a,meet(X3,X2)) = lojo(X4,X3,meet(X2,a)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c685,plain,
join(lojo(X4,a,meet(X3,X2)),meet(lojo(X4,a,meet(X3,X2)),lojo(X2,a,meet(X3,X4)))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c683,c684]) ).
cnf(c686,plain,
join(lojo(X4,a,meet(X3,X2)),lojo(meet(X4,X2),a,upme(X3,X4,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c682,c685]) ).
cnf(c687,plain,
join(X4,lojo(lojo(meet(X4,X2),a,upme(X3,X4,X2)),a,meet(X3,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c680,c686]) ).
cnf(c688,plain,
join(X4,join(meet(X4,X2),lome(a,upme(X3,X4,X2),meet(X3,X2)))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c678,c687]) ).
cnf(c689,plain,
join(X4,lojo(lome(a,upme(X3,X4,X2),meet(X3,X2)),X4,X2)) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c675,c688]) ).
cnf(c690,plain,
join(X4,lome(a,upme(X3,X4,X2),meet(X3,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c672,c689]) ).
cnf(c691,plain,
join(X4,lome(a,meet(X3,X2),upme(X3,X4,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c670,c690]) ).
cnf(c692,plain,
join(X4,upme(a,meet(X3,X2),upme(X3,X4,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c668,c691]) ).
cnf(c693,plain,
join(X4,meet(a,lojo(upme(X3,X4,X2),X3,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c313,c692]) ).
cnf(c694,plain,
lojo(X4,a,lojo(upme(X3,X4,X2),X3,X2)) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c310,c693]) ).
cnf(c695,plain,
lojo(X4,a,lome(X3,X2,join(X4,X2))) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c309,c694]) ).
cnf(c696,plain,
lojo(X4,a,upme(X3,X2,X4)) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c299,c695]) ).
cnf(c697,plain,
lojo(X4,X3,upme(a,X2,X4)) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c258,c696]) ).
cnf(c698,plain,
lojo(X4,X3,upme(a,X4,X2)) = lojo(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c221,c697]) ).
cnf(c699,plain,
lojo(meet(X4,X3),X4,upme(a,meet(X4,X3),X2)) = lojo(meet(X4,X3),X4,meet(X2,a)),
inference(substitution,[status(thm)],[c698]) ).
cnf(c700,plain,
lojo(meet(X4,X3),X4,meet(X2,a)) = lome(X4,X3,meet(X2,a)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c701,plain,
lojo(meet(X4,X3),X4,upme(a,meet(X4,X3),X2)) = lome(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c699,c700]) ).
cnf(c702,plain,
lome(X4,X3,upme(a,meet(X4,X3),X2)) = lome(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c219,c701]) ).
cnf(c703,plain,
lome(X4,X3,meet(a,lojo(X2,X4,X3))) = lome(X4,X3,meet(X2,a)),
inference(transitivity,[status(thm)],[c217,c702]) ).
cnf(c704,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(a,lojo(X4,meet(a,X5),lome(meet(a,X5),X3,X2)))) = lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(X4,a)),
inference(substitution,[status(thm)],[c703]) ).
cnf(c705,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(X4,a)) = lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(a,lojo(X4,meet(a,X5),lome(meet(a,X5),X3,X2)))),
inference(symmetry,[status(thm)],[c704]) ).
cnf(c706,plain,
lojo(X5,X4,lome(X4,X3,X2)) = lojo(X5,lome(X4,X3,X2),X4),
inference(substitution,[status(thm)],[c61]) ).
cnf(c707,plain,
X4 = join(X4,lome(X4,X3,X2)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c708,plain,
lojo(X5,lome(X4,X3,X2),X4) = lojo(X5,lome(X4,X3,X2),join(X4,lome(X4,X3,X2))),
inference(congruence,[status(thm)],[c707]) ).
cnf(c709,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c710,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c709]) ).
cnf(c711,plain,
lojo(X4,X3,join(X2,X3)) = lojo(X4,X3,join(X3,X2)),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
lojo(X4,X3,join(X3,X2)) = join(X4,meet(X3,join(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c713,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c49]) ).
cnf(c714,plain,
join(X4,meet(X3,join(X3,X2))) = join(X4,X3),
inference(congruence,[status(thm)],[c713]) ).
cnf(c715,plain,
lojo(X4,X3,join(X3,X2)) = join(X4,X3),
inference(transitivity,[status(thm)],[c712,c714]) ).
cnf(c716,plain,
lojo(X4,X3,join(X2,X3)) = join(X4,X3),
inference(transitivity,[status(thm)],[c711,c715]) ).
cnf(c717,plain,
lojo(X5,lome(X4,X3,X2),join(X4,lome(X4,X3,X2))) = join(X5,lome(X4,X3,X2)),
inference(substitution,[status(thm)],[c716]) ).
cnf(c718,plain,
lojo(X5,lome(X4,X3,X2),X4) = join(X5,lome(X4,X3,X2)),
inference(transitivity,[status(thm)],[c708,c717]) ).
cnf(c719,plain,
lojo(X5,X4,lome(X4,X3,X2)) = join(X5,lome(X4,X3,X2)),
inference(transitivity,[status(thm)],[c706,c718]) ).
cnf(c720,plain,
lojo(X4,meet(a,X5),lome(meet(a,X5),X3,X2)) = join(X4,lome(meet(a,X5),X3,X2)),
inference(substitution,[status(thm)],[c719]) ).
cnf(c721,plain,
meet(a,lojo(X4,meet(a,X5),lome(meet(a,X5),X3,X2))) = meet(a,join(X4,lome(meet(a,X5),X3,X2))),
inference(congruence,[status(thm)],[c720]) ).
cnf(c722,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(a,lojo(X4,meet(a,X5),lome(meet(a,X5),X3,X2)))) = lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(a,join(X4,lome(meet(a,X5),X3,X2)))),
inference(congruence,[status(thm)],[c721]) ).
cnf(c723,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c724,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c723]) ).
cnf(c725,plain,
lome(meet(X5,X4),X3,meet(X5,X2)) = lome(meet(X5,X4),X3,meet(X2,X5)),
inference(congruence,[status(thm)],[c724]) ).
cnf(c726,plain,
lome(meet(X5,X4),X3,meet(X5,X2)) = lome(meet(X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c725,c196]) ).
cnf(c727,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(a,join(X4,lome(meet(a,X5),X3,X2)))) = lome(meet(a,X5),lome(meet(a,X5),X3,X2),join(X4,lome(meet(a,X5),X3,X2))),
inference(substitution,[status(thm)],[c726]) ).
cnf(c728,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),join(X4,lome(meet(a,X5),X3,X2))) = upme(meet(a,X5),lome(meet(a,X5),X3,X2),X4),
inference(substitution,[status(thm)],[c296]) ).
cnf(c729,plain,
upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)) = upme(meet(a,X5),lome(meet(a,X5),X3,X2),X4),
inference(substitution,[status(thm)],[c78]) ).
cnf(c730,plain,
upme(meet(a,X5),lome(meet(a,X5),X3,X2),X4) = upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)),
inference(symmetry,[status(thm)],[c729]) ).
cnf(c731,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),join(X4,lome(meet(a,X5),X3,X2))) = upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)),
inference(transitivity,[status(thm)],[c728,c730]) ).
cnf(c732,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(a,join(X4,lome(meet(a,X5),X3,X2)))) = upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)),
inference(transitivity,[status(thm)],[c727,c731]) ).
cnf(c733,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(a,lojo(X4,meet(a,X5),lome(meet(a,X5),X3,X2)))) = upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)),
inference(transitivity,[status(thm)],[c722,c732]) ).
cnf(c734,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),meet(X4,a)) = upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)),
inference(transitivity,[status(thm)],[c705,c733]) ).
cnf(c735,plain,
lome(meet(a,X5),lome(meet(a,X5),X3,X2),X4) = upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)),
inference(transitivity,[status(thm)],[c198,c734]) ).
cnf(c736,plain,
lome(meet(a,X5),X4,lome(meet(a,X5),X3,X2)) = upme(meet(a,X5),X4,lome(meet(a,X5),X3,X2)),
inference(transitivity,[status(thm)],[c171,c735]) ).
cnf(c737,plain,
lome(meet(a,X4),X3,lome(meet(a,X4),X3,X2)) = upme(meet(a,X4),X3,lome(meet(a,X4),X3,X2)),
inference(substitution,[status(thm)],[c736]) ).
cnf(c738,plain,
upme(X5,X4,lome(meet(a,X3),X4,X2)) = meet(X5,join(X4,lome(meet(a,X3),X4,X2))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c739,plain,
lome(X3,X4,X2) = lome(X3,X2,X4),
inference(substitution,[status(thm)],[c111]) ).
cnf(c740,plain,
join(X4,lome(X3,X4,X2)) = join(X4,lome(X3,X2,X4)),
inference(congruence,[status(thm)],[c739]) ).
cnf(c741,plain,
lojo(meet(X3,X2),X3,X4) = lome(X3,X2,X4),
inference(substitution,[status(thm)],[c10]) ).
cnf(c742,plain,
lome(X3,X2,X4) = lojo(meet(X3,X2),X3,X4),
inference(symmetry,[status(thm)],[c741]) ).
cnf(c743,plain,
join(X4,lome(X3,X2,X4)) = join(X4,lojo(meet(X3,X2),X3,X4)),
inference(congruence,[status(thm)],[c742]) ).
cnf(c744,plain,
lojo(X3,X2,X4) = lojo(X3,X4,X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c745,plain,
join(X4,lojo(X3,X2,X4)) = join(X4,lojo(X3,X4,X2)),
inference(congruence,[status(thm)],[c744]) ).
cnf(c746,plain,
join(X4,lojo(X3,X2,X4)) = join(X4,X3),
inference(transitivity,[status(thm)],[c745,c28]) ).
cnf(c747,plain,
join(X4,lojo(meet(X3,X2),X3,X4)) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c746]) ).
cnf(c748,plain,
lojo(X4,X3,X2) = join(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c749,plain,
join(X4,meet(X3,X2)) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c748]) ).
cnf(c750,plain,
join(X4,lojo(meet(X3,X2),X3,X4)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c747,c749]) ).
cnf(c751,plain,
join(X4,lome(X3,X2,X4)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c743,c750]) ).
cnf(c752,plain,
join(X4,lome(X3,X4,X2)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c740,c751]) ).
cnf(c753,plain,
join(X4,lome(X2,X4,X3)) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c752]) ).
cnf(c754,plain,
lojo(X4,X3,X2) = lojo(X4,X2,X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c755,plain,
lojo(X4,X2,X3) = lojo(X4,X3,X2),
inference(symmetry,[status(thm)],[c754]) ).
cnf(c756,plain,
join(X4,lome(X2,X4,X3)) = lojo(X4,X3,X2),
inference(transitivity,[status(thm)],[c753,c755]) ).
cnf(c757,plain,
join(X4,lome(meet(a,X3),X4,X2)) = lojo(X4,X2,meet(a,X3)),
inference(substitution,[status(thm)],[c756]) ).
cnf(c758,plain,
lojo(X5,X3,meet(X4,X2)) = join(X5,meet(X3,meet(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c759,plain,
meet(X3,meet(X4,X2)) = meet(X4,meet(X3,X2)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c760,plain,
join(X5,meet(X3,meet(X4,X2))) = join(X5,meet(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c759]) ).
cnf(c761,plain,
lojo(X5,X4,meet(X3,X2)) = join(X5,meet(X4,meet(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c762,plain,
join(X5,meet(X4,meet(X3,X2))) = lojo(X5,X4,meet(X3,X2)),
inference(symmetry,[status(thm)],[c761]) ).
cnf(c763,plain,
join(X5,meet(X3,meet(X4,X2))) = lojo(X5,X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c760,c762]) ).
cnf(c764,plain,
lojo(X5,X3,meet(X4,X2)) = lojo(X5,X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c758,c763]) ).
cnf(c765,plain,
lojo(X5,X4,meet(X3,meet(X4,X2))) = lojo(X5,X3,meet(X4,meet(X4,X2))),
inference(substitution,[status(thm)],[c764]) ).
cnf(c766,plain,
lojo(X5,X3,meet(X4,meet(X4,X2))) = lojo(X5,X3,meet(X4,X2)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c767,plain,
lojo(X5,X4,meet(X3,meet(X4,X2))) = lojo(X5,X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c765,c766]) ).
cnf(c768,plain,
lojo(X4,a,meet(X2,meet(a,X3))) = lojo(X4,X2,meet(a,X3)),
inference(substitution,[status(thm)],[c767]) ).
cnf(c769,plain,
lojo(X4,X2,meet(a,X3)) = lojo(X4,a,meet(X2,meet(a,X3))),
inference(symmetry,[status(thm)],[c768]) ).
cnf(c770,plain,
meet(X2,upme(meet(a,X3),X4,X2)) = meet(X2,meet(a,X3)),
inference(substitution,[status(thm)],[c384]) ).
cnf(c771,plain,
meet(X2,meet(a,X3)) = meet(X2,upme(meet(a,X3),X4,X2)),
inference(symmetry,[status(thm)],[c770]) ).
cnf(c772,plain,
lojo(X4,a,meet(X2,meet(a,X3))) = lojo(X4,a,meet(X2,upme(meet(a,X3),X4,X2))),
inference(congruence,[status(thm)],[c771]) ).
cnf(c773,plain,
meet(upme(meet(a,X3),X4,X2),X2) = meet(X2,upme(meet(a,X3),X4,X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c774,plain,
meet(X2,upme(meet(a,X3),X4,X2)) = meet(upme(meet(a,X3),X4,X2),X2),
inference(symmetry,[status(thm)],[c773]) ).
cnf(c775,plain,
lojo(X4,a,meet(X2,upme(meet(a,X3),X4,X2))) = lojo(X4,a,meet(upme(meet(a,X3),X4,X2),X2)),
inference(congruence,[status(thm)],[c774]) ).
cnf(c776,plain,
lojo(X4,X2,meet(a,upme(meet(a,X3),X4,X2))) = lojo(X4,a,meet(upme(meet(a,X3),X4,X2),X2)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c777,plain,
lojo(X4,a,meet(upme(meet(a,X3),X4,X2),X2)) = lojo(X4,X2,meet(a,upme(meet(a,X3),X4,X2))),
inference(symmetry,[status(thm)],[c776]) ).
cnf(c778,plain,
lojo(X4,upme(meet(a,X3),X4,X2),meet(X2,a)) = lojo(X4,X2,meet(a,upme(meet(a,X3),X4,X2))),
inference(substitution,[status(thm)],[c242]) ).
cnf(c779,plain,
lojo(X4,X2,meet(a,upme(meet(a,X3),X4,X2))) = lojo(X4,upme(meet(a,X3),X4,X2),meet(X2,a)),
inference(symmetry,[status(thm)],[c778]) ).
cnf(c780,plain,
join(X4,lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(upme(meet(a,X3),X4,X2),X4,X2))) = lojo(X4,upme(meet(a,X3),X4,X2),meet(X2,a)),
inference(substitution,[status(thm)],[c625]) ).
cnf(c781,plain,
lojo(X4,upme(meet(a,X3),X4,X2),meet(X2,a)) = join(X4,lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(upme(meet(a,X3),X4,X2),X4,X2))),
inference(symmetry,[status(thm)],[c780]) ).
cnf(c782,plain,
meet(join(X3,X2),upme(X4,X3,X2)) = upme(upme(X4,X3,X2),X3,X2),
inference(substitution,[status(thm)],[c248]) ).
cnf(c783,plain,
upme(upme(X4,X3,X2),X3,X2) = meet(join(X3,X2),upme(X4,X3,X2)),
inference(symmetry,[status(thm)],[c782]) ).
cnf(c784,plain,
meet(X4,upme(join(X3,X2),X3,X2)) = meet(join(X3,X2),upme(X4,X3,X2)),
inference(substitution,[status(thm)],[c486]) ).
cnf(c785,plain,
meet(join(X3,X2),upme(X4,X3,X2)) = meet(X4,upme(join(X3,X2),X3,X2)),
inference(symmetry,[status(thm)],[c784]) ).
cnf(c786,plain,
meet(X4,upme(join(X3,X2),X3,X2)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c518]) ).
cnf(c787,plain,
upme(X4,X3,X2) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c788,plain,
meet(X4,join(X3,X2)) = upme(X4,X3,X2),
inference(symmetry,[status(thm)],[c787]) ).
cnf(c789,plain,
meet(X4,upme(join(X3,X2),X3,X2)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c786,c788]) ).
cnf(c790,plain,
meet(join(X3,X2),upme(X4,X3,X2)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c785,c789]) ).
cnf(c791,plain,
upme(upme(X4,X3,X2),X3,X2) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c783,c790]) ).
cnf(c792,plain,
upme(upme(meet(a,X3),X4,X2),X4,X2) = upme(meet(a,X3),X4,X2),
inference(substitution,[status(thm)],[c791]) ).
cnf(c793,plain,
lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(upme(meet(a,X3),X4,X2),X4,X2)) = lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2)),
inference(congruence,[status(thm)],[c792]) ).
cnf(c794,plain,
join(X4,lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(upme(meet(a,X3),X4,X2),X4,X2))) = join(X4,lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2))),
inference(congruence,[status(thm)],[c793]) ).
cnf(c795,plain,
lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2)) = upme(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2)),
inference(substitution,[status(thm)],[c665]) ).
cnf(c796,plain,
join(X4,lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2))) = join(X4,upme(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2))),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
upme(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2)) = meet(a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2)),
inference(substitution,[status(thm)],[c214]) ).
cnf(c798,plain,
join(X4,upme(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2))) = join(X4,meet(a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2))),
inference(congruence,[status(thm)],[c797]) ).
cnf(c799,plain,
lojo(X4,a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2)) = join(X4,meet(a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c800,plain,
join(X4,meet(a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2))) = lojo(X4,a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2)),
inference(symmetry,[status(thm)],[c799]) ).
cnf(c801,plain,
lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2) = upme(meet(a,X3),X4,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c802,plain,
lojo(X4,a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2)) = lojo(X4,a,upme(meet(a,X3),X4,X2)),
inference(congruence,[status(thm)],[c801]) ).
cnf(c803,plain,
meet(upme(X4,X3,X2),X4) = meet(X4,upme(X4,X3,X2)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c804,plain,
meet(X4,upme(X4,X3,X2)) = meet(upme(X4,X3,X2),X4),
inference(symmetry,[status(thm)],[c803]) ).
cnf(c805,plain,
upme(X4,X3,X2) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c806,plain,
join(X4,upme(X4,X3,X2)) = join(X4,meet(X4,join(X3,X2))),
inference(congruence,[status(thm)],[c805]) ).
cnf(c807,plain,
join(X4,meet(X4,join(X3,X2))) = X4,
inference(substitution,[status(thm)],[c24]) ).
cnf(c808,plain,
join(X4,upme(X4,X3,X2)) = X4,
inference(transitivity,[status(thm)],[c806,c807]) ).
cnf(c809,plain,
X4 = join(X4,upme(X4,X3,X2)),
inference(symmetry,[status(thm)],[c808]) ).
cnf(c810,plain,
meet(upme(X4,X3,X2),X4) = meet(upme(X4,X3,X2),join(X4,upme(X4,X3,X2))),
inference(congruence,[status(thm)],[c809]) ).
cnf(c811,plain,
meet(upme(X4,X3,X2),join(X4,upme(X4,X3,X2))) = upme(X4,X3,X2),
inference(substitution,[status(thm)],[c51]) ).
cnf(c812,plain,
meet(upme(X4,X3,X2),X4) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c810,c811]) ).
cnf(c813,plain,
meet(X4,upme(X4,X3,X2)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c804,c812]) ).
cnf(c814,plain,
meet(meet(X5,X4),upme(meet(X5,X4),X3,X2)) = upme(meet(X5,X4),X3,X2),
inference(substitution,[status(thm)],[c813]) ).
cnf(c815,plain,
upme(meet(X5,X4),X3,X2) = meet(meet(X5,X4),upme(meet(X5,X4),X3,X2)),
inference(symmetry,[status(thm)],[c814]) ).
cnf(c816,plain,
lojo(X6,X5,upme(meet(X5,X4),X3,X2)) = lojo(X6,X5,meet(meet(X5,X4),upme(meet(X5,X4),X3,X2))),
inference(congruence,[status(thm)],[c815]) ).
cnf(c817,plain,
lojo(X5,X4,meet(meet(X4,X3),X2)) = lojo(X5,meet(X4,X3),meet(X2,X4)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c818,plain,
lojo(X5,meet(X4,X3),meet(X2,X4)) = lojo(X5,X2,meet(X4,meet(X4,X3))),
inference(substitution,[status(thm)],[c242]) ).
cnf(c819,plain,
lojo(X5,X2,meet(X4,meet(X4,X3))) = lojo(X5,X2,meet(X4,X3)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c820,plain,
lojo(X5,meet(X4,X3),meet(X2,X4)) = lojo(X5,X2,meet(X4,X3)),
inference(transitivity,[status(thm)],[c818,c819]) ).
cnf(c821,plain,
lojo(X5,X4,meet(meet(X4,X3),X2)) = lojo(X5,X2,meet(X4,X3)),
inference(transitivity,[status(thm)],[c817,c820]) ).
cnf(c822,plain,
lojo(X6,X5,meet(meet(X5,X4),upme(meet(X5,X4),X3,X2))) = lojo(X6,upme(meet(X5,X4),X3,X2),meet(X5,X4)),
inference(substitution,[status(thm)],[c821]) ).
cnf(c823,plain,
lojo(X6,meet(X5,X4),upme(meet(X5,X4),X3,X2)) = lojo(X6,upme(meet(X5,X4),X3,X2),meet(X5,X4)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c824,plain,
lojo(X6,upme(meet(X5,X4),X3,X2),meet(X5,X4)) = lojo(X6,meet(X5,X4),upme(meet(X5,X4),X3,X2)),
inference(symmetry,[status(thm)],[c823]) ).
cnf(c825,plain,
lojo(X5,X4,upme(X4,X3,X2)) = lojo(X5,upme(X4,X3,X2),X4),
inference(substitution,[status(thm)],[c61]) ).
cnf(c826,plain,
X4 = join(X4,upme(X4,X3,X2)),
inference(symmetry,[status(thm)],[c808]) ).
cnf(c827,plain,
lojo(X5,upme(X4,X3,X2),X4) = lojo(X5,upme(X4,X3,X2),join(X4,upme(X4,X3,X2))),
inference(congruence,[status(thm)],[c826]) ).
cnf(c828,plain,
lojo(X5,upme(X4,X3,X2),join(X4,upme(X4,X3,X2))) = join(X5,upme(X4,X3,X2)),
inference(substitution,[status(thm)],[c716]) ).
cnf(c829,plain,
lojo(X5,upme(X4,X3,X2),X4) = join(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c827,c828]) ).
cnf(c830,plain,
lojo(X5,X4,upme(X4,X3,X2)) = join(X5,upme(X4,X3,X2)),
inference(transitivity,[status(thm)],[c825,c829]) ).
cnf(c831,plain,
lojo(X6,meet(X5,X4),upme(meet(X5,X4),X3,X2)) = join(X6,upme(meet(X5,X4),X3,X2)),
inference(substitution,[status(thm)],[c830]) ).
cnf(c832,plain,
lojo(X6,upme(meet(X5,X4),X3,X2),meet(X5,X4)) = join(X6,upme(meet(X5,X4),X3,X2)),
inference(transitivity,[status(thm)],[c824,c831]) ).
cnf(c833,plain,
lojo(X6,X5,meet(meet(X5,X4),upme(meet(X5,X4),X3,X2))) = join(X6,upme(meet(X5,X4),X3,X2)),
inference(transitivity,[status(thm)],[c822,c832]) ).
cnf(c834,plain,
lojo(X6,X5,upme(meet(X5,X4),X3,X2)) = join(X6,upme(meet(X5,X4),X3,X2)),
inference(transitivity,[status(thm)],[c816,c833]) ).
cnf(c835,plain,
lojo(X4,a,upme(meet(a,X3),X4,X2)) = join(X4,upme(meet(a,X3),X4,X2)),
inference(substitution,[status(thm)],[c834]) ).
cnf(c836,plain,
lojo(X4,a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2)) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c802,c835]) ).
cnf(c837,plain,
join(X4,meet(a,lojo(upme(meet(a,X3),X4,X2),upme(meet(a,X3),X4,X2),X2))) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c800,c836]) ).
cnf(c838,plain,
join(X4,upme(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2))) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c798,c837]) ).
cnf(c839,plain,
join(X4,lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(meet(a,X3),X4,X2))) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c796,c838]) ).
cnf(c840,plain,
join(X4,lome(a,meet(upme(meet(a,X3),X4,X2),X2),upme(upme(meet(a,X3),X4,X2),X4,X2))) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c794,c839]) ).
cnf(c841,plain,
lojo(X4,upme(meet(a,X3),X4,X2),meet(X2,a)) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c781,c840]) ).
cnf(c842,plain,
lojo(X4,X2,meet(a,upme(meet(a,X3),X4,X2))) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c779,c841]) ).
cnf(c843,plain,
lojo(X4,a,meet(upme(meet(a,X3),X4,X2),X2)) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c777,c842]) ).
cnf(c844,plain,
lojo(X4,a,meet(X2,upme(meet(a,X3),X4,X2))) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c775,c843]) ).
cnf(c845,plain,
lojo(X4,a,meet(X2,meet(a,X3))) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c772,c844]) ).
cnf(c846,plain,
lojo(X4,X2,meet(a,X3)) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c769,c845]) ).
cnf(c847,plain,
join(X4,lome(meet(a,X3),X4,X2)) = join(X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c757,c846]) ).
cnf(c848,plain,
meet(X5,join(X4,lome(meet(a,X3),X4,X2))) = meet(X5,join(X4,upme(meet(a,X3),X4,X2))),
inference(congruence,[status(thm)],[c847]) ).
cnf(c849,plain,
upme(X5,X4,upme(meet(a,X3),X4,X2)) = meet(X5,join(X4,upme(meet(a,X3),X4,X2))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c850,plain,
meet(X5,join(X4,upme(meet(a,X3),X4,X2))) = upme(X5,X4,upme(meet(a,X3),X4,X2)),
inference(symmetry,[status(thm)],[c849]) ).
cnf(c851,plain,
meet(X5,join(X4,lome(meet(a,X3),X4,X2))) = upme(X5,X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c848,c850]) ).
cnf(c852,plain,
upme(X5,X4,lome(meet(a,X3),X4,X2)) = upme(X5,X4,upme(meet(a,X3),X4,X2)),
inference(transitivity,[status(thm)],[c738,c851]) ).
cnf(c853,plain,
upme(meet(a,X4),X3,lome(meet(a,X4),X3,X2)) = upme(meet(a,X4),X3,upme(meet(a,X4),X3,X2)),
inference(substitution,[status(thm)],[c852]) ).
cnf(c854,plain,
upme(X4,X3,upme(X4,X3,X2)) = meet(X4,join(X3,upme(X4,X3,X2))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c855,plain,
upjo(X4,X3,upme(X2,X4,X3)) = upjo(X4,upme(X2,X4,X3),X3),
inference(substitution,[status(thm)],[c458]) ).
cnf(c856,plain,
upjo(X5,X4,join(X3,upme(X2,X5,X3))) = upjo(X5,join(X3,upme(X2,X5,X3)),X4),
inference(substitution,[status(thm)],[c458]) ).
cnf(c857,plain,
lojo(X3,X2,join(X4,X3)) = join(X3,upme(X2,X4,X3)),
inference(substitution,[status(thm)],[c84]) ).
cnf(c858,plain,
join(X3,upme(X2,X4,X3)) = lojo(X3,X2,join(X4,X3)),
inference(symmetry,[status(thm)],[c857]) ).
cnf(c859,plain,
upjo(X5,join(X3,upme(X2,X5,X3)),X4) = upjo(X5,lojo(X3,X2,join(X5,X3)),X4),
inference(congruence,[status(thm)],[c858]) ).
cnf(c860,plain,
upme(join(X5,lojo(X3,X2,join(X5,X3))),X5,X4) = upjo(X5,lojo(X3,X2,join(X5,X3)),X4),
inference(substitution,[status(thm)],[c412]) ).
cnf(c861,plain,
upjo(X5,lojo(X3,X2,join(X5,X3)),X4) = upme(join(X5,lojo(X3,X2,join(X5,X3))),X5,X4),
inference(symmetry,[status(thm)],[c860]) ).
cnf(c862,plain,
lojo(X3,X2,join(X4,X3)) = lojo(X3,join(X4,X3),X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c863,plain,
join(X4,lojo(X3,X2,join(X4,X3))) = join(X4,lojo(X3,join(X4,X3),X2)),
inference(congruence,[status(thm)],[c862]) ).
cnf(c864,plain,
lojo(X3,join(X4,X3),X2) = join(X3,meet(join(X4,X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c865,plain,
join(X4,lojo(X3,join(X4,X3),X2)) = join(X4,join(X3,meet(join(X4,X3),X2))),
inference(congruence,[status(thm)],[c864]) ).
cnf(c866,plain,
join(X4,join(X3,meet(join(X4,X3),X2))) = join(join(X4,X3),meet(join(X4,X3),X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c867,plain,
join(join(X4,X3),meet(join(X4,X3),X2)) = join(X4,X3),
inference(substitution,[status(thm)],[c24]) ).
cnf(c868,plain,
join(X4,join(X3,meet(join(X4,X3),X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c866,c867]) ).
cnf(c869,plain,
join(X4,lojo(X3,join(X4,X3),X2)) = join(X4,X3),
inference(transitivity,[status(thm)],[c865,c868]) ).
cnf(c870,plain,
join(X4,lojo(X3,X2,join(X4,X3))) = join(X4,X3),
inference(transitivity,[status(thm)],[c863,c869]) ).
cnf(c871,plain,
upme(join(X5,lojo(X3,X2,join(X5,X3))),X5,X4) = upme(join(X5,X3),X5,X4),
inference(congruence,[status(thm)],[c870]) ).
cnf(c872,plain,
upme(join(X4,X2),X4,X3) = upjo(X4,X2,X3),
inference(substitution,[status(thm)],[c412]) ).
cnf(c873,plain,
upme(join(X5,lojo(X3,X2,join(X5,X3))),X5,X4) = upjo(X5,X3,X4),
inference(transitivity,[status(thm)],[c871,c872]) ).
cnf(c874,plain,
upjo(X5,lojo(X3,X2,join(X5,X3)),X4) = upjo(X5,X3,X4),
inference(transitivity,[status(thm)],[c861,c873]) ).
cnf(c875,plain,
upjo(X5,join(X3,upme(X2,X5,X3)),X4) = upjo(X5,X3,X4),
inference(transitivity,[status(thm)],[c859,c874]) ).
cnf(c876,plain,
upjo(X5,X4,join(X3,upme(X2,X5,X3))) = upjo(X5,X3,X4),
inference(transitivity,[status(thm)],[c856,c875]) ).
cnf(c877,plain,
upjo(X4,X3,X2) = upjo(X4,X2,X3),
inference(substitution,[status(thm)],[c458]) ).
cnf(c878,plain,
upjo(X4,X2,X3) = upjo(X4,X3,X2),
inference(symmetry,[status(thm)],[c877]) ).
cnf(c879,plain,
upjo(X5,X4,join(X3,upme(X2,X5,X3))) = upjo(X5,X4,X3),
inference(transitivity,[status(thm)],[c876,c878]) ).
cnf(c880,plain,
upjo(X4,upme(X2,X4,X3),join(X3,upme(X2,X4,X3))) = upjo(X4,upme(X2,X4,X3),X3),
inference(substitution,[status(thm)],[c879]) ).
cnf(c881,plain,
upjo(X4,upme(X2,X4,X3),X3) = upjo(X4,upme(X2,X4,X3),join(X3,upme(X2,X4,X3))),
inference(symmetry,[status(thm)],[c880]) ).
cnf(c882,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c883,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c882]) ).
cnf(c884,plain,
upjo(X4,X3,join(X2,X3)) = upjo(X4,X3,join(X3,X2)),
inference(congruence,[status(thm)],[c883]) ).
cnf(c885,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c886,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c885]) ).
cnf(c887,plain,
upjo(X4,X3,join(X3,X2)) = upjo(X4,X3,join(X2,X3)),
inference(congruence,[status(thm)],[c886]) ).
cnf(c888,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c889,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c888]) ).
cnf(c890,plain,
upme(join(X4,X3),X3,X2) = upme(join(X3,X4),X3,X2),
inference(congruence,[status(thm)],[c889]) ).
cnf(c891,plain,
upme(join(X3,X4),X3,X2) = upjo(X3,X4,X2),
inference(substitution,[status(thm)],[c412]) ).
cnf(c892,plain,
upme(join(X4,X3),X3,X2) = upjo(X3,X4,X2),
inference(transitivity,[status(thm)],[c890,c891]) ).
cnf(c893,plain,
upme(join(X3,X4),X4,join(X2,X3)) = upjo(X4,X3,join(X2,X3)),
inference(substitution,[status(thm)],[c892]) ).
cnf(c894,plain,
upjo(X4,X3,join(X2,X3)) = upme(join(X3,X4),X4,join(X2,X3)),
inference(symmetry,[status(thm)],[c893]) ).
cnf(c895,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c896,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c895]) ).
cnf(c897,plain,
upme(X5,X2,join(X4,X3)) = upme(X5,X2,join(X3,X4)),
inference(congruence,[status(thm)],[c896]) ).
cnf(c898,plain,
upme(X5,X2,join(X3,X4)) = meet(X5,join(X2,join(X3,X4))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c899,plain,
join(X2,join(X3,X4)) = join(join(X2,X3),X4),
inference(substitution,[status(thm)],[c22]) ).
cnf(c900,plain,
meet(X5,join(X2,join(X3,X4))) = meet(X5,join(join(X2,X3),X4)),
inference(congruence,[status(thm)],[c899]) ).
cnf(c901,plain,
upme(X5,join(X2,X3),X4) = meet(X5,join(join(X2,X3),X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c902,plain,
meet(X5,join(join(X2,X3),X4)) = upme(X5,join(X2,X3),X4),
inference(symmetry,[status(thm)],[c901]) ).
cnf(c903,plain,
upme(X5,X4,join(X2,X3)) = upme(X5,join(X2,X3),X4),
inference(substitution,[status(thm)],[c78]) ).
cnf(c904,plain,
upme(X5,join(X2,X3),X4) = upme(X5,X4,join(X2,X3)),
inference(symmetry,[status(thm)],[c903]) ).
cnf(c905,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c906,plain,
upme(X5,X4,join(X2,X3)) = upme(X5,X4,join(X3,X2)),
inference(congruence,[status(thm)],[c905]) ).
cnf(c907,plain,
upme(X5,join(X2,X3),X4) = upme(X5,X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c904,c906]) ).
cnf(c908,plain,
meet(X5,join(join(X2,X3),X4)) = upme(X5,X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c902,c907]) ).
cnf(c909,plain,
meet(X5,join(X2,join(X3,X4))) = upme(X5,X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c900,c908]) ).
cnf(c910,plain,
upme(X5,X2,join(X3,X4)) = upme(X5,X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c898,c909]) ).
cnf(c911,plain,
upme(X5,X2,join(X4,X3)) = upme(X5,X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c897,c910]) ).
cnf(c912,plain,
upme(join(X3,X4),X4,join(X2,X3)) = upme(join(X3,X4),X2,join(X3,X4)),
inference(substitution,[status(thm)],[c911]) ).
cnf(c913,plain,
upme(X3,X2,X3) = meet(X3,join(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c914,plain,
upme(X3,X2,X3) = X3,
inference(transitivity,[status(thm)],[c913,c51]) ).
cnf(c915,plain,
upme(join(X3,X4),X2,join(X3,X4)) = join(X3,X4),
inference(substitution,[status(thm)],[c914]) ).
cnf(c916,plain,
upme(join(X3,X4),X4,join(X2,X3)) = join(X3,X4),
inference(transitivity,[status(thm)],[c912,c915]) ).
cnf(c917,plain,
upjo(X4,X3,join(X2,X3)) = join(X3,X4),
inference(transitivity,[status(thm)],[c894,c916]) ).
cnf(c918,plain,
upjo(X4,X3,join(X3,X2)) = join(X3,X4),
inference(transitivity,[status(thm)],[c887,c917]) ).
cnf(c919,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c920,plain,
upjo(X4,X3,join(X3,X2)) = join(X4,X3),
inference(transitivity,[status(thm)],[c918,c919]) ).
cnf(c921,plain,
upjo(X4,X3,join(X2,X3)) = join(X4,X3),
inference(transitivity,[status(thm)],[c884,c920]) ).
cnf(c922,plain,
upjo(X4,upme(X2,X4,X3),join(X3,upme(X2,X4,X3))) = join(X4,upme(X2,X4,X3)),
inference(substitution,[status(thm)],[c921]) ).
cnf(c923,plain,
upjo(X4,upme(X2,X4,X3),X3) = join(X4,upme(X2,X4,X3)),
inference(transitivity,[status(thm)],[c881,c922]) ).
cnf(c924,plain,
upjo(X4,X3,upme(X2,X4,X3)) = join(X4,upme(X2,X4,X3)),
inference(transitivity,[status(thm)],[c855,c923]) ).
cnf(c925,plain,
upjo(X3,X2,upme(X4,X3,X2)) = join(X3,upme(X4,X3,X2)),
inference(substitution,[status(thm)],[c924]) ).
cnf(c926,plain,
join(X3,upme(X4,X3,X2)) = upjo(X3,X2,upme(X4,X3,X2)),
inference(symmetry,[status(thm)],[c925]) ).
cnf(c927,plain,
meet(X4,join(X3,upme(X4,X3,X2))) = meet(X4,upjo(X3,X2,upme(X4,X3,X2))),
inference(congruence,[status(thm)],[c926]) ).
cnf(c928,plain,
upme(X4,X3,X2) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c929,plain,
upjo(X3,X2,upme(X4,X3,X2)) = upjo(X3,X2,meet(X4,join(X3,X2))),
inference(congruence,[status(thm)],[c928]) ).
cnf(c930,plain,
meet(X4,upjo(X3,X2,upme(X4,X3,X2))) = meet(X4,upjo(X3,X2,meet(X4,join(X3,X2)))),
inference(congruence,[status(thm)],[c929]) ).
cnf(c931,plain,
upme(join(X3,X2),X3,meet(X4,join(X3,X2))) = upjo(X3,X2,meet(X4,join(X3,X2))),
inference(substitution,[status(thm)],[c412]) ).
cnf(c932,plain,
upjo(X3,X2,meet(X4,join(X3,X2))) = upme(join(X3,X2),X3,meet(X4,join(X3,X2))),
inference(symmetry,[status(thm)],[c931]) ).
cnf(c933,plain,
meet(X4,upjo(X3,X2,meet(X4,join(X3,X2)))) = meet(X4,upme(join(X3,X2),X3,meet(X4,join(X3,X2)))),
inference(congruence,[status(thm)],[c932]) ).
cnf(c934,plain,
upme(X3,X2,meet(X4,X3)) = upme(X3,meet(X4,X3),X2),
inference(substitution,[status(thm)],[c78]) ).
cnf(c935,plain,
meet(X4,upme(X3,X2,meet(X4,X3))) = meet(X4,upme(X3,meet(X4,X3),X2)),
inference(congruence,[status(thm)],[c934]) ).
cnf(c936,plain,
upme(X3,meet(X4,X3),X2) = meet(X3,join(meet(X4,X3),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c937,plain,
meet(X4,upme(X3,meet(X4,X3),X2)) = meet(X4,meet(X3,join(meet(X4,X3),X2))),
inference(congruence,[status(thm)],[c936]) ).
cnf(c938,plain,
meet(X4,meet(X3,join(meet(X4,X3),X2))) = meet(meet(X4,X3),join(meet(X4,X3),X2)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c939,plain,
meet(meet(X4,X3),join(meet(X4,X3),X2)) = meet(X4,X3),
inference(substitution,[status(thm)],[c49]) ).
cnf(c940,plain,
meet(X4,meet(X3,join(meet(X4,X3),X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c938,c939]) ).
cnf(c941,plain,
meet(X4,upme(X3,meet(X4,X3),X2)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c937,c940]) ).
cnf(c942,plain,
meet(X4,upme(X3,X2,meet(X4,X3))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c935,c941]) ).
cnf(c943,plain,
meet(X4,upme(join(X3,X2),X3,meet(X4,join(X3,X2)))) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c942]) ).
cnf(c944,plain,
upme(X4,X3,X2) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c945,plain,
meet(X4,join(X3,X2)) = upme(X4,X3,X2),
inference(symmetry,[status(thm)],[c944]) ).
cnf(c946,plain,
meet(X4,upme(join(X3,X2),X3,meet(X4,join(X3,X2)))) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c943,c945]) ).
cnf(c947,plain,
meet(X4,upjo(X3,X2,meet(X4,join(X3,X2)))) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c933,c946]) ).
cnf(c948,plain,
meet(X4,upjo(X3,X2,upme(X4,X3,X2))) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c930,c947]) ).
cnf(c949,plain,
meet(X4,join(X3,upme(X4,X3,X2))) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c927,c948]) ).
cnf(c950,plain,
upme(X4,X3,upme(X4,X3,X2)) = upme(X4,X3,X2),
inference(transitivity,[status(thm)],[c854,c949]) ).
cnf(c951,plain,
upme(meet(a,X4),X3,upme(meet(a,X4),X3,X2)) = upme(meet(a,X4),X3,X2),
inference(substitution,[status(thm)],[c950]) ).
cnf(c952,plain,
upme(meet(a,X4),X3,lome(meet(a,X4),X3,X2)) = upme(meet(a,X4),X3,X2),
inference(transitivity,[status(thm)],[c853,c951]) ).
cnf(c953,plain,
lome(meet(a,X4),X3,lome(meet(a,X4),X3,X2)) = upme(meet(a,X4),X3,X2),
inference(transitivity,[status(thm)],[c737,c952]) ).
cnf(c954,plain,
lome(meet(a,X4),X3,X2) = upme(meet(a,X4),X3,X2),
inference(transitivity,[status(thm)],[c170,c953]) ).
cnf(c955,plain,
lome(meet(a,z1),z2,z3) = upme(meet(a,z1),z2,z3),
inference(substitution,[status(thm)],[c954]) ).
cnf(c956,plain,
upme(meet(a,z1),z2,z3) = lome(meet(a,z1),z2,z3),
inference(symmetry,[status(thm)],[c955]) ).
cnf(c957,plain,
$false,
inference(resolution,[status(thm)],[c1,c956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT399-2 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n001.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 15:21:31 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.47/4.97 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 35.47/4.97
% 35.47/4.97 % SZS status Unsatisfiable
% 35.47/4.97
% 36.57/5.07 % SZS output start CNFRefutation
% See solution above
% 40.22/5.58
% 40.22/5.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------