%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL040+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:33:28 PM UTC 2026
% Result : Theorem 139.34s 17.91s
% Output : CNFRefutation 142.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 182
% Number of leaves : 15
% Syntax : Number of formulae : 1335 (1329 unt; 0 def)
% Number of atoms : 1341 (1340 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 2018 ( 117 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0,X1,X2] :
( join(composition(converse(X0),X0),one) = one
=> composition(X0,meet(X1,X2)) = meet(composition(X0,X1),composition(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( join(composition(converse(X0_2),X0_2),one) = one
=> composition(X0_2,meet(X1_2,X2_2)) = meet(composition(X0_2,X1_2),composition(X0_2,X2_2)) ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( composition(x0,meet(x1,x2)) != meet(composition(x0,x1),composition(x0,x2))
& join(composition(converse(x0),x0),one) = one ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
composition(x0,meet(x1,x2)) != meet(composition(x0,x1),composition(x0,x2)),
inference(clausify,[status(thm)],[c3]) ).
cnf(c5,axiom,
meet(X0_2,X1_2) = complement(join(complement(X0_2),complement(X1_2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
cnf(c6,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c8,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c12,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
meet(X,X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c6,c13]) ).
cnf(c15,plain,
meet(composition(x0,X3),composition(x0,X)) = meet(composition(x0,X),composition(x0,X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
join(join(X3,X4),X) = join(X,join(X3,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c17,plain,
join(X3,join(X4,X)) = join(join(X4,X),X3),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,axiom,
join(X0_2,join(X1_2,X2_2)) = join(join(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c19,plain,
join(X4,join(X,X3)) = join(join(X4,X),X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
join(join(X4,X),X3) = join(X4,join(X,X3)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c22,plain,
join(X4,join(X,X3)) = join(X4,join(X3,X)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
join(join(X4,X),X3) = join(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
join(X3,join(X4,X)) = join(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c17,c23]) ).
cnf(c25,plain,
join(X3,join(complement(X4),X)) = join(complement(X4),join(X3,X)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
meet(X4,join(X3,join(complement(X4),X))) = meet(X4,join(complement(X4),join(X3,X))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c28,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
meet(X3,join(complement(X3),X)) = meet(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(complement(X3),X) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c31,plain,
complement(meet(complement(X3),X)) = complement(meet(X,complement(X3))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
meet(X3,complement(X)) = meet(complement(X),X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c33,plain,
complement(meet(X3,complement(X))) = complement(meet(complement(X),X3)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c35,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c36,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c39,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c41,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c37,c43]) ).
cnf(c45,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c49,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c51,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c47,c52]) ).
cnf(c54,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c57,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
composition(converse(join(composition(converse(x0),x0),one)),X) = composition(converse(join(composition(converse(x0),x0),one)),converse(converse(X))),
inference(congruence,[status(thm)],[c58]) ).
fof(c60,conjecture,
! [X0_2,X1_2,X2_2] :
( join(composition(converse(X0_2),X0_2),one) = one
=> composition(X0_2,meet(X1_2,X2_2)) = meet(composition(X0_2,X1_2),composition(X0_2,X2_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c61,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( join(composition(converse(X0_2),X0_2),one) = one
=> composition(X0_2,meet(X1_2,X2_2)) = meet(composition(X0_2,X1_2),composition(X0_2,X2_2)) ),
inference(negate_conjecture,[status(cth)],[c60]) ).
fof(c62,plain,
( composition(x0,meet(x1,x2)) != meet(composition(x0,x1),composition(x0,x2))
& join(composition(converse(x0),x0),one) = one ),
inference(clausify,[status(esa)],[c61]) ).
cnf(c63,plain,
join(composition(converse(x0),x0),one) = one,
inference(clausify,[status(thm)],[c62]) ).
cnf(c64,plain,
converse(join(composition(converse(x0),x0),one)) = converse(one),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
composition(converse(join(composition(converse(x0),x0),one)),converse(X)) = composition(converse(one),converse(X)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c67,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c70,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c68,c71]) ).
cnf(c73,plain,
composition(converse(join(composition(converse(x0),x0),one)),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c65,c72]) ).
cnf(c74,plain,
composition(converse(join(composition(converse(x0),x0),one)),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c76,plain,
composition(converse(join(composition(converse(x0),x0),one)),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
composition(converse(join(composition(converse(x0),x0),one)),X) = X,
inference(transitivity,[status(thm)],[c59,c76]) ).
cnf(c78,plain,
composition(converse(join(composition(converse(x0),x0),one)),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
complement(X) = composition(converse(join(composition(converse(x0),x0),one)),complement(X)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(join(composition(converse(x0),x0),one)),complement(X))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
composition(converse(join(composition(converse(x0),x0),one)),one) = converse(join(composition(converse(x0),x0),one)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c82,plain,
converse(join(composition(converse(x0),x0),one)) = composition(converse(join(composition(converse(x0),x0),one)),one),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
composition(converse(join(composition(converse(x0),x0),one)),one) = one,
inference(substitution,[status(thm)],[c77]) ).
cnf(c84,plain,
one = join(composition(converse(x0),x0),one),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c85,plain,
composition(converse(join(composition(converse(x0),x0),one)),one) = join(composition(converse(x0),x0),one),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
converse(join(composition(converse(x0),x0),one)) = join(composition(converse(x0),x0),one),
inference(transitivity,[status(thm)],[c82,c85]) ).
cnf(c87,plain,
join(composition(converse(x0),x0),one) = converse(join(composition(converse(x0),x0),one)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
composition(join(composition(converse(x0),x0),one),X) = composition(converse(join(composition(converse(x0),x0),one)),X),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
composition(join(composition(converse(x0),x0),one),X) = X,
inference(transitivity,[status(thm)],[c88,c77]) ).
cnf(c90,plain,
X = composition(join(composition(converse(x0),x0),one),X),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
complement(X) = complement(composition(join(composition(converse(x0),x0),one),X)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
composition(converse(join(composition(converse(x0),x0),one)),complement(X)) = composition(converse(join(composition(converse(x0),x0),one)),complement(composition(join(composition(converse(x0),x0),one),X))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
join(complement(X),composition(converse(join(composition(converse(x0),x0),one)),complement(X))) = join(complement(X),composition(converse(join(composition(converse(x0),x0),one)),complement(composition(join(composition(converse(x0),x0),one),X)))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = join(complement(X3),composition(converse(X),complement(composition(X,X3)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c95,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = join(composition(converse(X),complement(composition(X,X3))),complement(X3)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,axiom,
join(composition(converse(X0_2),complement(composition(X0_2,X1_2))),complement(X1_2)) = complement(X1_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
cnf(c97,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c95,c97]) ).
cnf(c99,plain,
join(complement(X),composition(converse(join(composition(converse(x0),x0),one)),complement(composition(join(composition(converse(x0),x0),one),X)))) = complement(X),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
join(complement(X),composition(converse(join(composition(converse(x0),x0),one)),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c93,c99]) ).
cnf(c101,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c80,c100]) ).
cnf(c102,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c105,plain,
complement(join(complement(X),complement(X))) = meet(X,X),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
complement(complement(X)) = meet(X,X),
inference(transitivity,[status(thm)],[c103,c105]) ).
cnf(c107,plain,
join(zero,complement(complement(X))) = join(zero,meet(X,X)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
complement(join(zero,complement(complement(X)))) = complement(join(zero,meet(X,X))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c110,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c112,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c114,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,axiom,
X0_2 = join(complement(join(complement(X0_2),complement(X1_2))),complement(join(complement(X0_2),X1_2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
cnf(c116,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c114,c117]) ).
cnf(c119,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c112,c119]) ).
cnf(c121,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c110,c120]) ).
cnf(c122,plain,
complement(join(zero,meet(X,X))) = complement(X),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(transitivity,[status(thm)],[c108,c122]) ).
cnf(c124,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c55,c123]) ).
cnf(c125,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c34,c124]) ).
cnf(c126,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c129,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c131,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c133,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c135,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c138,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c141,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c139,c142]) ).
cnf(c144,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c136,c144]) ).
cnf(c146,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
converse(top) = join(complement(X),converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(complement(converse(complement(X)))))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c150,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c153,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c156,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c157,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c7]) ).
cnf(c160,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c158,c159]) ).
cnf(c161,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c155,c160]) ).
cnf(c162,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c154,c161]) ).
cnf(c163,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c164,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c162]) ).
cnf(c166,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c168,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c169,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c167,c169]) ).
cnf(c171,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c166,c170]) ).
cnf(c172,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c164,c171]) ).
cnf(c173,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c162]) ).
cnf(c176,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c162]) ).
cnf(c177,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c172]) ).
cnf(c179,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c175,c179]) ).
cnf(c181,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c174,c180]) ).
cnf(c182,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
join(X4,join(X3,complement(X4))) = join(X,top),
inference(transitivity,[status(thm)],[c162,c182]) ).
cnf(c184,plain,
join(X4,join(complement(X4),X3)) = join(X,top),
inference(transitivity,[status(thm)],[c151,c183]) ).
cnf(c185,plain,
join(X3,join(complement(X3),converse(complement(converse(complement(X3)))))) = join(X,top),
inference(substitution,[status(thm)],[c184]) ).
cnf(c186,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = join(X4,top),
inference(substitution,[status(thm)],[c184]) ).
cnf(c187,plain,
join(X4,top) = join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = join(X3,complement(X3)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c189,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c190,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = top,
inference(transitivity,[status(thm)],[c188,c190]) ).
cnf(c192,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c187,c191]) ).
cnf(c193,plain,
join(X,join(complement(X),converse(complement(converse(complement(X)))))) = top,
inference(transitivity,[status(thm)],[c185,c192]) ).
cnf(c194,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c148,c193]) ).
cnf(c195,plain,
top = join(X,converse(top)),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
converse(top) = converse(join(X,converse(top))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
converse(join(X,converse(top))) = join(converse(X),converse(converse(top))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c198,plain,
converse(converse(top)) = top,
inference(substitution,[status(thm)],[c56]) ).
cnf(c199,plain,
join(converse(X),converse(converse(top))) = join(converse(X),top),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
join(converse(X),top) = top,
inference(substitution,[status(thm)],[c192]) ).
cnf(c201,plain,
join(converse(X),converse(converse(top))) = top,
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
converse(join(X,converse(top))) = top,
inference(transitivity,[status(thm)],[c197,c201]) ).
cnf(c203,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c196,c202]) ).
cnf(c204,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
meet(X,top) = meet(X,converse(top)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
join(meet(X,top),complement(top)) = join(meet(X,converse(top)),complement(top)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
join(complement(X),converse(top)) = top,
inference(substitution,[status(thm)],[c194]) ).
cnf(c208,plain,
top = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
complement(top) = complement(join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
join(meet(X,converse(top)),complement(top)) = join(meet(X,converse(top)),complement(join(complement(X),converse(top)))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
join(meet(X,converse(top)),complement(join(complement(X),converse(top)))) = X,
inference(substitution,[status(thm)],[c118]) ).
cnf(c212,plain,
join(meet(X,converse(top)),complement(top)) = X,
inference(transitivity,[status(thm)],[c210,c211]) ).
cnf(c213,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c206,c212]) ).
cnf(c214,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c133,c213]) ).
cnf(c215,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c131,c214]) ).
cnf(c216,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c129,c215]) ).
cnf(c217,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c216]) ).
cnf(c218,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c127,c217]) ).
cnf(c219,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
meet(complement(X),X3) = meet(join(zero,complement(X)),X3),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
complement(meet(complement(X),X3)) = complement(meet(join(zero,complement(X)),X3)),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c223,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c225,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c226,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c218]) ).
cnf(c227,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c229,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c228,c215]) ).
cnf(c230,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c227,c229]) ).
cnf(c231,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c225,c230]) ).
cnf(c232,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c224,c231]) ).
cnf(c233,plain,
meet(top,join(complement(X),complement(X3))) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
join(complement(X),complement(X3)) = meet(top,join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c236,plain,
join(complement(X4),meet(X3,X)) = join(complement(X4),meet(X,X3)),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
complement(join(complement(X4),meet(X3,X))) = complement(join(complement(X4),meet(X,X3))),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
join(meet(X,X3),complement(X4)) = join(complement(X4),meet(X,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c239,plain,
join(complement(X4),meet(X,X3)) = join(meet(X,X3),complement(X4)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
complement(join(complement(X4),meet(X,X3))) = complement(join(meet(X,X3),complement(X4))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c242,plain,
join(meet(X,X3),complement(X4)) = join(complement(join(complement(X),complement(X3))),complement(X4)),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
complement(join(meet(X,X3),complement(X4))) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
meet(join(complement(X),complement(X3)),X4) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c245,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = meet(join(complement(X),complement(X3)),X4),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
meet(X4,join(complement(X),complement(X3))) = meet(join(complement(X),complement(X3)),X4),
inference(substitution,[status(thm)],[c14]) ).
cnf(c247,plain,
meet(join(complement(X),complement(X3)),X4) = meet(X4,join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c249,plain,
meet(X4,join(complement(X),complement(X3))) = meet(X4,join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
meet(join(complement(X),complement(X3)),X4) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c247,c249]) ).
cnf(c251,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c245,c250]) ).
cnf(c252,plain,
complement(join(meet(X,X3),complement(X4))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c243,c251]) ).
cnf(c253,plain,
complement(join(complement(X4),meet(X,X3))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c240,c252]) ).
cnf(c254,plain,
complement(join(complement(X4),meet(X3,X))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c237,c253]) ).
cnf(c255,plain,
complement(join(complement(top),meet(X,X3))) = meet(top,join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
meet(top,join(complement(X),complement(X3))) = complement(join(complement(top),meet(X,X3))),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
join(complement(top),meet(X,X3)) = join(zero,meet(X,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c258,plain,
complement(join(complement(top),meet(X,X3))) = complement(join(zero,meet(X,X3))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c260,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c262,plain,
join(X,zero) = join(X,complement(top)),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c192]) ).
cnf(c264,plain,
top = join(complement(X),top),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
complement(top) = complement(join(complement(X),top)),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
join(X,complement(top)) = join(X,complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c268,plain,
join(X,complement(join(complement(X),top))) = join(meet(X,top),complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
join(meet(X,top),complement(join(complement(X),top))) = X,
inference(substitution,[status(thm)],[c118]) ).
cnf(c270,plain,
join(X,complement(join(complement(X),top))) = X,
inference(transitivity,[status(thm)],[c268,c269]) ).
cnf(c271,plain,
join(X,complement(top)) = X,
inference(transitivity,[status(thm)],[c266,c270]) ).
cnf(c272,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c262,c271]) ).
cnf(c273,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c260,c272]) ).
cnf(c274,plain,
join(zero,meet(X,X3)) = meet(X,X3),
inference(substitution,[status(thm)],[c273]) ).
cnf(c275,plain,
complement(join(zero,meet(X,X3))) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c277,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
complement(meet(X,X3)) = complement(meet(X3,X)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
complement(join(zero,meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c275,c278]) ).
cnf(c280,plain,
complement(join(complement(top),meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c258,c279]) ).
cnf(c281,plain,
meet(top,join(complement(X),complement(X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c256,c280]) ).
cnf(c282,plain,
join(complement(X),complement(X3)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c234,c281]) ).
cnf(c283,plain,
join(complement(X3),complement(X)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c223,c282]) ).
cnf(c284,plain,
join(complement(join(zero,complement(X))),complement(X3)) = complement(meet(join(zero,complement(X)),X3)),
inference(substitution,[status(thm)],[c283]) ).
cnf(c285,plain,
complement(meet(join(zero,complement(X)),X3)) = join(complement(join(zero,complement(X))),complement(X3)),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
join(complement(join(zero,complement(X))),complement(X3)) = join(meet(X,top),complement(X3)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c287,plain,
join(meet(X,top),complement(X3)) = join(X,complement(X3)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c288,plain,
join(complement(join(zero,complement(X))),complement(X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c286,c287]) ).
cnf(c289,plain,
complement(meet(join(zero,complement(X)),X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c285,c288]) ).
cnf(c290,plain,
complement(meet(complement(X),X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c221,c289]) ).
cnf(c291,plain,
complement(meet(X3,complement(X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c33,c290]) ).
cnf(c292,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c291]) ).
cnf(c293,plain,
complement(meet(complement(X3),X)) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c31,c292]) ).
cnf(c294,plain,
complement(meet(complement(X),X3)) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c293]) ).
cnf(c295,plain,
join(X,complement(X3)) = complement(meet(complement(X),X3)),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
meet(X3,join(X,complement(X3))) = meet(X3,complement(meet(complement(X),X3))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
meet(complement(X),X3) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c298,plain,
join(meet(X3,X),meet(complement(X),X3)) = join(meet(X3,X),meet(X3,complement(X))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,X),meet(X3,complement(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c300,plain,
join(meet(X3,X),meet(X3,complement(X))) = join(meet(X3,complement(X)),meet(X3,X)),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c302,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c118]) ).
cnf(c304,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c302,c303]) ).
cnf(c305,plain,
join(meet(X3,X),meet(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c300,c304]) ).
cnf(c306,plain,
join(meet(X3,X),meet(complement(X),X3)) = X3,
inference(transitivity,[status(thm)],[c298,c305]) ).
cnf(c307,plain,
join(meet(meet(X3,complement(meet(complement(X),X3))),X),meet(complement(X),meet(X3,complement(meet(complement(X),X3))))) = meet(X3,complement(meet(complement(X),X3))),
inference(substitution,[status(thm)],[c306]) ).
cnf(c308,plain,
meet(X3,complement(meet(complement(X),X3))) = join(meet(meet(X3,complement(meet(complement(X),X3))),X),meet(complement(X),meet(X3,complement(meet(complement(X),X3))))),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
meet(X,complement(meet(X3,X))) = meet(complement(meet(X3,X)),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c310,plain,
meet(X3,meet(X,complement(meet(X3,X)))) = meet(X3,meet(complement(meet(X3,X)),X)),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c312,plain,
meet(X3,meet(X4,X)) = meet(X3,meet(X,X4)),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
meet(meet(X3,meet(X,X4)),top) = meet(X3,meet(X,X4)),
inference(substitution,[status(thm)],[c231]) ).
cnf(c314,plain,
meet(X3,meet(X,X4)) = meet(meet(X3,meet(X,X4)),top),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
complement(join(zero,complement(meet(X3,meet(X,X4))))) = meet(meet(X3,meet(X,X4)),top),
inference(substitution,[status(thm)],[c53]) ).
cnf(c316,plain,
meet(meet(X3,meet(X,X4)),top) = complement(join(zero,complement(meet(X3,meet(X,X4))))),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
meet(X3,meet(X,X4)) = meet(X3,meet(X4,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c318,plain,
complement(meet(X3,meet(X,X4))) = complement(meet(X3,meet(X4,X))),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c320,plain,
meet(X3,meet(X4,X)) = meet(X3,complement(join(complement(X4),complement(X)))),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
complement(meet(X3,meet(X4,X))) = complement(meet(X3,complement(join(complement(X4),complement(X))))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
complement(meet(X3,complement(join(complement(X4),complement(X))))) = join(join(complement(X4),complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c291]) ).
cnf(c323,plain,
join(complement(X4),join(complement(X),complement(X3))) = join(join(complement(X4),complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c324,plain,
join(join(complement(X4),complement(X)),complement(X3)) = join(complement(X4),join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
join(complement(X),complement(X3)) = complement(meet(X,X3)),
inference(substitution,[status(thm)],[c283]) ).
cnf(c326,plain,
join(complement(X4),join(complement(X),complement(X3))) = join(complement(X4),complement(meet(X,X3))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
join(complement(X4),complement(meet(X,X3))) = complement(meet(X4,meet(X,X3))),
inference(substitution,[status(thm)],[c283]) ).
cnf(c328,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c329,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
meet(X4,meet(X,X3)) = meet(X4,meet(X3,X)),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
complement(meet(X4,meet(X,X3))) = complement(meet(X4,meet(X3,X))),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
join(complement(X4),complement(meet(X,X3))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c327,c331]) ).
cnf(c333,plain,
join(complement(X4),join(complement(X),complement(X3))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c326,c332]) ).
cnf(c334,plain,
join(join(complement(X4),complement(X)),complement(X3)) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c324,c333]) ).
cnf(c335,plain,
complement(meet(X3,complement(join(complement(X4),complement(X))))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c322,c334]) ).
cnf(c336,plain,
complement(meet(X3,meet(X4,X))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c321,c335]) ).
cnf(c337,plain,
complement(meet(X3,meet(X,X4))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c318,c336]) ).
cnf(c338,plain,
join(zero,complement(meet(X3,meet(X,X4)))) = join(zero,complement(meet(X4,meet(X3,X)))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
complement(join(zero,complement(meet(X3,meet(X,X4))))) = complement(join(zero,complement(meet(X4,meet(X3,X))))),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
complement(join(zero,complement(meet(X4,meet(X3,X))))) = meet(meet(X4,meet(X3,X)),top),
inference(substitution,[status(thm)],[c53]) ).
cnf(c341,plain,
meet(meet(X4,meet(X3,X)),top) = meet(X4,meet(X3,X)),
inference(substitution,[status(thm)],[c231]) ).
cnf(c342,plain,
complement(join(zero,complement(meet(X4,meet(X3,X))))) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c340,c341]) ).
cnf(c343,plain,
complement(join(zero,complement(meet(X3,meet(X,X4))))) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c339,c342]) ).
cnf(c344,plain,
meet(meet(X3,meet(X,X4)),top) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c316,c343]) ).
cnf(c345,plain,
meet(X3,meet(X,X4)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c314,c344]) ).
cnf(c346,plain,
meet(X3,meet(X4,X)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c312,c345]) ).
cnf(c347,plain,
meet(X3,meet(complement(meet(X3,X)),X)) = meet(complement(meet(X3,X)),meet(X3,X)),
inference(substitution,[status(thm)],[c346]) ).
cnf(c348,plain,
complement(meet(X3,X)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c349,plain,
meet(complement(meet(X3,X)),meet(X3,X)) = meet(join(complement(X3),complement(X)),meet(X3,X)),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c351,plain,
meet(join(complement(X3),complement(X)),meet(X3,X)) = meet(join(complement(X3),complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
zero = meet(join(complement(X3),complement(X)),complement(join(complement(X3),complement(X)))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c353,plain,
meet(join(complement(X3),complement(X)),complement(join(complement(X3),complement(X)))) = zero,
inference(symmetry,[status(thm)],[c352]) ).
cnf(c354,plain,
meet(join(complement(X3),complement(X)),meet(X3,X)) = zero,
inference(transitivity,[status(thm)],[c351,c353]) ).
cnf(c355,plain,
meet(complement(meet(X3,X)),meet(X3,X)) = zero,
inference(transitivity,[status(thm)],[c349,c354]) ).
cnf(c356,plain,
meet(X3,meet(complement(meet(X3,X)),X)) = zero,
inference(transitivity,[status(thm)],[c347,c355]) ).
cnf(c357,plain,
meet(X3,meet(X,complement(meet(X3,X)))) = zero,
inference(transitivity,[status(thm)],[c310,c356]) ).
cnf(c358,plain,
meet(complement(X),meet(X3,complement(meet(complement(X),X3)))) = zero,
inference(substitution,[status(thm)],[c357]) ).
cnf(c359,plain,
join(meet(meet(X3,complement(meet(complement(X),X3))),X),meet(complement(X),meet(X3,complement(meet(complement(X),X3))))) = join(meet(meet(X3,complement(meet(complement(X),X3))),X),zero),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
join(meet(meet(X3,complement(meet(complement(X),X3))),X),zero) = meet(meet(X3,complement(meet(complement(X),X3))),X),
inference(substitution,[status(thm)],[c272]) ).
cnf(c361,plain,
meet(meet(X4,X3),X) = meet(X,meet(X4,X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c362,plain,
meet(X4,meet(X,X3)) = meet(X,meet(X4,X3)),
inference(substitution,[status(thm)],[c346]) ).
cnf(c363,plain,
meet(X,meet(X4,X3)) = meet(X4,meet(X,X3)),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
meet(meet(X4,X3),X) = meet(X4,meet(X,X3)),
inference(transitivity,[status(thm)],[c361,c363]) ).
cnf(c365,plain,
meet(meet(X3,complement(meet(complement(X),X3))),X) = meet(X3,meet(X,complement(meet(complement(X),X3)))),
inference(substitution,[status(thm)],[c364]) ).
cnf(c366,plain,
complement(meet(complement(X),X3)) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c293]) ).
cnf(c367,plain,
meet(X,complement(meet(complement(X),X3))) = meet(X,join(X,complement(X3))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
meet(X3,meet(X,complement(meet(complement(X),X3)))) = meet(X3,meet(X,join(X,complement(X3)))),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c291]) ).
cnf(c370,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c369]) ).
cnf(c371,plain,
meet(X3,join(X3,complement(X))) = meet(X3,complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
join(complement(X),complement(complement(X3))) = complement(meet(X,complement(X3))),
inference(substitution,[status(thm)],[c283]) ).
cnf(c373,plain,
complement(meet(X,complement(X3))) = join(complement(X),complement(complement(X3))),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
meet(X3,complement(meet(X,complement(X3)))) = meet(X3,join(complement(X),complement(complement(X3)))),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = meet(X3,join(complement(X),complement(complement(X3)))),
inference(substitution,[status(thm)],[c254]) ).
cnf(c376,plain,
meet(X3,join(complement(X),complement(complement(X3)))) = complement(join(complement(X3),meet(X,complement(X3)))),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = complement(join(complement(X3),meet(X,complement(X3)))),
inference(substitution,[status(thm)],[c218]) ).
cnf(c378,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = join(zero,complement(join(complement(X3),meet(X,complement(X3))))),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
meet(X,complement(X3)) = meet(complement(X3),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c380,plain,
meet(X3,meet(X,complement(X3))) = meet(X3,meet(complement(X3),X)),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
meet(X3,meet(complement(X3),X)) = complement(join(complement(X3),complement(meet(complement(X3),X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c382,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c383,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
join(X3,complement(meet(X3,X))) = join(X3,complement(meet(X,X3))),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
join(complement(X),complement(X3)) = complement(meet(X,X3)),
inference(substitution,[status(thm)],[c283]) ).
cnf(c386,plain,
complement(meet(X,X3)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c385]) ).
cnf(c387,plain,
join(X3,complement(meet(X,X3))) = join(X3,join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
join(X3,join(complement(X),complement(X3))) = join(complement(X),top),
inference(substitution,[status(thm)],[c162]) ).
cnf(c389,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c192]) ).
cnf(c390,plain,
join(X3,join(complement(X),complement(X3))) = top,
inference(transitivity,[status(thm)],[c388,c389]) ).
cnf(c391,plain,
join(X3,complement(meet(X,X3))) = top,
inference(transitivity,[status(thm)],[c387,c390]) ).
cnf(c392,plain,
join(X3,complement(meet(X3,X))) = top,
inference(transitivity,[status(thm)],[c384,c391]) ).
cnf(c393,plain,
join(complement(X3),complement(meet(complement(X3),X))) = top,
inference(substitution,[status(thm)],[c392]) ).
cnf(c394,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = complement(top),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = zero,
inference(transitivity,[status(thm)],[c394,c44]) ).
cnf(c396,plain,
meet(X3,meet(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c381,c395]) ).
cnf(c397,plain,
meet(X3,meet(X,complement(X3))) = zero,
inference(transitivity,[status(thm)],[c380,c396]) ).
cnf(c398,plain,
zero = meet(X3,meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = join(meet(X3,meet(X,complement(X3))),complement(join(complement(X3),meet(X,complement(X3))))),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
join(meet(X3,meet(X,complement(X3))),complement(join(complement(X3),meet(X,complement(X3))))) = X3,
inference(substitution,[status(thm)],[c118]) ).
cnf(c401,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = X3,
inference(transitivity,[status(thm)],[c399,c400]) ).
cnf(c402,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c378,c401]) ).
cnf(c403,plain,
meet(X3,join(complement(X),complement(complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c376,c402]) ).
cnf(c404,plain,
meet(X3,complement(meet(X,complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c374,c403]) ).
cnf(c405,plain,
meet(X3,join(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c371,c404]) ).
cnf(c406,plain,
meet(X,join(X,complement(X3))) = X,
inference(substitution,[status(thm)],[c405]) ).
cnf(c407,plain,
meet(X3,meet(X,join(X,complement(X3)))) = meet(X3,X),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
meet(X3,meet(X,complement(meet(complement(X),X3)))) = meet(X3,X),
inference(transitivity,[status(thm)],[c368,c407]) ).
cnf(c409,plain,
meet(meet(X3,complement(meet(complement(X),X3))),X) = meet(X3,X),
inference(transitivity,[status(thm)],[c365,c408]) ).
cnf(c410,plain,
join(meet(meet(X3,complement(meet(complement(X),X3))),X),zero) = meet(X3,X),
inference(transitivity,[status(thm)],[c360,c409]) ).
cnf(c411,plain,
join(meet(meet(X3,complement(meet(complement(X),X3))),X),meet(complement(X),meet(X3,complement(meet(complement(X),X3))))) = meet(X3,X),
inference(transitivity,[status(thm)],[c359,c410]) ).
cnf(c412,plain,
meet(X3,complement(meet(complement(X),X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c308,c411]) ).
cnf(c413,plain,
meet(X3,join(X,complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c296,c412]) ).
cnf(c414,plain,
meet(X3,join(complement(X3),X)) = meet(X3,X),
inference(transitivity,[status(thm)],[c29,c413]) ).
cnf(c415,plain,
meet(X4,join(complement(X4),join(X3,X))) = meet(X4,join(X3,X)),
inference(substitution,[status(thm)],[c414]) ).
cnf(c416,plain,
meet(X4,join(X3,join(complement(X4),X))) = meet(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c26,c415]) ).
cnf(c417,plain,
meet(composition(x0,X3),join(X,join(complement(composition(x0,X3)),composition(x0,complement(X3))))) = meet(composition(x0,X3),join(X,composition(x0,complement(X3)))),
inference(substitution,[status(thm)],[c416]) ).
cnf(c418,plain,
meet(composition(x0,X3),join(X,composition(x0,complement(X3)))) = meet(composition(x0,X3),join(X,join(complement(composition(x0,X3)),composition(x0,complement(X3))))),
inference(symmetry,[status(thm)],[c417]) ).
cnf(c419,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c420,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c419]) ).
cnf(c421,plain,
composition(composition(converse(x0),x0),X) = composition(composition(converse(x0),x0),converse(converse(X))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
complement(composition(composition(converse(x0),x0),X)) = complement(composition(composition(converse(x0),x0),converse(converse(X)))),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
composition(x0,complement(composition(composition(converse(x0),x0),X))) = composition(x0,complement(composition(composition(converse(x0),x0),converse(converse(X))))),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c425,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c426,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c424,c426]) ).
cnf(c428,plain,
converse(composition(converse(x0),x0)) = composition(converse(x0),x0),
inference(substitution,[status(thm)],[c427]) ).
cnf(c429,plain,
composition(converse(x0),x0) = converse(composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c428]) ).
cnf(c430,plain,
composition(composition(converse(x0),x0),converse(X)) = composition(converse(composition(converse(x0),x0)),converse(X)),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
complement(composition(composition(converse(x0),x0),converse(X))) = complement(composition(converse(composition(converse(x0),x0)),converse(X))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
composition(x0,complement(composition(composition(converse(x0),x0),converse(X)))) = composition(x0,complement(composition(converse(composition(converse(x0),x0)),converse(X)))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
converse(composition(X,composition(converse(x0),x0))) = composition(converse(composition(converse(x0),x0)),converse(X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c434,plain,
composition(converse(composition(converse(x0),x0)),converse(X)) = converse(composition(X,composition(converse(x0),x0))),
inference(symmetry,[status(thm)],[c433]) ).
cnf(c435,plain,
complement(composition(converse(composition(converse(x0),x0)),converse(X))) = complement(converse(composition(X,composition(converse(x0),x0)))),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
composition(x0,complement(composition(converse(composition(converse(x0),x0)),converse(X)))) = composition(x0,complement(converse(composition(X,composition(converse(x0),x0))))),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
meet(complement(X3),X) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c438,plain,
join(meet(X3,X),meet(complement(X3),X)) = join(meet(X3,X),meet(X,complement(X3))),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c440,plain,
join(meet(X3,X),meet(X,complement(X3))) = join(meet(X,X3),meet(X,complement(X3))),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
join(meet(X,X3),meet(X,complement(X3))) = X,
inference(substitution,[status(thm)],[c305]) ).
cnf(c442,plain,
join(meet(X3,X),meet(X,complement(X3))) = X,
inference(transitivity,[status(thm)],[c440,c441]) ).
cnf(c443,plain,
join(meet(X3,X),meet(complement(X3),X)) = X,
inference(transitivity,[status(thm)],[c438,c442]) ).
cnf(c444,plain,
join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))) = converse(complement(converse(X))),
inference(substitution,[status(thm)],[c443]) ).
cnf(c445,plain,
converse(complement(converse(X))) = join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))),
inference(symmetry,[status(thm)],[c444]) ).
cnf(c446,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c218]) ).
cnf(c447,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c446]) ).
cnf(c448,plain,
join(zero,complement(complement(X))) = join(zero,meet(X,X)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c449,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c448,c121]) ).
cnf(c450,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c447,c449]) ).
cnf(c451,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c450]) ).
cnf(c452,plain,
converse(X) = converse(complement(complement(X))),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
complement(converse(X)) = complement(converse(complement(complement(X)))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
converse(complement(converse(X))) = converse(complement(converse(complement(complement(X))))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
meet(X,converse(complement(converse(X)))) = meet(X,converse(complement(converse(complement(complement(X)))))),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))) = meet(X,converse(complement(converse(complement(complement(X)))))),
inference(substitution,[status(thm)],[c414]) ).
cnf(c457,plain,
meet(X,converse(complement(converse(complement(complement(X)))))) = meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))),
inference(symmetry,[status(thm)],[c456]) ).
cnf(c458,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c459,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c458]) ).
cnf(c460,plain,
join(X,converse(complement(converse(complement(X))))) = join(converse(converse(X)),converse(complement(converse(complement(X))))),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
converse(join(converse(X),complement(converse(complement(X))))) = join(converse(converse(X)),converse(complement(converse(complement(X))))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c462,plain,
join(converse(converse(X)),converse(complement(converse(complement(X))))) = converse(join(converse(X),complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
meet(complement(X3),complement(X)) = meet(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c464,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c465,plain,
meet(complement(X),complement(X3)) = meet(join(zero,complement(X)),complement(X3)),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
join(zero,join(X3,complement(X))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c467,plain,
join(X3,complement(X)) = join(zero,join(X3,complement(X))),
inference(symmetry,[status(thm)],[c466]) ).
cnf(c468,plain,
complement(join(X3,complement(X))) = complement(join(zero,join(X3,complement(X)))),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c291]) ).
cnf(c470,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c469]) ).
cnf(c471,plain,
join(zero,join(X3,complement(X))) = join(zero,complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
complement(join(zero,join(X3,complement(X)))) = complement(join(zero,complement(meet(X,complement(X3))))),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
complement(join(zero,complement(meet(X,complement(X3))))) = meet(meet(X,complement(X3)),top),
inference(substitution,[status(thm)],[c53]) ).
cnf(c474,plain,
meet(meet(X,complement(X3)),top) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c231]) ).
cnf(c475,plain,
complement(join(zero,complement(meet(X,complement(X3))))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c473,c474]) ).
cnf(c476,plain,
complement(join(zero,join(X3,complement(X)))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c472,c475]) ).
cnf(c477,plain,
complement(join(X3,complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c468,c476]) ).
cnf(c478,plain,
complement(join(X3,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c477]) ).
cnf(c479,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c478]) ).
cnf(c480,plain,
join(X3,complement(join(zero,complement(X)))) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c481,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
join(X3,meet(X,top)) = join(X3,X),
inference(congruence,[status(thm)],[c231]) ).
cnf(c483,plain,
complement(join(X3,meet(X,top))) = complement(join(X3,X)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c481,c483]) ).
cnf(c485,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c479,c484]) ).
cnf(c486,plain,
meet(complement(X),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c465,c485]) ).
cnf(c487,plain,
meet(complement(X3),complement(X)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c463,c486]) ).
cnf(c488,plain,
complement(join(X3,X)) = meet(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c487]) ).
cnf(c489,plain,
join(X3,complement(join(X3,X))) = join(X3,meet(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
X3 = meet(X3,join(X3,complement(X))),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c491,plain,
join(X3,meet(complement(X3),complement(X))) = join(meet(X3,join(X3,complement(X))),meet(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
join(X3,complement(X)) = complement(meet(complement(X3),X)),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c493,plain,
meet(X3,join(X3,complement(X))) = meet(X3,complement(meet(complement(X3),X))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
join(meet(X3,join(X3,complement(X))),meet(complement(X3),complement(X))) = join(meet(X3,complement(meet(complement(X3),X))),meet(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c496,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
meet(X3,complement(meet(X3,X))) = meet(X3,complement(meet(X,X3))),
inference(congruence,[status(thm)],[c496]) ).
cnf(c498,plain,
join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(X3,complement(meet(X,X3))),
inference(substitution,[status(thm)],[c442]) ).
cnf(c499,plain,
meet(X3,complement(meet(X,X3))) = join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))),
inference(symmetry,[status(thm)],[c498]) ).
cnf(c500,plain,
meet(X,meet(X3,complement(meet(X,X3)))) = zero,
inference(substitution,[status(thm)],[c357]) ).
cnf(c501,plain,
join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))) = join(zero,meet(meet(X3,complement(meet(X,X3))),complement(X))),
inference(congruence,[status(thm)],[c500]) ).
cnf(c502,plain,
join(zero,meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(meet(X3,complement(meet(X,X3))),complement(X)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c503,plain,
meet(meet(X3,complement(meet(X,X3))),complement(X)) = meet(X3,meet(complement(X),complement(meet(X,X3)))),
inference(substitution,[status(thm)],[c364]) ).
cnf(c504,plain,
meet(complement(X),complement(meet(X,X3))) = complement(join(X,meet(X,X3))),
inference(substitution,[status(thm)],[c487]) ).
cnf(c505,plain,
meet(X3,meet(complement(X),complement(meet(X,X3)))) = meet(X3,complement(join(X,meet(X,X3)))),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c507,plain,
join(X3,meet(X3,X)) = join(X3,complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c506]) ).
cnf(c508,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = join(X3,complement(join(complement(X3),complement(X)))),
inference(substitution,[status(thm)],[c293]) ).
cnf(c509,plain,
join(X3,complement(join(complement(X3),complement(X)))) = complement(meet(complement(X3),join(complement(X3),complement(X)))),
inference(symmetry,[status(thm)],[c508]) ).
cnf(c510,plain,
meet(complement(X3),join(complement(X3),complement(X))) = complement(X3),
inference(substitution,[status(thm)],[c405]) ).
cnf(c511,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = complement(complement(X3)),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = X3,
inference(transitivity,[status(thm)],[c511,c450]) ).
cnf(c513,plain,
join(X3,complement(join(complement(X3),complement(X)))) = X3,
inference(transitivity,[status(thm)],[c509,c512]) ).
cnf(c514,plain,
join(X3,meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c507,c513]) ).
cnf(c515,plain,
join(X,meet(X,X3)) = X,
inference(substitution,[status(thm)],[c514]) ).
cnf(c516,plain,
complement(join(X,meet(X,X3))) = complement(X),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
meet(X3,complement(join(X,meet(X,X3)))) = meet(X3,complement(X)),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
meet(X3,meet(complement(X),complement(meet(X,X3)))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c505,c517]) ).
cnf(c519,plain,
meet(meet(X3,complement(meet(X,X3))),complement(X)) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c503,c518]) ).
cnf(c520,plain,
join(zero,meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c502,c519]) ).
cnf(c521,plain,
join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c501,c520]) ).
cnf(c522,plain,
meet(X3,complement(meet(X,X3))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c499,c521]) ).
cnf(c523,plain,
meet(X3,complement(meet(X3,X))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c497,c522]) ).
cnf(c524,plain,
meet(complement(X3),complement(meet(complement(X3),X))) = meet(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c523]) ).
cnf(c525,plain,
meet(complement(X3),complement(X)) = meet(complement(X3),complement(meet(complement(X3),X))),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c526,plain,
join(meet(X3,complement(meet(complement(X3),X))),meet(complement(X3),complement(X))) = join(meet(X3,complement(meet(complement(X3),X))),meet(complement(X3),complement(meet(complement(X3),X)))),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
join(meet(X3,complement(meet(complement(X3),X))),meet(complement(X3),complement(meet(complement(X3),X)))) = complement(meet(complement(X3),X)),
inference(substitution,[status(thm)],[c443]) ).
cnf(c528,plain,
join(meet(X3,complement(meet(complement(X3),X))),meet(complement(X3),complement(meet(complement(X3),X)))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c527,c293]) ).
cnf(c529,plain,
join(meet(X3,complement(meet(complement(X3),X))),meet(complement(X3),complement(X))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c526,c528]) ).
cnf(c530,plain,
join(meet(X3,join(X3,complement(X))),meet(complement(X3),complement(X))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c494,c529]) ).
cnf(c531,plain,
join(X3,meet(complement(X3),complement(X))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c491,c530]) ).
cnf(c532,plain,
join(X3,complement(join(X3,X))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c489,c531]) ).
cnf(c533,plain,
join(converse(X),complement(join(converse(X),converse(complement(X))))) = join(converse(X),complement(converse(complement(X)))),
inference(substitution,[status(thm)],[c532]) ).
cnf(c534,plain,
join(converse(X),complement(converse(complement(X)))) = join(converse(X),complement(join(converse(X),converse(complement(X))))),
inference(symmetry,[status(thm)],[c533]) ).
cnf(c535,plain,
complement(join(converse(X),converse(complement(X)))) = complement(converse(top)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c536,plain,
join(converse(X),complement(join(converse(X),converse(complement(X))))) = join(converse(X),complement(converse(top))),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
complement(converse(top)) = complement(top),
inference(congruence,[status(thm)],[c203]) ).
cnf(c538,plain,
join(converse(X),complement(converse(top))) = join(converse(X),complement(top)),
inference(congruence,[status(thm)],[c537]) ).
cnf(c539,plain,
join(converse(X),complement(top)) = join(converse(X),zero),
inference(congruence,[status(thm)],[c44]) ).
cnf(c540,plain,
join(converse(X),zero) = converse(X),
inference(substitution,[status(thm)],[c272]) ).
cnf(c541,plain,
join(converse(X),complement(top)) = converse(X),
inference(transitivity,[status(thm)],[c539,c540]) ).
cnf(c542,plain,
join(converse(X),complement(converse(top))) = converse(X),
inference(transitivity,[status(thm)],[c538,c541]) ).
cnf(c543,plain,
join(converse(X),complement(join(converse(X),converse(complement(X))))) = converse(X),
inference(transitivity,[status(thm)],[c536,c542]) ).
cnf(c544,plain,
join(converse(X),complement(converse(complement(X)))) = converse(X),
inference(transitivity,[status(thm)],[c534,c543]) ).
cnf(c545,plain,
converse(join(converse(X),complement(converse(complement(X))))) = converse(converse(X)),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c547,plain,
converse(join(converse(X),complement(converse(complement(X))))) = X,
inference(transitivity,[status(thm)],[c545,c546]) ).
cnf(c548,plain,
join(converse(converse(X)),converse(complement(converse(complement(X))))) = X,
inference(transitivity,[status(thm)],[c462,c547]) ).
cnf(c549,plain,
join(X,converse(complement(converse(complement(X))))) = X,
inference(transitivity,[status(thm)],[c460,c548]) ).
cnf(c550,plain,
join(complement(X),converse(complement(converse(complement(complement(X)))))) = complement(X),
inference(substitution,[status(thm)],[c549]) ).
cnf(c551,plain,
meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))) = meet(X,complement(X)),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c553,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c552]) ).
cnf(c554,plain,
meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))) = zero,
inference(transitivity,[status(thm)],[c551,c553]) ).
cnf(c555,plain,
meet(X,converse(complement(converse(complement(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c457,c554]) ).
cnf(c556,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c455,c555]) ).
cnf(c557,plain,
join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))) = join(zero,meet(complement(X),converse(complement(converse(X))))),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
join(zero,meet(complement(X),converse(complement(converse(X))))) = meet(complement(X),converse(complement(converse(X)))),
inference(substitution,[status(thm)],[c273]) ).
cnf(c559,plain,
meet(complement(X),converse(complement(converse(X)))) = meet(converse(complement(converse(X))),complement(X)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c560,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c561,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
meet(complement(X3),join(X3,X)) = meet(complement(X3),join(X,X3)),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c564,plain,
join(X,X3) = join(X,meet(X3,top)),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
meet(complement(X3),join(X,X3)) = meet(complement(X3),join(X,meet(X3,top))),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c567,plain,
meet(complement(X3),join(X,meet(X3,top))) = meet(join(zero,complement(X3)),join(X,meet(X3,top))),
inference(congruence,[status(thm)],[c566]) ).
cnf(c568,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c569,plain,
join(X,meet(X3,top)) = join(X,complement(join(zero,complement(X3)))),
inference(congruence,[status(thm)],[c568]) ).
cnf(c570,plain,
meet(join(zero,complement(X3)),join(X,meet(X3,top))) = meet(join(zero,complement(X3)),join(X,complement(join(zero,complement(X3))))),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
meet(join(zero,complement(X3)),join(X,complement(join(zero,complement(X3))))) = meet(join(zero,complement(X3)),X),
inference(substitution,[status(thm)],[c413]) ).
cnf(c572,plain,
meet(join(zero,complement(X3)),X) = meet(complement(X3),X),
inference(congruence,[status(thm)],[c218]) ).
cnf(c573,plain,
meet(X,complement(X3)) = meet(complement(X3),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c574,plain,
meet(complement(X3),X) = meet(X,complement(X3)),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
meet(join(zero,complement(X3)),X) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c572,c574]) ).
cnf(c576,plain,
meet(join(zero,complement(X3)),join(X,complement(join(zero,complement(X3))))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c571,c575]) ).
cnf(c577,plain,
meet(join(zero,complement(X3)),join(X,meet(X3,top))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c570,c576]) ).
cnf(c578,plain,
meet(complement(X3),join(X,meet(X3,top))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c567,c577]) ).
cnf(c579,plain,
meet(complement(X3),join(X,X3)) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c565,c578]) ).
cnf(c580,plain,
meet(complement(X3),join(X3,X)) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c562,c579]) ).
cnf(c581,plain,
meet(complement(X),join(X,converse(complement(converse(X))))) = meet(converse(complement(converse(X))),complement(X)),
inference(substitution,[status(thm)],[c580]) ).
cnf(c582,plain,
meet(converse(complement(converse(X))),complement(X)) = meet(complement(X),join(X,converse(complement(converse(X))))),
inference(symmetry,[status(thm)],[c581]) ).
cnf(c583,plain,
meet(complement(X),join(X,converse(complement(converse(X))))) = meet(complement(X),converse(top)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c584,plain,
meet(complement(X),converse(top)) = meet(complement(X),top),
inference(congruence,[status(thm)],[c203]) ).
cnf(c585,plain,
meet(complement(X),top) = complement(X),
inference(substitution,[status(thm)],[c231]) ).
cnf(c586,plain,
meet(complement(X),converse(top)) = complement(X),
inference(transitivity,[status(thm)],[c584,c585]) ).
cnf(c587,plain,
meet(complement(X),join(X,converse(complement(converse(X))))) = complement(X),
inference(transitivity,[status(thm)],[c583,c586]) ).
cnf(c588,plain,
meet(converse(complement(converse(X))),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c582,c587]) ).
cnf(c589,plain,
meet(complement(X),converse(complement(converse(X)))) = complement(X),
inference(transitivity,[status(thm)],[c559,c588]) ).
cnf(c590,plain,
join(zero,meet(complement(X),converse(complement(converse(X))))) = complement(X),
inference(transitivity,[status(thm)],[c558,c589]) ).
cnf(c591,plain,
join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))) = complement(X),
inference(transitivity,[status(thm)],[c557,c590]) ).
cnf(c592,plain,
converse(complement(converse(X))) = complement(X),
inference(transitivity,[status(thm)],[c445,c591]) ).
cnf(c593,plain,
complement(X) = converse(complement(converse(X))),
inference(symmetry,[status(thm)],[c592]) ).
cnf(c594,plain,
converse(complement(X)) = converse(converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
converse(converse(complement(converse(X)))) = complement(converse(X)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c596,plain,
converse(complement(X)) = complement(converse(X)),
inference(transitivity,[status(thm)],[c594,c595]) ).
cnf(c597,plain,
converse(complement(composition(X,composition(converse(x0),x0)))) = complement(converse(composition(X,composition(converse(x0),x0)))),
inference(substitution,[status(thm)],[c596]) ).
cnf(c598,plain,
complement(converse(composition(X,composition(converse(x0),x0)))) = converse(complement(composition(X,composition(converse(x0),x0)))),
inference(symmetry,[status(thm)],[c597]) ).
cnf(c599,plain,
composition(x0,complement(converse(composition(X,composition(converse(x0),x0))))) = composition(x0,converse(complement(composition(X,composition(converse(x0),x0))))),
inference(congruence,[status(thm)],[c598]) ).
cnf(c600,plain,
converse(converse(x0)) = x0,
inference(substitution,[status(thm)],[c56]) ).
cnf(c601,plain,
x0 = converse(converse(x0)),
inference(symmetry,[status(thm)],[c600]) ).
cnf(c602,plain,
composition(x0,converse(complement(composition(X,composition(converse(x0),x0))))) = composition(converse(converse(x0)),converse(complement(composition(X,composition(converse(x0),x0))))),
inference(congruence,[status(thm)],[c601]) ).
cnf(c603,plain,
converse(composition(complement(composition(X,composition(converse(x0),x0))),converse(x0))) = composition(converse(converse(x0)),converse(complement(composition(X,composition(converse(x0),x0))))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c604,plain,
composition(converse(converse(x0)),converse(complement(composition(X,composition(converse(x0),x0))))) = converse(composition(complement(composition(X,composition(converse(x0),x0))),converse(x0))),
inference(symmetry,[status(thm)],[c603]) ).
cnf(c605,plain,
meet(X,join(complement(X),composition(top,composition(converse(x0),x0)))) = meet(X,composition(top,composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c414]) ).
cnf(c606,plain,
meet(X,composition(top,composition(converse(x0),x0))) = meet(X,join(complement(X),composition(top,composition(converse(x0),x0)))),
inference(symmetry,[status(thm)],[c605]) ).
cnf(c607,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c608,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c607]) ).
cnf(c609,plain,
composition(join(X3,X),composition(converse(x0),x0)) = composition(join(X,X3),composition(converse(x0),x0)),
inference(congruence,[status(thm)],[c608]) ).
cnf(c610,plain,
join(X3,composition(join(X3,X),composition(converse(x0),x0))) = join(X3,composition(join(X,X3),composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c609]) ).
cnf(c611,plain,
join(composition(X4,X3),X) = join(X,composition(X4,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c612,plain,
join(X3,composition(X,X4)) = join(composition(X,X4),X3),
inference(symmetry,[status(thm)],[c611]) ).
cnf(c613,plain,
join(composition(X5,X4),join(X3,composition(X,X4))) = join(composition(X5,X4),join(composition(X,X4),X3)),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
join(composition(X5,X4),join(composition(X,X4),X3)) = join(composition(X,X4),join(composition(X5,X4),X3)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c615,plain,
join(composition(X,X4),join(composition(X5,X4),X3)) = join(join(composition(X,X4),composition(X5,X4)),X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c616,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c617,plain,
composition(join(X,X4),X3) = join(composition(X,X3),composition(X4,X3)),
inference(substitution,[status(thm)],[c616]) ).
cnf(c618,plain,
join(composition(X,X3),composition(X4,X3)) = composition(join(X,X4),X3),
inference(symmetry,[status(thm)],[c617]) ).
cnf(c619,plain,
join(join(composition(X,X4),composition(X5,X4)),X3) = join(composition(join(X,X5),X4),X3),
inference(congruence,[status(thm)],[c618]) ).
cnf(c620,plain,
join(composition(join(X,X5),X4),X3) = join(X3,composition(join(X,X5),X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c621,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c622,plain,
composition(join(X,X4),X3) = composition(join(X4,X),X3),
inference(congruence,[status(thm)],[c621]) ).
cnf(c623,plain,
join(X3,composition(join(X,X5),X4)) = join(X3,composition(join(X5,X),X4)),
inference(congruence,[status(thm)],[c622]) ).
cnf(c624,plain,
join(composition(join(X,X5),X4),X3) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c620,c623]) ).
cnf(c625,plain,
join(join(composition(X,X4),composition(X5,X4)),X3) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c619,c624]) ).
cnf(c626,plain,
join(composition(X,X4),join(composition(X5,X4),X3)) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c615,c625]) ).
cnf(c627,plain,
join(composition(X5,X4),join(composition(X,X4),X3)) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c614,c626]) ).
cnf(c628,plain,
join(composition(X5,X4),join(X3,composition(X,X4))) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c613,c627]) ).
cnf(c629,plain,
join(composition(X,composition(converse(x0),x0)),join(X3,composition(X3,composition(converse(x0),x0)))) = join(X3,composition(join(X,X3),composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c628]) ).
cnf(c630,plain,
join(X3,composition(join(X,X3),composition(converse(x0),x0))) = join(composition(X,composition(converse(x0),x0)),join(X3,composition(X3,composition(converse(x0),x0)))),
inference(symmetry,[status(thm)],[c629]) ).
cnf(c631,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c632,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c631]) ).
cnf(c633,plain,
composition(X,composition(converse(x0),x0)) = composition(converse(converse(X)),composition(converse(x0),x0)),
inference(congruence,[status(thm)],[c632]) ).
cnf(c634,plain,
join(X,composition(X,composition(converse(x0),x0))) = join(X,composition(converse(converse(X)),composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c633]) ).
cnf(c635,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c636,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c635]) ).
cnf(c637,plain,
join(X,composition(converse(converse(X)),composition(converse(x0),x0))) = join(converse(converse(X)),composition(converse(converse(X)),composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c636]) ).
cnf(c638,plain,
converse(composition(converse(x0),x0)) = composition(converse(x0),x0),
inference(substitution,[status(thm)],[c427]) ).
cnf(c639,plain,
composition(converse(x0),x0) = converse(composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c638]) ).
cnf(c640,plain,
composition(converse(X),composition(converse(x0),x0)) = composition(converse(X),converse(composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c639]) ).
cnf(c641,plain,
join(converse(X),composition(converse(X),composition(converse(x0),x0))) = join(converse(X),composition(converse(X),converse(composition(converse(x0),x0)))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c642,plain,
converse(composition(composition(converse(x0),x0),X)) = composition(converse(X),converse(composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c643,plain,
composition(converse(X),converse(composition(converse(x0),x0))) = converse(composition(composition(converse(x0),x0),X)),
inference(symmetry,[status(thm)],[c642]) ).
cnf(c644,plain,
join(converse(X),composition(converse(X),converse(composition(converse(x0),x0)))) = join(converse(X),converse(composition(composition(converse(x0),x0),X))),
inference(congruence,[status(thm)],[c643]) ).
cnf(c645,plain,
converse(join(X,composition(composition(converse(x0),x0),X))) = join(converse(X),converse(composition(composition(converse(x0),x0),X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c646,plain,
join(converse(X),converse(composition(composition(converse(x0),x0),X))) = converse(join(X,composition(composition(converse(x0),x0),X))),
inference(symmetry,[status(thm)],[c645]) ).
cnf(c647,plain,
join(X,join(composition(converse(x0),x0),one)) = join(join(composition(converse(x0),x0),one),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c648,plain,
join(join(composition(converse(x0),x0),one),X) = join(X,join(composition(converse(x0),x0),one)),
inference(symmetry,[status(thm)],[c647]) ).
cnf(c649,plain,
composition(join(join(composition(converse(x0),x0),one),X),X3) = composition(join(X,join(composition(converse(x0),x0),one)),X3),
inference(congruence,[status(thm)],[c648]) ).
cnf(c650,plain,
join(join(composition(converse(x0),x0),one),X) = join(X,join(composition(converse(x0),x0),one)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c651,plain,
join(X,join(composition(converse(x0),x0),one)) = join(join(composition(converse(x0),x0),one),X),
inference(symmetry,[status(thm)],[c650]) ).
cnf(c652,plain,
composition(join(X3,join(composition(converse(x0),x0),one)),X) = composition(join(join(composition(converse(x0),x0),one),X3),X),
inference(congruence,[status(thm)],[c651]) ).
cnf(c653,plain,
join(composition(converse(x0),x0),one) = converse(join(composition(converse(x0),x0),one)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c654,plain,
join(join(composition(converse(x0),x0),one),X) = join(converse(join(composition(converse(x0),x0),one)),X),
inference(congruence,[status(thm)],[c653]) ).
cnf(c655,plain,
composition(join(join(composition(converse(x0),x0),one),X3),X) = composition(join(converse(join(composition(converse(x0),x0),one)),X3),X),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
composition(join(converse(join(composition(converse(x0),x0),one)),X3),X) = join(composition(converse(join(composition(converse(x0),x0),one)),X),composition(X3,X)),
inference(substitution,[status(thm)],[c616]) ).
cnf(c657,plain,
join(composition(converse(join(composition(converse(x0),x0),one)),X),composition(X3,X)) = join(X,composition(X3,X)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c658,plain,
composition(join(converse(join(composition(converse(x0),x0),one)),X3),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c656,c657]) ).
cnf(c659,plain,
composition(join(join(composition(converse(x0),x0),one),X3),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c655,c658]) ).
cnf(c660,plain,
composition(join(X3,join(composition(converse(x0),x0),one)),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c652,c659]) ).
cnf(c661,plain,
composition(join(X,join(composition(converse(x0),x0),one)),X3) = join(X3,composition(X,X3)),
inference(substitution,[status(thm)],[c660]) ).
cnf(c662,plain,
composition(join(join(composition(converse(x0),x0),one),X),X3) = join(X3,composition(X,X3)),
inference(transitivity,[status(thm)],[c649,c661]) ).
cnf(c663,plain,
composition(join(join(composition(converse(x0),x0),one),composition(converse(x0),x0)),X) = join(X,composition(composition(converse(x0),x0),X)),
inference(substitution,[status(thm)],[c662]) ).
cnf(c664,plain,
join(X,composition(composition(converse(x0),x0),X)) = composition(join(join(composition(converse(x0),x0),one),composition(converse(x0),x0)),X),
inference(symmetry,[status(thm)],[c663]) ).
cnf(c665,plain,
join(join(composition(converse(x0),x0),one),X) = join(one,X),
inference(congruence,[status(thm)],[c63]) ).
cnf(c666,plain,
join(X,one) = join(one,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c667,plain,
join(one,X) = join(X,one),
inference(symmetry,[status(thm)],[c666]) ).
cnf(c668,plain,
join(join(composition(converse(x0),x0),one),X) = join(X,one),
inference(transitivity,[status(thm)],[c665,c667]) ).
cnf(c669,plain,
join(join(composition(converse(x0),x0),one),composition(converse(x0),x0)) = join(composition(converse(x0),x0),one),
inference(substitution,[status(thm)],[c668]) ).
cnf(c670,plain,
composition(join(join(composition(converse(x0),x0),one),composition(converse(x0),x0)),X) = composition(join(composition(converse(x0),x0),one),X),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
composition(join(join(composition(converse(x0),x0),one),composition(converse(x0),x0)),X) = X,
inference(transitivity,[status(thm)],[c670,c89]) ).
cnf(c672,plain,
join(X,composition(composition(converse(x0),x0),X)) = X,
inference(transitivity,[status(thm)],[c664,c671]) ).
cnf(c673,plain,
converse(join(X,composition(composition(converse(x0),x0),X))) = converse(X),
inference(congruence,[status(thm)],[c672]) ).
cnf(c674,plain,
join(converse(X),converse(composition(composition(converse(x0),x0),X))) = converse(X),
inference(transitivity,[status(thm)],[c646,c673]) ).
cnf(c675,plain,
join(converse(X),composition(converse(X),converse(composition(converse(x0),x0)))) = converse(X),
inference(transitivity,[status(thm)],[c644,c674]) ).
cnf(c676,plain,
join(converse(X),composition(converse(X),composition(converse(x0),x0))) = converse(X),
inference(transitivity,[status(thm)],[c641,c675]) ).
cnf(c677,plain,
join(converse(converse(X)),composition(converse(converse(X)),composition(converse(x0),x0))) = converse(converse(X)),
inference(substitution,[status(thm)],[c676]) ).
cnf(c678,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c679,plain,
join(converse(converse(X)),composition(converse(converse(X)),composition(converse(x0),x0))) = X,
inference(transitivity,[status(thm)],[c677,c678]) ).
cnf(c680,plain,
join(X,composition(converse(converse(X)),composition(converse(x0),x0))) = X,
inference(transitivity,[status(thm)],[c637,c679]) ).
cnf(c681,plain,
join(X,composition(X,composition(converse(x0),x0))) = X,
inference(transitivity,[status(thm)],[c634,c680]) ).
cnf(c682,plain,
join(composition(X,composition(converse(x0),x0)),join(X3,composition(X3,composition(converse(x0),x0)))) = join(composition(X,composition(converse(x0),x0)),X3),
inference(congruence,[status(thm)],[c681]) ).
cnf(c683,plain,
join(composition(X,composition(converse(x0),x0)),X3) = join(X3,composition(X,composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c684,plain,
join(composition(X,composition(converse(x0),x0)),join(X3,composition(X3,composition(converse(x0),x0)))) = join(X3,composition(X,composition(converse(x0),x0))),
inference(transitivity,[status(thm)],[c682,c683]) ).
cnf(c685,plain,
join(X3,composition(join(X,X3),composition(converse(x0),x0))) = join(X3,composition(X,composition(converse(x0),x0))),
inference(transitivity,[status(thm)],[c630,c684]) ).
cnf(c686,plain,
join(X3,composition(join(X3,X),composition(converse(x0),x0))) = join(X3,composition(X,composition(converse(x0),x0))),
inference(transitivity,[status(thm)],[c610,c685]) ).
cnf(c687,plain,
join(X,composition(join(X,complement(X)),composition(converse(x0),x0))) = join(X,composition(complement(X),composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c686]) ).
cnf(c688,plain,
join(X,composition(complement(X),composition(converse(x0),x0))) = join(X,composition(join(X,complement(X)),composition(converse(x0),x0))),
inference(symmetry,[status(thm)],[c687]) ).
cnf(c689,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c690,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c689]) ).
cnf(c691,plain,
composition(join(X,complement(X)),composition(converse(x0),x0)) = composition(top,composition(converse(x0),x0)),
inference(congruence,[status(thm)],[c690]) ).
cnf(c692,plain,
join(X,composition(join(X,complement(X)),composition(converse(x0),x0))) = join(X,composition(top,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c691]) ).
cnf(c693,plain,
join(X,composition(complement(X),composition(converse(x0),x0))) = join(X,composition(top,composition(converse(x0),x0))),
inference(transitivity,[status(thm)],[c688,c692]) ).
cnf(c694,plain,
join(complement(X),composition(complement(complement(X)),composition(converse(x0),x0))) = join(complement(X),composition(top,composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c693]) ).
cnf(c695,plain,
join(complement(X),composition(top,composition(converse(x0),x0))) = join(complement(X),composition(complement(complement(X)),composition(converse(x0),x0))),
inference(symmetry,[status(thm)],[c694]) ).
cnf(c696,plain,
meet(X,join(complement(X),composition(top,composition(converse(x0),x0)))) = meet(X,join(complement(X),composition(complement(complement(X)),composition(converse(x0),x0)))),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
meet(X,join(complement(X),composition(complement(complement(X)),composition(converse(x0),x0)))) = meet(X,composition(complement(complement(X)),composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c414]) ).
cnf(c698,plain,
composition(complement(complement(X)),composition(converse(x0),x0)) = composition(X,composition(converse(x0),x0)),
inference(congruence,[status(thm)],[c450]) ).
cnf(c699,plain,
meet(X,composition(complement(complement(X)),composition(converse(x0),x0))) = meet(X,composition(X,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c698]) ).
cnf(c700,plain,
meet(X,composition(X,composition(converse(x0),x0))) = meet(composition(X,composition(converse(x0),x0)),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c701,plain,
X = join(X,composition(X,composition(converse(x0),x0))),
inference(symmetry,[status(thm)],[c681]) ).
cnf(c702,plain,
meet(composition(X,composition(converse(x0),x0)),X) = meet(composition(X,composition(converse(x0),x0)),join(X,composition(X,composition(converse(x0),x0)))),
inference(congruence,[status(thm)],[c701]) ).
cnf(c703,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c704,plain,
join(X,X3) = join(X3,X),
inference(symmetry,[status(thm)],[c703]) ).
cnf(c705,plain,
meet(X3,join(X,X3)) = meet(X3,join(X3,X)),
inference(congruence,[status(thm)],[c704]) ).
cnf(c706,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c707,plain,
join(X3,X) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c706]) ).
cnf(c708,plain,
meet(X3,join(X3,X)) = meet(X3,join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c707]) ).
cnf(c709,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c710,plain,
join(X3,meet(X,top)) = join(X3,complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c709]) ).
cnf(c711,plain,
meet(X3,join(X3,meet(X,top))) = meet(X3,join(X3,complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
meet(X3,join(X3,complement(join(zero,complement(X))))) = X3,
inference(substitution,[status(thm)],[c405]) ).
cnf(c713,plain,
meet(X3,join(X3,meet(X,top))) = X3,
inference(transitivity,[status(thm)],[c711,c712]) ).
cnf(c714,plain,
meet(X3,join(X3,X)) = X3,
inference(transitivity,[status(thm)],[c708,c713]) ).
cnf(c715,plain,
meet(X3,join(X,X3)) = X3,
inference(transitivity,[status(thm)],[c705,c714]) ).
cnf(c716,plain,
meet(composition(X,composition(converse(x0),x0)),join(X,composition(X,composition(converse(x0),x0)))) = composition(X,composition(converse(x0),x0)),
inference(substitution,[status(thm)],[c715]) ).
cnf(c717,plain,
meet(composition(X,composition(converse(x0),x0)),X) = composition(X,composition(converse(x0),x0)),
inference(transitivity,[status(thm)],[c702,c716]) ).
cnf(c718,plain,
meet(X,composition(X,composition(converse(x0),x0))) = composition(X,composition(converse(x0),x0)),
inference(transitivity,[status(thm)],[c700,c717]) ).
cnf(c719,plain,
meet(X,composition(complement(complement(X)),composition(converse(x0),x0))) = composition(X,composition(converse(x0),x0)),
inference(transitivity,[status(thm)],[c699,c718]) ).
cnf(c720,plain,
meet(X,join(complement(X),composition(complement(complement(X)),composition(converse(x0),x0)))) = composition(X,composition(converse(x0),x0)),
inference(transitivity,[status(thm)],[c697,c719]) ).
cnf(c721,plain,
meet(X,join(complement(X),composition(top,composition(converse(x0),x0)))) = composition(X,composition(converse(x0),x0)),
inference(transitivity,[status(thm)],[c696,c720]) ).
cnf(c722,plain,
meet(X,composition(top,composition(converse(x0),x0))) = composition(X,composition(converse(x0),x0)),
inference(transitivity,[status(thm)],[c606,c721]) ).
cnf(c723,plain,
composition(X,composition(converse(x0),x0)) = meet(X,composition(top,composition(converse(x0),x0))),
inference(symmetry,[status(thm)],[c722]) ).
cnf(c724,plain,
complement(composition(X,composition(converse(x0),x0))) = complement(meet(X,composition(top,composition(converse(x0),x0)))),
inference(congruence,[status(thm)],[c723]) ).
cnf(c725,plain,
composition(complement(composition(X,composition(converse(x0),x0))),converse(x0)) = composition(complement(meet(X,composition(top,composition(converse(x0),x0)))),converse(x0)),
inference(congruence,[status(thm)],[c724]) ).
cnf(c726,plain,
join(complement(X),complement(composition(top,composition(converse(x0),x0)))) = complement(meet(X,composition(top,composition(converse(x0),x0)))),
inference(substitution,[status(thm)],[c283]) ).
cnf(c727,plain,
complement(meet(X,composition(top,composition(converse(x0),x0)))) = join(complement(X),complement(composition(top,composition(converse(x0),x0)))),
inference(symmetry,[status(thm)],[c726]) ).
cnf(c728,plain,
composition(complement(meet(X,composition(top,composition(converse(x0),x0)))),converse(x0)) = composition(join(complement(X),complement(composition(top,composition(converse(x0),x0)))),converse(x0)),
inference(congruence,[status(thm)],[c727]) ).
cnf(c729,plain,
converse(composition(converse(x0),x0)) = composition(converse(x0),x0),
inference(substitution,[status(thm)],[c427]) ).
cnf(c730,plain,
composition(converse(x0),x0) = converse(composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c729]) ).
cnf(c731,plain,
composition(x0,composition(converse(x0),x0)) = composition(x0,converse(composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c730]) ).
cnf(c732,plain,
converse(converse(x0)) = x0,
inference(substitution,[status(thm)],[c56]) ).
cnf(c733,plain,
x0 = converse(converse(x0)),
inference(symmetry,[status(thm)],[c732]) ).
cnf(c734,plain,
composition(x0,converse(composition(converse(x0),x0))) = composition(converse(converse(x0)),converse(composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c733]) ).
cnf(c735,plain,
converse(composition(composition(converse(x0),x0),converse(x0))) = composition(converse(converse(x0)),converse(composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c736,plain,
composition(converse(converse(x0)),converse(composition(converse(x0),x0))) = converse(composition(composition(converse(x0),x0),converse(x0))),
inference(symmetry,[status(thm)],[c735]) ).
cnf(c737,plain,
join(complement(composition(top,X)),X3) = join(X3,complement(composition(top,X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c738,plain,
join(X3,complement(composition(top,X))) = join(complement(composition(top,X)),X3),
inference(symmetry,[status(thm)],[c737]) ).
cnf(c739,plain,
composition(join(X3,complement(composition(top,X))),converse(X)) = composition(join(complement(composition(top,X)),X3),converse(X)),
inference(congruence,[status(thm)],[c738]) ).
cnf(c740,plain,
composition(join(complement(composition(top,X)),X3),converse(X)) = join(composition(complement(composition(top,X)),converse(X)),composition(X3,converse(X))),
inference(substitution,[status(thm)],[c616]) ).
cnf(c741,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c742,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c741]) ).
cnf(c743,plain,
composition(top,X) = composition(top,converse(converse(X))),
inference(congruence,[status(thm)],[c742]) ).
cnf(c744,plain,
complement(composition(top,X)) = complement(composition(top,converse(converse(X)))),
inference(congruence,[status(thm)],[c743]) ).
cnf(c745,plain,
composition(complement(composition(top,X)),converse(X)) = composition(complement(composition(top,converse(converse(X)))),converse(X)),
inference(congruence,[status(thm)],[c744]) ).
cnf(c746,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c747,plain,
composition(top,converse(converse(X))) = composition(converse(top),converse(converse(X))),
inference(congruence,[status(thm)],[c746]) ).
cnf(c748,plain,
complement(composition(top,converse(converse(X)))) = complement(composition(converse(top),converse(converse(X)))),
inference(congruence,[status(thm)],[c747]) ).
cnf(c749,plain,
composition(complement(composition(top,converse(converse(X)))),converse(X)) = composition(complement(composition(converse(top),converse(converse(X)))),converse(X)),
inference(congruence,[status(thm)],[c748]) ).
cnf(c750,plain,
converse(composition(converse(X),top)) = composition(converse(top),converse(converse(X))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c751,plain,
composition(converse(top),converse(converse(X))) = converse(composition(converse(X),top)),
inference(symmetry,[status(thm)],[c750]) ).
cnf(c752,plain,
complement(composition(converse(top),converse(converse(X)))) = complement(converse(composition(converse(X),top))),
inference(congruence,[status(thm)],[c751]) ).
cnf(c753,plain,
composition(complement(composition(converse(top),converse(converse(X)))),converse(X)) = composition(complement(converse(composition(converse(X),top))),converse(X)),
inference(congruence,[status(thm)],[c752]) ).
cnf(c754,plain,
converse(complement(composition(converse(X),top))) = complement(converse(composition(converse(X),top))),
inference(substitution,[status(thm)],[c596]) ).
cnf(c755,plain,
complement(converse(composition(converse(X),top))) = converse(complement(composition(converse(X),top))),
inference(symmetry,[status(thm)],[c754]) ).
cnf(c756,plain,
composition(complement(converse(composition(converse(X),top))),converse(X)) = composition(converse(complement(composition(converse(X),top))),converse(X)),
inference(congruence,[status(thm)],[c755]) ).
cnf(c757,plain,
converse(composition(X,complement(composition(converse(X),top)))) = composition(converse(complement(composition(converse(X),top))),converse(X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c758,plain,
composition(converse(complement(composition(converse(X),top))),converse(X)) = converse(composition(X,complement(composition(converse(X),top)))),
inference(symmetry,[status(thm)],[c757]) ).
cnf(c759,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c760,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c759]) ).
cnf(c761,plain,
composition(X,complement(composition(converse(X),top))) = composition(converse(converse(X)),complement(composition(converse(X),top))),
inference(congruence,[status(thm)],[c760]) ).
cnf(c762,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = composition(converse(X),complement(composition(X,top))),
inference(substitution,[status(thm)],[c273]) ).
cnf(c763,plain,
composition(converse(X),complement(composition(X,top))) = join(zero,composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c762]) ).
cnf(c764,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c765,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = join(complement(top),composition(converse(X),complement(composition(X,top)))),
inference(congruence,[status(thm)],[c764]) ).
cnf(c766,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = complement(top),
inference(substitution,[status(thm)],[c98]) ).
cnf(c767,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c766,c44]) ).
cnf(c768,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c765,c767]) ).
cnf(c769,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c763,c768]) ).
cnf(c770,plain,
composition(converse(converse(X)),complement(composition(converse(X),top))) = zero,
inference(substitution,[status(thm)],[c769]) ).
cnf(c771,plain,
composition(X,complement(composition(converse(X),top))) = zero,
inference(transitivity,[status(thm)],[c761,c770]) ).
cnf(c772,plain,
converse(composition(X,complement(composition(converse(X),top)))) = converse(zero),
inference(congruence,[status(thm)],[c771]) ).
cnf(c773,plain,
meet(converse(zero),top) = converse(zero),
inference(substitution,[status(thm)],[c231]) ).
cnf(c774,plain,
converse(zero) = meet(converse(zero),top),
inference(symmetry,[status(thm)],[c773]) ).
cnf(c775,plain,
join(X,converse(zero)) = join(converse(zero),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c776,plain,
join(converse(zero),X) = join(X,converse(zero)),
inference(symmetry,[status(thm)],[c775]) ).
cnf(c777,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c778,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c777]) ).
cnf(c779,plain,
join(X,converse(zero)) = join(converse(converse(X)),converse(zero)),
inference(congruence,[status(thm)],[c778]) ).
cnf(c780,plain,
meet(X,X) = complement(complement(X)),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c781,plain,
meet(X,X) = X,
inference(transitivity,[status(thm)],[c780,c450]) ).
cnf(c782,plain,
X = meet(X,X),
inference(symmetry,[status(thm)],[c781]) ).
cnf(c783,plain,
converse(X) = converse(meet(X,X)),
inference(congruence,[status(thm)],[c782]) ).
cnf(c784,plain,
join(converse(X),converse(zero)) = join(converse(meet(X,X)),converse(zero)),
inference(congruence,[status(thm)],[c783]) ).
cnf(c785,plain,
join(converse(zero),converse(meet(X,X))) = join(converse(meet(X,X)),converse(zero)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c786,plain,
join(converse(meet(X,X)),converse(zero)) = join(converse(zero),converse(meet(X,X))),
inference(symmetry,[status(thm)],[c785]) ).
cnf(c787,plain,
converse(join(zero,meet(X,X))) = join(converse(zero),converse(meet(X,X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c788,plain,
join(converse(zero),converse(meet(X,X))) = converse(join(zero,meet(X,X))),
inference(symmetry,[status(thm)],[c787]) ).
cnf(c789,plain,
converse(join(zero,meet(X,X))) = converse(X),
inference(congruence,[status(thm)],[c121]) ).
cnf(c790,plain,
join(converse(zero),converse(meet(X,X))) = converse(X),
inference(transitivity,[status(thm)],[c788,c789]) ).
cnf(c791,plain,
join(converse(meet(X,X)),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c786,c790]) ).
cnf(c792,plain,
join(converse(X),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c784,c791]) ).
cnf(c793,plain,
join(converse(converse(X)),converse(zero)) = converse(converse(X)),
inference(substitution,[status(thm)],[c792]) ).
cnf(c794,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c795,plain,
join(converse(converse(X)),converse(zero)) = X,
inference(transitivity,[status(thm)],[c793,c794]) ).
cnf(c796,plain,
join(X,converse(zero)) = X,
inference(transitivity,[status(thm)],[c779,c795]) ).
cnf(c797,plain,
join(converse(zero),X) = X,
inference(transitivity,[status(thm)],[c776,c796]) ).
cnf(c798,plain,
join(converse(zero),complement(converse(zero))) = complement(converse(zero)),
inference(substitution,[status(thm)],[c797]) ).
cnf(c799,plain,
complement(converse(zero)) = join(converse(zero),complement(converse(zero))),
inference(symmetry,[status(thm)],[c798]) ).
cnf(c800,plain,
top = join(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c801,plain,
join(converse(zero),complement(converse(zero))) = top,
inference(symmetry,[status(thm)],[c800]) ).
cnf(c802,plain,
complement(converse(zero)) = top,
inference(transitivity,[status(thm)],[c799,c801]) ).
cnf(c803,plain,
top = complement(converse(zero)),
inference(symmetry,[status(thm)],[c802]) ).
cnf(c804,plain,
meet(converse(zero),top) = meet(converse(zero),complement(converse(zero))),
inference(congruence,[status(thm)],[c803]) ).
cnf(c805,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c806,plain,
meet(converse(zero),complement(converse(zero))) = zero,
inference(symmetry,[status(thm)],[c805]) ).
cnf(c807,plain,
meet(converse(zero),top) = zero,
inference(transitivity,[status(thm)],[c804,c806]) ).
cnf(c808,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c774,c807]) ).
cnf(c809,plain,
converse(composition(X,complement(composition(converse(X),top)))) = zero,
inference(transitivity,[status(thm)],[c772,c808]) ).
cnf(c810,plain,
composition(converse(complement(composition(converse(X),top))),converse(X)) = zero,
inference(transitivity,[status(thm)],[c758,c809]) ).
cnf(c811,plain,
composition(complement(converse(composition(converse(X),top))),converse(X)) = zero,
inference(transitivity,[status(thm)],[c756,c810]) ).
cnf(c812,plain,
composition(complement(composition(converse(top),converse(converse(X)))),converse(X)) = zero,
inference(transitivity,[status(thm)],[c753,c811]) ).
cnf(c813,plain,
composition(complement(composition(top,converse(converse(X)))),converse(X)) = zero,
inference(transitivity,[status(thm)],[c749,c812]) ).
cnf(c814,plain,
composition(complement(composition(top,X)),converse(X)) = zero,
inference(transitivity,[status(thm)],[c745,c813]) ).
cnf(c815,plain,
join(composition(complement(composition(top,X)),converse(X)),composition(X3,converse(X))) = join(zero,composition(X3,converse(X))),
inference(congruence,[status(thm)],[c814]) ).
cnf(c816,plain,
join(zero,composition(X3,converse(X))) = composition(X3,converse(X)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c817,plain,
join(composition(complement(composition(top,X)),converse(X)),composition(X3,converse(X))) = composition(X3,converse(X)),
inference(transitivity,[status(thm)],[c815,c816]) ).
cnf(c818,plain,
composition(join(complement(composition(top,X)),X3),converse(X)) = composition(X3,converse(X)),
inference(transitivity,[status(thm)],[c740,c817]) ).
cnf(c819,plain,
composition(join(X3,complement(composition(top,X))),converse(X)) = composition(X3,converse(X)),
inference(transitivity,[status(thm)],[c739,c818]) ).
cnf(c820,plain,
composition(join(composition(converse(x0),x0),complement(composition(top,x0))),converse(x0)) = composition(composition(converse(x0),x0),converse(x0)),
inference(substitution,[status(thm)],[c819]) ).
cnf(c821,plain,
composition(composition(converse(x0),x0),converse(x0)) = composition(join(composition(converse(x0),x0),complement(composition(top,x0))),converse(x0)),
inference(symmetry,[status(thm)],[c820]) ).
cnf(c822,plain,
join(complement(X3),meet(X,X3)) = join(complement(X3),meet(X3,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c823,plain,
join(meet(X3,X),complement(X3)) = join(complement(X3),meet(X3,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c824,plain,
join(complement(X3),meet(X3,X)) = join(meet(X3,X),complement(X3)),
inference(symmetry,[status(thm)],[c823]) ).
cnf(c825,plain,
meet(complement(X3),join(X,complement(X3))) = complement(X3),
inference(substitution,[status(thm)],[c715]) ).
cnf(c826,plain,
complement(X3) = meet(complement(X3),join(X,complement(X3))),
inference(symmetry,[status(thm)],[c825]) ).
cnf(c827,plain,
join(meet(X3,X),complement(X3)) = join(meet(X3,X),meet(complement(X3),join(X,complement(X3)))),
inference(congruence,[status(thm)],[c826]) ).
cnf(c828,plain,
meet(X3,X) = meet(X3,join(X,complement(X3))),
inference(symmetry,[status(thm)],[c413]) ).
cnf(c829,plain,
join(meet(X3,X),meet(complement(X3),join(X,complement(X3)))) = join(meet(X3,join(X,complement(X3))),meet(complement(X3),join(X,complement(X3)))),
inference(congruence,[status(thm)],[c828]) ).
cnf(c830,plain,
join(meet(X3,join(X,complement(X3))),meet(complement(X3),join(X,complement(X3)))) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c443]) ).
cnf(c831,plain,
join(meet(X3,X),meet(complement(X3),join(X,complement(X3)))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c829,c830]) ).
cnf(c832,plain,
join(meet(X3,X),complement(X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c827,c831]) ).
cnf(c833,plain,
join(complement(X3),meet(X3,X)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c824,c832]) ).
cnf(c834,plain,
join(complement(X3),meet(X,X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c822,c833]) ).
cnf(c835,plain,
join(complement(composition(top,x0)),meet(join(composition(converse(x0),x0),one),composition(top,x0))) = join(join(composition(converse(x0),x0),one),complement(composition(top,x0))),
inference(substitution,[status(thm)],[c834]) ).
cnf(c836,plain,
join(join(composition(converse(x0),x0),one),complement(composition(top,x0))) = join(complement(composition(top,x0)),meet(join(composition(converse(x0),x0),one),composition(top,x0))),
inference(symmetry,[status(thm)],[c835]) ).
cnf(c837,plain,
meet(join(composition(converse(x0),x0),one),join(complement(join(composition(converse(x0),x0),one)),composition(top,x0))) = meet(join(composition(converse(x0),x0),one),composition(top,x0)),
inference(substitution,[status(thm)],[c414]) ).
cnf(c838,plain,
meet(join(composition(converse(x0),x0),one),composition(top,x0)) = meet(join(composition(converse(x0),x0),one),join(complement(join(composition(converse(x0),x0),one)),composition(top,x0))),
inference(symmetry,[status(thm)],[c837]) ).
cnf(c839,plain,
join(composition(complement(X4),X3),X) = join(X,composition(complement(X4),X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c840,plain,
join(X,composition(complement(X4),X3)) = join(composition(complement(X4),X3),X),
inference(symmetry,[status(thm)],[c839]) ).
cnf(c841,plain,
join(composition(X4,X3),join(X,composition(complement(X4),X3))) = join(composition(X4,X3),join(composition(complement(X4),X3),X)),
inference(congruence,[status(thm)],[c840]) ).
cnf(c842,plain,
join(composition(X4,X3),join(composition(complement(X4),X3),X)) = join(join(composition(X4,X3),composition(complement(X4),X3)),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c843,plain,
composition(join(X3,complement(X3)),X) = join(composition(X3,X),composition(complement(X3),X)),
inference(substitution,[status(thm)],[c616]) ).
cnf(c844,plain,
join(composition(X3,X),composition(complement(X3),X)) = composition(join(X3,complement(X3)),X),
inference(symmetry,[status(thm)],[c843]) ).
cnf(c845,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c846,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c845]) ).
cnf(c847,plain,
composition(join(X3,complement(X3)),X) = composition(top,X),
inference(congruence,[status(thm)],[c846]) ).
cnf(c848,plain,
join(composition(X3,X),composition(complement(X3),X)) = composition(top,X),
inference(transitivity,[status(thm)],[c844,c847]) ).
cnf(c849,plain,
join(join(composition(X4,X3),composition(complement(X4),X3)),X) = join(composition(top,X3),X),
inference(congruence,[status(thm)],[c848]) ).
cnf(c850,plain,
join(composition(top,X3),X) = join(X,composition(top,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c851,plain,
join(join(composition(X4,X3),composition(complement(X4),X3)),X) = join(X,composition(top,X3)),
inference(transitivity,[status(thm)],[c849,c850]) ).
cnf(c852,plain,
join(composition(X4,X3),join(composition(complement(X4),X3),X)) = join(X,composition(top,X3)),
inference(transitivity,[status(thm)],[c842,c851]) ).
cnf(c853,plain,
join(composition(X4,X3),join(X,composition(complement(X4),X3))) = join(X,composition(top,X3)),
inference(transitivity,[status(thm)],[c841,c852]) ).
cnf(c854,plain,
join(composition(converse(X),X),join(complement(join(composition(converse(x0),x0),one)),composition(complement(converse(X)),X))) = join(complement(join(composition(converse(x0),x0),one)),composition(top,X)),
inference(substitution,[status(thm)],[c853]) ).
cnf(c855,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(top,X)) = join(composition(converse(X),X),join(complement(join(composition(converse(x0),x0),one)),composition(complement(converse(X)),X))),
inference(symmetry,[status(thm)],[c854]) ).
cnf(c856,plain,
complement(converse(X)) = converse(complement(X)),
inference(symmetry,[status(thm)],[c596]) ).
cnf(c857,plain,
composition(complement(converse(X)),X) = composition(converse(complement(X)),X),
inference(congruence,[status(thm)],[c856]) ).
cnf(c858,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(complement(converse(X)),X)) = join(complement(join(composition(converse(x0),x0),one)),composition(converse(complement(X)),X)),
inference(congruence,[status(thm)],[c857]) ).
cnf(c859,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c860,plain,
composition(converse(complement(X)),X) = composition(converse(complement(X)),meet(X,top)),
inference(congruence,[status(thm)],[c859]) ).
cnf(c861,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(complement(X)),X)) = join(complement(join(composition(converse(x0),x0),one)),composition(converse(complement(X)),meet(X,top))),
inference(congruence,[status(thm)],[c860]) ).
cnf(c862,plain,
join(converse(zero),converse(complement(X))) = converse(complement(X)),
inference(substitution,[status(thm)],[c797]) ).
cnf(c863,plain,
converse(complement(X)) = join(converse(zero),converse(complement(X))),
inference(symmetry,[status(thm)],[c862]) ).
cnf(c864,plain,
composition(converse(complement(X)),meet(X,top)) = composition(join(converse(zero),converse(complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c863]) ).
cnf(c865,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(complement(X)),meet(X,top))) = join(complement(join(composition(converse(x0),x0),one)),composition(join(converse(zero),converse(complement(X))),meet(X,top))),
inference(congruence,[status(thm)],[c864]) ).
cnf(c866,plain,
converse(join(zero,complement(X))) = join(converse(zero),converse(complement(X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c867,plain,
join(converse(zero),converse(complement(X))) = converse(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c866]) ).
cnf(c868,plain,
composition(join(converse(zero),converse(complement(X))),meet(X,top)) = composition(converse(join(zero,complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c867]) ).
cnf(c869,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(join(converse(zero),converse(complement(X))),meet(X,top))) = join(complement(join(composition(converse(x0),x0),one)),composition(converse(join(zero,complement(X))),meet(X,top))),
inference(congruence,[status(thm)],[c868]) ).
cnf(c870,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c871,plain,
composition(converse(join(zero,complement(X))),meet(X,top)) = composition(converse(join(zero,complement(X))),complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c870]) ).
cnf(c872,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(join(zero,complement(X))),meet(X,top))) = join(complement(join(composition(converse(x0),x0),one)),composition(converse(join(zero,complement(X))),complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c871]) ).
cnf(c873,plain,
complement(join(composition(converse(x0),x0),one)) = complement(one),
inference(congruence,[status(thm)],[c63]) ).
cnf(c874,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(X),complement(X))) = join(complement(one),composition(converse(X),complement(X))),
inference(congruence,[status(thm)],[c873]) ).
cnf(c875,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c69]) ).
cnf(c876,plain,
X = composition(X,one),
inference(symmetry,[status(thm)],[c875]) ).
cnf(c877,plain,
complement(X) = complement(composition(X,one)),
inference(congruence,[status(thm)],[c876]) ).
cnf(c878,plain,
composition(converse(X),complement(X)) = composition(converse(X),complement(composition(X,one))),
inference(congruence,[status(thm)],[c877]) ).
cnf(c879,plain,
join(complement(one),composition(converse(X),complement(X))) = join(complement(one),composition(converse(X),complement(composition(X,one)))),
inference(congruence,[status(thm)],[c878]) ).
cnf(c880,plain,
join(complement(one),composition(converse(X),complement(composition(X,one)))) = complement(one),
inference(substitution,[status(thm)],[c98]) ).
cnf(c881,plain,
one = join(composition(converse(x0),x0),one),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c882,plain,
complement(one) = complement(join(composition(converse(x0),x0),one)),
inference(congruence,[status(thm)],[c881]) ).
cnf(c883,plain,
join(complement(one),composition(converse(X),complement(composition(X,one)))) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c880,c882]) ).
cnf(c884,plain,
join(complement(one),composition(converse(X),complement(X))) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c879,c883]) ).
cnf(c885,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(X),complement(X))) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c874,c884]) ).
cnf(c886,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(join(zero,complement(X))),complement(join(zero,complement(X))))) = complement(join(composition(converse(x0),x0),one)),
inference(substitution,[status(thm)],[c885]) ).
cnf(c887,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(join(zero,complement(X))),meet(X,top))) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c872,c886]) ).
cnf(c888,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(join(converse(zero),converse(complement(X))),meet(X,top))) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c869,c887]) ).
cnf(c889,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(complement(X)),meet(X,top))) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c865,c888]) ).
cnf(c890,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(converse(complement(X)),X)) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c861,c889]) ).
cnf(c891,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(complement(converse(X)),X)) = complement(join(composition(converse(x0),x0),one)),
inference(transitivity,[status(thm)],[c858,c890]) ).
cnf(c892,plain,
join(composition(converse(X),X),join(complement(join(composition(converse(x0),x0),one)),composition(complement(converse(X)),X))) = join(composition(converse(X),X),complement(join(composition(converse(x0),x0),one))),
inference(congruence,[status(thm)],[c891]) ).
cnf(c893,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(top,X)) = join(composition(converse(X),X),complement(join(composition(converse(x0),x0),one))),
inference(transitivity,[status(thm)],[c855,c892]) ).
cnf(c894,plain,
join(complement(join(composition(converse(x0),x0),one)),composition(top,x0)) = join(composition(converse(x0),x0),complement(join(composition(converse(x0),x0),one))),
inference(substitution,[status(thm)],[c893]) ).
cnf(c895,plain,
meet(join(composition(converse(x0),x0),one),join(complement(join(composition(converse(x0),x0),one)),composition(top,x0))) = meet(join(composition(converse(x0),x0),one),join(composition(converse(x0),x0),complement(join(composition(converse(x0),x0),one)))),
inference(congruence,[status(thm)],[c894]) ).
cnf(c896,plain,
meet(join(composition(converse(x0),x0),one),join(composition(converse(x0),x0),complement(join(composition(converse(x0),x0),one)))) = meet(join(composition(converse(x0),x0),one),composition(converse(x0),x0)),
inference(substitution,[status(thm)],[c413]) ).
cnf(c897,plain,
meet(join(X,one),X) = meet(X,join(X,one)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c898,plain,
meet(X,join(X,one)) = complement(join(complement(X),complement(join(X,one)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c899,plain,
join(zero,complement(join(complement(X),complement(join(X,one))))) = complement(join(complement(X),complement(join(X,one)))),
inference(substitution,[status(thm)],[c218]) ).
cnf(c900,plain,
complement(join(complement(X),complement(join(X,one)))) = join(zero,complement(join(complement(X),complement(join(X,one))))),
inference(symmetry,[status(thm)],[c899]) ).
cnf(c901,plain,
complement(join(join(X,one),complement(X))) = meet(X,complement(join(X,one))),
inference(substitution,[status(thm)],[c477]) ).
cnf(c902,plain,
meet(X,complement(join(X,one))) = complement(join(join(X,one),complement(X))),
inference(symmetry,[status(thm)],[c901]) ).
cnf(c903,plain,
join(join(composition(converse(x0),x0),one),top) = join(top,join(composition(converse(x0),x0),one)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c904,plain,
join(top,join(composition(converse(x0),x0),one)) = join(join(composition(converse(x0),x0),one),top),
inference(symmetry,[status(thm)],[c903]) ).
cnf(c905,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c906,plain,
join(join(composition(converse(x0),x0),one),top) = join(join(composition(converse(x0),x0),one),join(X,complement(X))),
inference(congruence,[status(thm)],[c905]) ).
cnf(c907,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c908,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c907]) ).
cnf(c909,plain,
join(join(composition(converse(x0),x0),one),join(X3,X)) = join(join(composition(converse(x0),x0),one),join(X,X3)),
inference(congruence,[status(thm)],[c908]) ).
cnf(c910,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c911,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c910]) ).
cnf(c912,plain,
join(join(composition(converse(x0),x0),one),join(X3,X)) = join(join(composition(converse(x0),x0),one),join(X,X3)),
inference(congruence,[status(thm)],[c911]) ).
cnf(c913,plain,
join(join(composition(converse(x0),x0),one),join(X,X3)) = join(join(join(composition(converse(x0),x0),one),X),X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c914,plain,
join(join(join(composition(converse(x0),x0),one),X),X3) = join(join(X,one),X3),
inference(congruence,[status(thm)],[c668]) ).
cnf(c915,plain,
join(join(X,one),X3) = join(X3,join(X,one)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c916,plain,
join(join(join(composition(converse(x0),x0),one),X),X3) = join(X3,join(X,one)),
inference(transitivity,[status(thm)],[c914,c915]) ).
cnf(c917,plain,
join(join(composition(converse(x0),x0),one),join(X,X3)) = join(X3,join(X,one)),
inference(transitivity,[status(thm)],[c913,c916]) ).
cnf(c918,plain,
join(join(composition(converse(x0),x0),one),join(X3,X)) = join(X3,join(X,one)),
inference(transitivity,[status(thm)],[c912,c917]) ).
cnf(c919,plain,
join(join(composition(converse(x0),x0),one),join(X,X3)) = join(X,join(X3,one)),
inference(substitution,[status(thm)],[c918]) ).
cnf(c920,plain,
join(join(composition(converse(x0),x0),one),join(X3,X)) = join(X,join(X3,one)),
inference(transitivity,[status(thm)],[c909,c919]) ).
cnf(c921,plain,
join(join(composition(converse(x0),x0),one),join(X,complement(X))) = join(complement(X),join(X,one)),
inference(substitution,[status(thm)],[c920]) ).
cnf(c922,plain,
join(complement(X),join(X,one)) = join(join(X,one),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c923,plain,
join(join(composition(converse(x0),x0),one),join(X,complement(X))) = join(join(X,one),complement(X)),
inference(transitivity,[status(thm)],[c921,c922]) ).
cnf(c924,plain,
join(join(composition(converse(x0),x0),one),top) = join(join(X,one),complement(X)),
inference(transitivity,[status(thm)],[c906,c923]) ).
cnf(c925,plain,
join(top,join(composition(converse(x0),x0),one)) = join(join(X,one),complement(X)),
inference(transitivity,[status(thm)],[c904,c924]) ).
cnf(c926,plain,
join(join(X,one),complement(X)) = join(top,join(composition(converse(x0),x0),one)),
inference(symmetry,[status(thm)],[c925]) ).
cnf(c927,plain,
complement(join(join(X,one),complement(X))) = complement(join(top,join(composition(converse(x0),x0),one))),
inference(congruence,[status(thm)],[c926]) ).
cnf(c928,plain,
join(complement(X),join(X,one)) = join(join(X,one),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c929,plain,
join(join(X,one),complement(X)) = join(complement(X),join(X,one)),
inference(symmetry,[status(thm)],[c928]) ).
cnf(c930,plain,
join(join(composition(converse(x0),x0),one),X) = join(X,join(composition(converse(x0),x0),one)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c931,plain,
join(X,join(composition(converse(x0),x0),one)) = join(join(composition(converse(x0),x0),one),X),
inference(symmetry,[status(thm)],[c930]) ).
cnf(c932,plain,
join(X3,join(X,join(composition(converse(x0),x0),one))) = join(X3,join(join(composition(converse(x0),x0),one),X)),
inference(congruence,[status(thm)],[c931]) ).
cnf(c933,plain,
join(join(composition(converse(x0),x0),one),X) = join(one,X),
inference(congruence,[status(thm)],[c63]) ).
cnf(c934,plain,
join(X3,join(join(composition(converse(x0),x0),one),X)) = join(X3,join(one,X)),
inference(congruence,[status(thm)],[c933]) ).
cnf(c935,plain,
join(X3,join(one,X)) = join(join(X3,one),X),
inference(substitution,[status(thm)],[c18]) ).
cnf(c936,plain,
join(join(X3,one),X) = join(X,join(X3,one)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c937,plain,
join(X3,join(one,X)) = join(X,join(X3,one)),
inference(transitivity,[status(thm)],[c935,c936]) ).
cnf(c938,plain,
join(X3,join(join(composition(converse(x0),x0),one),X)) = join(X,join(X3,one)),
inference(transitivity,[status(thm)],[c934,c937]) ).
cnf(c939,plain,
join(X3,join(X,join(composition(converse(x0),x0),one))) = join(X,join(X3,one)),
inference(transitivity,[status(thm)],[c932,c938]) ).
cnf(c940,plain,
join(X,join(complement(X),join(composition(converse(x0),x0),one))) = join(complement(X),join(X,one)),
inference(substitution,[status(thm)],[c939]) ).
cnf(c941,plain,
join(complement(X),join(X,one)) = join(X,join(complement(X),join(composition(converse(x0),x0),one))),
inference(symmetry,[status(thm)],[c940]) ).
cnf(c942,plain,
join(X3,join(complement(X3),join(composition(converse(x0),x0),one))) = join(X,top),
inference(substitution,[status(thm)],[c184]) ).
cnf(c943,plain,
join(X,join(complement(X),join(composition(converse(x0),x0),one))) = top,
inference(transitivity,[status(thm)],[c942,c192]) ).
cnf(c944,plain,
join(complement(X),join(X,one)) = top,
inference(transitivity,[status(thm)],[c941,c943]) ).
cnf(c945,plain,
join(join(X,one),complement(X)) = top,
inference(transitivity,[status(thm)],[c929,c944]) ).
cnf(c946,plain,
join(top,join(composition(converse(x0),x0),one)) = top,
inference(transitivity,[status(thm)],[c925,c945]) ).
cnf(c947,plain,
complement(join(top,join(composition(converse(x0),x0),one))) = complement(top),
inference(congruence,[status(thm)],[c946]) ).
cnf(c948,plain,
complement(join(top,join(composition(converse(x0),x0),one))) = zero,
inference(transitivity,[status(thm)],[c947,c44]) ).
cnf(c949,plain,
complement(join(join(X,one),complement(X))) = zero,
inference(transitivity,[status(thm)],[c927,c948]) ).
cnf(c950,plain,
meet(X,complement(join(X,one))) = zero,
inference(transitivity,[status(thm)],[c902,c949]) ).
cnf(c951,plain,
zero = meet(X,complement(join(X,one))),
inference(symmetry,[status(thm)],[c950]) ).
cnf(c952,plain,
join(zero,complement(join(complement(X),complement(join(X,one))))) = join(meet(X,complement(join(X,one))),complement(join(complement(X),complement(join(X,one))))),
inference(congruence,[status(thm)],[c951]) ).
cnf(c953,plain,
join(meet(X,complement(join(X,one))),complement(join(complement(X),complement(join(X,one))))) = X,
inference(substitution,[status(thm)],[c118]) ).
cnf(c954,plain,
join(zero,complement(join(complement(X),complement(join(X,one))))) = X,
inference(transitivity,[status(thm)],[c952,c953]) ).
cnf(c955,plain,
complement(join(complement(X),complement(join(X,one)))) = X,
inference(transitivity,[status(thm)],[c900,c954]) ).
cnf(c956,plain,
meet(X,join(X,one)) = X,
inference(transitivity,[status(thm)],[c898,c955]) ).
cnf(c957,plain,
meet(join(X,one),X) = X,
inference(transitivity,[status(thm)],[c897,c956]) ).
cnf(c958,plain,
meet(join(composition(converse(x0),x0),one),composition(converse(x0),x0)) = composition(converse(x0),x0),
inference(substitution,[status(thm)],[c957]) ).
cnf(c959,plain,
meet(join(composition(converse(x0),x0),one),join(composition(converse(x0),x0),complement(join(composition(converse(x0),x0),one)))) = composition(converse(x0),x0),
inference(transitivity,[status(thm)],[c896,c958]) ).
cnf(c960,plain,
meet(join(composition(converse(x0),x0),one),join(complement(join(composition(converse(x0),x0),one)),composition(top,x0))) = composition(converse(x0),x0),
inference(transitivity,[status(thm)],[c895,c959]) ).
cnf(c961,plain,
meet(join(composition(converse(x0),x0),one),composition(top,x0)) = composition(converse(x0),x0),
inference(transitivity,[status(thm)],[c838,c960]) ).
cnf(c962,plain,
join(complement(composition(top,x0)),meet(join(composition(converse(x0),x0),one),composition(top,x0))) = join(complement(composition(top,x0)),composition(converse(x0),x0)),
inference(congruence,[status(thm)],[c961]) ).
cnf(c963,plain,
join(complement(composition(top,x0)),composition(converse(x0),x0)) = join(composition(converse(x0),x0),complement(composition(top,x0))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c964,plain,
join(complement(composition(top,x0)),meet(join(composition(converse(x0),x0),one),composition(top,x0))) = join(composition(converse(x0),x0),complement(composition(top,x0))),
inference(transitivity,[status(thm)],[c962,c963]) ).
cnf(c965,plain,
join(join(composition(converse(x0),x0),one),complement(composition(top,x0))) = join(composition(converse(x0),x0),complement(composition(top,x0))),
inference(transitivity,[status(thm)],[c836,c964]) ).
cnf(c966,plain,
join(composition(converse(x0),x0),complement(composition(top,x0))) = join(join(composition(converse(x0),x0),one),complement(composition(top,x0))),
inference(symmetry,[status(thm)],[c965]) ).
cnf(c967,plain,
composition(join(composition(converse(x0),x0),complement(composition(top,x0))),converse(x0)) = composition(join(join(composition(converse(x0),x0),one),complement(composition(top,x0))),converse(x0)),
inference(congruence,[status(thm)],[c966]) ).
cnf(c968,plain,
composition(join(join(composition(converse(x0),x0),one),complement(composition(top,x0))),converse(x0)) = composition(join(composition(converse(x0),x0),one),converse(x0)),
inference(substitution,[status(thm)],[c819]) ).
cnf(c969,plain,
composition(join(composition(converse(x0),x0),one),converse(x0)) = converse(x0),
inference(substitution,[status(thm)],[c89]) ).
cnf(c970,plain,
composition(join(join(composition(converse(x0),x0),one),complement(composition(top,x0))),converse(x0)) = converse(x0),
inference(transitivity,[status(thm)],[c968,c969]) ).
cnf(c971,plain,
composition(join(composition(converse(x0),x0),complement(composition(top,x0))),converse(x0)) = converse(x0),
inference(transitivity,[status(thm)],[c967,c970]) ).
cnf(c972,plain,
composition(composition(converse(x0),x0),converse(x0)) = converse(x0),
inference(transitivity,[status(thm)],[c821,c971]) ).
cnf(c973,plain,
converse(composition(composition(converse(x0),x0),converse(x0))) = converse(converse(x0)),
inference(congruence,[status(thm)],[c972]) ).
cnf(c974,plain,
converse(converse(x0)) = x0,
inference(substitution,[status(thm)],[c56]) ).
cnf(c975,plain,
converse(composition(composition(converse(x0),x0),converse(x0))) = x0,
inference(transitivity,[status(thm)],[c973,c974]) ).
cnf(c976,plain,
composition(converse(converse(x0)),converse(composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c736,c975]) ).
cnf(c977,plain,
composition(x0,converse(composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c734,c976]) ).
cnf(c978,plain,
composition(x0,composition(converse(x0),x0)) = x0,
inference(transitivity,[status(thm)],[c731,c977]) ).
cnf(c979,plain,
x0 = composition(x0,composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c978]) ).
cnf(c980,plain,
join(composition(converse(x0),x0),x0) = join(composition(converse(x0),x0),composition(x0,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c979]) ).
cnf(c981,plain,
composition(top,join(composition(converse(x0),x0),x0)) = composition(top,join(composition(converse(x0),x0),composition(x0,composition(converse(x0),x0)))),
inference(congruence,[status(thm)],[c980]) ).
cnf(c982,plain,
join(X3,composition(X,X3)) = composition(join(join(composition(converse(x0),x0),one),X),X3),
inference(symmetry,[status(thm)],[c662]) ).
cnf(c983,plain,
composition(top,join(X3,composition(X,X3))) = composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)),
inference(congruence,[status(thm)],[c982]) ).
cnf(c984,plain,
composition(join(top,join(composition(converse(x0),x0),one)),X) = join(X,composition(top,X)),
inference(substitution,[status(thm)],[c660]) ).
cnf(c985,plain,
join(X,composition(top,X)) = composition(join(top,join(composition(converse(x0),x0),one)),X),
inference(symmetry,[status(thm)],[c984]) ).
cnf(c986,plain,
composition(join(top,join(composition(converse(x0),x0),one)),X) = composition(top,X),
inference(congruence,[status(thm)],[c946]) ).
cnf(c987,plain,
join(X,composition(top,X)) = composition(top,X),
inference(transitivity,[status(thm)],[c985,c986]) ).
cnf(c988,plain,
join(composition(join(join(composition(converse(x0),x0),one),X),X3),composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3))) = composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)),
inference(substitution,[status(thm)],[c987]) ).
cnf(c989,plain,
composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)) = join(composition(join(join(composition(converse(x0),x0),one),X),X3),composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3))),
inference(symmetry,[status(thm)],[c988]) ).
cnf(c990,plain,
join(composition(join(join(composition(converse(x0),x0),one),X),X4),X3) = join(join(X4,composition(X,X4)),X3),
inference(congruence,[status(thm)],[c662]) ).
cnf(c991,plain,
join(X4,join(composition(X,X4),X3)) = join(join(X4,composition(X,X4)),X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c992,plain,
join(join(X4,composition(X,X4)),X3) = join(X4,join(composition(X,X4),X3)),
inference(symmetry,[status(thm)],[c991]) ).
cnf(c993,plain,
join(composition(X,X4),X3) = join(X3,composition(X,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c994,plain,
join(X4,join(composition(X,X4),X3)) = join(X4,join(X3,composition(X,X4))),
inference(congruence,[status(thm)],[c993]) ).
cnf(c995,plain,
join(join(X4,composition(X,X4)),X3) = join(X4,join(X3,composition(X,X4))),
inference(transitivity,[status(thm)],[c992,c994]) ).
cnf(c996,plain,
join(composition(join(join(composition(converse(x0),x0),one),X),X4),X3) = join(X4,join(X3,composition(X,X4))),
inference(transitivity,[status(thm)],[c990,c995]) ).
cnf(c997,plain,
join(composition(join(join(composition(converse(x0),x0),one),X),X3),composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3))) = join(X3,join(composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)),composition(X,X3))),
inference(substitution,[status(thm)],[c996]) ).
cnf(c998,axiom,
composition(X0_2,composition(X1_2,X2_2)) = composition(composition(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c999,plain,
composition(X4,composition(X3,X)) = composition(composition(X4,X3),X),
inference(substitution,[status(thm)],[c998]) ).
cnf(c1000,plain,
join(composition(X5,composition(X4,X3)),composition(X,X3)) = join(composition(composition(X5,X4),X3),composition(X,X3)),
inference(congruence,[status(thm)],[c999]) ).
cnf(c1001,plain,
composition(join(composition(X5,X4),X),X3) = join(composition(composition(X5,X4),X3),composition(X,X3)),
inference(substitution,[status(thm)],[c616]) ).
cnf(c1002,plain,
join(composition(composition(X5,X4),X3),composition(X,X3)) = composition(join(composition(X5,X4),X),X3),
inference(symmetry,[status(thm)],[c1001]) ).
cnf(c1003,plain,
join(composition(X4,X3),X) = join(X,composition(X4,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1004,plain,
composition(join(composition(X5,X4),X),X3) = composition(join(X,composition(X5,X4)),X3),
inference(congruence,[status(thm)],[c1003]) ).
cnf(c1005,plain,
join(composition(composition(X5,X4),X3),composition(X,X3)) = composition(join(X,composition(X5,X4)),X3),
inference(transitivity,[status(thm)],[c1002,c1004]) ).
cnf(c1006,plain,
join(composition(X5,composition(X4,X3)),composition(X,X3)) = composition(join(X,composition(X5,X4)),X3),
inference(transitivity,[status(thm)],[c1000,c1005]) ).
cnf(c1007,plain,
join(composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)),composition(X,X3)) = composition(join(X,composition(top,join(join(composition(converse(x0),x0),one),X))),X3),
inference(substitution,[status(thm)],[c1006]) ).
cnf(c1008,plain,
join(X3,join(composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)),composition(X,X3))) = join(X3,composition(join(X,composition(top,join(join(composition(converse(x0),x0),one),X))),X3)),
inference(congruence,[status(thm)],[c1007]) ).
cnf(c1009,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1010,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c1009]) ).
cnf(c1011,plain,
join(join(composition(converse(x0),x0),one),X) = join(join(composition(converse(x0),x0),one),converse(converse(X))),
inference(congruence,[status(thm)],[c1010]) ).
cnf(c1012,plain,
composition(top,join(join(composition(converse(x0),x0),one),X)) = composition(top,join(join(composition(converse(x0),x0),one),converse(converse(X)))),
inference(congruence,[status(thm)],[c1011]) ).
cnf(c1013,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c1014,plain,
composition(top,join(join(composition(converse(x0),x0),one),converse(X))) = composition(converse(top),join(join(composition(converse(x0),x0),one),converse(X))),
inference(congruence,[status(thm)],[c1013]) ).
cnf(c1015,plain,
join(converse(X),join(composition(converse(x0),x0),one)) = join(join(composition(converse(x0),x0),one),converse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1016,plain,
join(join(composition(converse(x0),x0),one),converse(X)) = join(converse(X),join(composition(converse(x0),x0),one)),
inference(symmetry,[status(thm)],[c1015]) ).
cnf(c1017,plain,
composition(converse(X3),join(join(composition(converse(x0),x0),one),converse(X))) = composition(converse(X3),join(converse(X),join(composition(converse(x0),x0),one))),
inference(congruence,[status(thm)],[c1016]) ).
cnf(c1018,plain,
join(composition(converse(x0),x0),one) = converse(join(composition(converse(x0),x0),one)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c1019,plain,
join(converse(X),join(composition(converse(x0),x0),one)) = join(converse(X),converse(join(composition(converse(x0),x0),one))),
inference(congruence,[status(thm)],[c1018]) ).
cnf(c1020,plain,
composition(converse(X3),join(converse(X),join(composition(converse(x0),x0),one))) = composition(converse(X3),join(converse(X),converse(join(composition(converse(x0),x0),one)))),
inference(congruence,[status(thm)],[c1019]) ).
cnf(c1021,plain,
converse(join(X,join(composition(converse(x0),x0),one))) = join(converse(X),converse(join(composition(converse(x0),x0),one))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c1022,plain,
join(converse(X),converse(join(composition(converse(x0),x0),one))) = converse(join(X,join(composition(converse(x0),x0),one))),
inference(symmetry,[status(thm)],[c1021]) ).
cnf(c1023,plain,
composition(converse(X3),join(converse(X),converse(join(composition(converse(x0),x0),one)))) = composition(converse(X3),converse(join(X,join(composition(converse(x0),x0),one)))),
inference(congruence,[status(thm)],[c1022]) ).
cnf(c1024,plain,
converse(composition(join(X,join(composition(converse(x0),x0),one)),X3)) = composition(converse(X3),converse(join(X,join(composition(converse(x0),x0),one)))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1025,plain,
composition(converse(X3),converse(join(X,join(composition(converse(x0),x0),one)))) = converse(composition(join(X,join(composition(converse(x0),x0),one)),X3)),
inference(symmetry,[status(thm)],[c1024]) ).
cnf(c1026,plain,
composition(join(X,join(composition(converse(x0),x0),one)),X3) = join(X3,composition(X,X3)),
inference(substitution,[status(thm)],[c660]) ).
cnf(c1027,plain,
converse(composition(join(X,join(composition(converse(x0),x0),one)),X3)) = converse(join(X3,composition(X,X3))),
inference(congruence,[status(thm)],[c1026]) ).
cnf(c1028,plain,
converse(join(X3,composition(X,X3))) = join(converse(X3),converse(composition(X,X3))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c1029,plain,
converse(composition(X,X3)) = composition(converse(X3),converse(X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1030,plain,
join(converse(X3),converse(composition(X,X3))) = join(converse(X3),composition(converse(X3),converse(X))),
inference(congruence,[status(thm)],[c1029]) ).
cnf(c1031,plain,
converse(join(X3,composition(X,X3))) = join(converse(X3),composition(converse(X3),converse(X))),
inference(transitivity,[status(thm)],[c1028,c1030]) ).
cnf(c1032,plain,
converse(composition(join(X,join(composition(converse(x0),x0),one)),X3)) = join(converse(X3),composition(converse(X3),converse(X))),
inference(transitivity,[status(thm)],[c1027,c1031]) ).
cnf(c1033,plain,
composition(converse(X3),converse(join(X,join(composition(converse(x0),x0),one)))) = join(converse(X3),composition(converse(X3),converse(X))),
inference(transitivity,[status(thm)],[c1025,c1032]) ).
cnf(c1034,plain,
composition(converse(X3),join(converse(X),converse(join(composition(converse(x0),x0),one)))) = join(converse(X3),composition(converse(X3),converse(X))),
inference(transitivity,[status(thm)],[c1023,c1033]) ).
cnf(c1035,plain,
composition(converse(X3),join(converse(X),join(composition(converse(x0),x0),one))) = join(converse(X3),composition(converse(X3),converse(X))),
inference(transitivity,[status(thm)],[c1020,c1034]) ).
cnf(c1036,plain,
composition(converse(X3),join(join(composition(converse(x0),x0),one),converse(X))) = join(converse(X3),composition(converse(X3),converse(X))),
inference(transitivity,[status(thm)],[c1017,c1035]) ).
cnf(c1037,plain,
composition(converse(top),join(join(composition(converse(x0),x0),one),converse(X))) = join(converse(top),composition(converse(top),converse(X))),
inference(substitution,[status(thm)],[c1036]) ).
cnf(c1038,plain,
join(converse(top),composition(converse(top),converse(X))) = join(top,composition(converse(top),converse(X))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c1039,plain,
composition(converse(top),converse(X)) = composition(top,converse(X)),
inference(congruence,[status(thm)],[c203]) ).
cnf(c1040,plain,
join(top,composition(converse(top),converse(X))) = join(top,composition(top,converse(X))),
inference(congruence,[status(thm)],[c1039]) ).
cnf(c1041,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1042,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c1041]) ).
cnf(c1043,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c1044,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c1043,c192]) ).
cnf(c1045,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c1042,c1044]) ).
cnf(c1046,plain,
join(top,composition(top,converse(X))) = top,
inference(substitution,[status(thm)],[c1045]) ).
cnf(c1047,plain,
join(top,composition(converse(top),converse(X))) = top,
inference(transitivity,[status(thm)],[c1040,c1046]) ).
cnf(c1048,plain,
join(converse(top),composition(converse(top),converse(X))) = top,
inference(transitivity,[status(thm)],[c1038,c1047]) ).
cnf(c1049,plain,
composition(converse(top),join(join(composition(converse(x0),x0),one),converse(X))) = top,
inference(transitivity,[status(thm)],[c1037,c1048]) ).
cnf(c1050,plain,
composition(top,join(join(composition(converse(x0),x0),one),converse(X))) = top,
inference(transitivity,[status(thm)],[c1014,c1049]) ).
cnf(c1051,plain,
composition(top,join(join(composition(converse(x0),x0),one),converse(converse(X)))) = top,
inference(substitution,[status(thm)],[c1050]) ).
cnf(c1052,plain,
composition(top,join(join(composition(converse(x0),x0),one),X)) = top,
inference(transitivity,[status(thm)],[c1012,c1051]) ).
cnf(c1053,plain,
join(X,composition(top,join(join(composition(converse(x0),x0),one),X))) = join(X,top),
inference(congruence,[status(thm)],[c1052]) ).
cnf(c1054,plain,
composition(join(X,composition(top,join(join(composition(converse(x0),x0),one),X))),X3) = composition(join(X,top),X3),
inference(congruence,[status(thm)],[c1053]) ).
cnf(c1055,plain,
join(X3,composition(join(X,composition(top,join(join(composition(converse(x0),x0),one),X))),X3)) = join(X3,composition(join(X,top),X3)),
inference(congruence,[status(thm)],[c1054]) ).
cnf(c1056,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c1057,plain,
composition(join(X3,top),X4) = composition(join(X,top),X4),
inference(congruence,[status(thm)],[c1056]) ).
cnf(c1058,plain,
join(X4,composition(join(X3,top),X4)) = join(X4,composition(join(X,top),X4)),
inference(congruence,[status(thm)],[c1057]) ).
cnf(c1059,plain,
composition(join(X,top),X3) = composition(top,X3),
inference(congruence,[status(thm)],[c192]) ).
cnf(c1060,plain,
join(X3,composition(join(X,top),X3)) = join(X3,composition(top,X3)),
inference(congruence,[status(thm)],[c1059]) ).
cnf(c1061,plain,
join(X3,composition(join(X,top),X3)) = composition(top,X3),
inference(transitivity,[status(thm)],[c1060,c987]) ).
cnf(c1062,plain,
join(X3,composition(join(X,top),X3)) = composition(top,X3),
inference(transitivity,[status(thm)],[c1058,c1061]) ).
cnf(c1063,plain,
join(X3,composition(join(X,composition(top,join(join(composition(converse(x0),x0),one),X))),X3)) = composition(top,X3),
inference(transitivity,[status(thm)],[c1055,c1062]) ).
cnf(c1064,plain,
join(X3,join(composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)),composition(X,X3))) = composition(top,X3),
inference(transitivity,[status(thm)],[c1008,c1063]) ).
cnf(c1065,plain,
join(composition(join(join(composition(converse(x0),x0),one),X),X3),composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3))) = composition(top,X3),
inference(transitivity,[status(thm)],[c997,c1064]) ).
cnf(c1066,plain,
composition(top,composition(join(join(composition(converse(x0),x0),one),X),X3)) = composition(top,X3),
inference(transitivity,[status(thm)],[c989,c1065]) ).
cnf(c1067,plain,
composition(top,join(X3,composition(X,X3))) = composition(top,X3),
inference(transitivity,[status(thm)],[c983,c1066]) ).
cnf(c1068,plain,
composition(top,join(composition(converse(x0),x0),composition(x0,composition(converse(x0),x0)))) = composition(top,composition(converse(x0),x0)),
inference(substitution,[status(thm)],[c1067]) ).
cnf(c1069,plain,
composition(top,join(composition(converse(x0),x0),x0)) = composition(top,composition(converse(x0),x0)),
inference(transitivity,[status(thm)],[c981,c1068]) ).
cnf(c1070,plain,
composition(top,composition(converse(x0),x0)) = composition(top,join(composition(converse(x0),x0),x0)),
inference(symmetry,[status(thm)],[c1069]) ).
cnf(c1071,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1072,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c1071]) ).
cnf(c1073,plain,
join(composition(converse(X3),X),X) = join(composition(converse(X3),X),converse(converse(X))),
inference(congruence,[status(thm)],[c1072]) ).
cnf(c1074,plain,
composition(top,join(composition(converse(X3),X),X)) = composition(top,join(composition(converse(X3),X),converse(converse(X)))),
inference(congruence,[status(thm)],[c1073]) ).
cnf(c1075,plain,
converse(composition(converse(X),X3)) = composition(converse(X3),X),
inference(substitution,[status(thm)],[c427]) ).
cnf(c1076,plain,
composition(converse(X3),X) = converse(composition(converse(X),X3)),
inference(symmetry,[status(thm)],[c1075]) ).
cnf(c1077,plain,
join(composition(converse(X3),X),converse(converse(X))) = join(converse(composition(converse(X),X3)),converse(converse(X))),
inference(congruence,[status(thm)],[c1076]) ).
cnf(c1078,plain,
composition(top,join(composition(converse(X3),X),converse(converse(X)))) = composition(top,join(converse(composition(converse(X),X3)),converse(converse(X)))),
inference(congruence,[status(thm)],[c1077]) ).
cnf(c1079,plain,
converse(join(composition(converse(X),X3),converse(X))) = join(converse(composition(converse(X),X3)),converse(converse(X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c1080,plain,
join(converse(composition(converse(X),X3)),converse(converse(X))) = converse(join(composition(converse(X),X3),converse(X))),
inference(symmetry,[status(thm)],[c1079]) ).
cnf(c1081,plain,
composition(top,join(converse(composition(converse(X),X3)),converse(converse(X)))) = composition(top,converse(join(composition(converse(X),X3),converse(X)))),
inference(congruence,[status(thm)],[c1080]) ).
cnf(c1082,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c1083,plain,
composition(top,converse(join(composition(converse(X),X3),converse(X)))) = composition(converse(top),converse(join(composition(converse(X),X3),converse(X)))),
inference(congruence,[status(thm)],[c1082]) ).
cnf(c1084,plain,
converse(composition(join(composition(converse(X),X3),converse(X)),top)) = composition(converse(top),converse(join(composition(converse(X),X3),converse(X)))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1085,plain,
composition(converse(top),converse(join(composition(converse(X),X3),converse(X)))) = converse(composition(join(composition(converse(X),X3),converse(X)),top)),
inference(symmetry,[status(thm)],[c1084]) ).
cnf(c1086,plain,
join(converse(X3),composition(converse(X3),X)) = join(composition(converse(X3),X),converse(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1087,plain,
join(composition(converse(X3),X),converse(X3)) = join(converse(X3),composition(converse(X3),X)),
inference(symmetry,[status(thm)],[c1086]) ).
cnf(c1088,plain,
composition(join(composition(converse(X3),X),converse(X3)),top) = composition(join(converse(X3),composition(converse(X3),X)),top),
inference(congruence,[status(thm)],[c1087]) ).
cnf(c1089,plain,
composition(join(converse(X3),composition(converse(X3),X)),top) = join(composition(converse(X3),top),composition(composition(converse(X3),X),top)),
inference(substitution,[status(thm)],[c616]) ).
cnf(c1090,plain,
join(zero,meet(top,complement(zero))) = complement(zero),
inference(substitution,[status(thm)],[c216]) ).
cnf(c1091,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(symmetry,[status(thm)],[c1090]) ).
cnf(c1092,plain,
meet(top,zero) = zero,
inference(substitution,[status(thm)],[c232]) ).
cnf(c1093,plain,
zero = meet(top,zero),
inference(symmetry,[status(thm)],[c1092]) ).
cnf(c1094,plain,
join(zero,meet(top,complement(zero))) = join(meet(top,zero),meet(top,complement(zero))),
inference(congruence,[status(thm)],[c1093]) ).
cnf(c1095,plain,
join(meet(top,zero),meet(top,complement(zero))) = top,
inference(substitution,[status(thm)],[c305]) ).
cnf(c1096,plain,
join(zero,meet(top,complement(zero))) = top,
inference(transitivity,[status(thm)],[c1094,c1095]) ).
cnf(c1097,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c1091,c1096]) ).
cnf(c1098,plain,
top = complement(zero),
inference(symmetry,[status(thm)],[c1097]) ).
cnf(c1099,plain,
composition(composition(converse(X3),X),top) = composition(composition(converse(X3),X),complement(zero)),
inference(congruence,[status(thm)],[c1098]) ).
cnf(c1100,plain,
join(composition(converse(X3),top),composition(composition(converse(X3),X),top)) = join(composition(converse(X3),top),composition(composition(converse(X3),X),complement(zero))),
inference(congruence,[status(thm)],[c1099]) ).
cnf(c1101,plain,
converse(composition(converse(X),X3)) = composition(converse(X3),X),
inference(substitution,[status(thm)],[c427]) ).
cnf(c1102,plain,
composition(converse(X3),X) = converse(composition(converse(X),X3)),
inference(symmetry,[status(thm)],[c1101]) ).
cnf(c1103,plain,
composition(composition(converse(X3),X),complement(zero)) = composition(converse(composition(converse(X),X3)),complement(zero)),
inference(congruence,[status(thm)],[c1102]) ).
cnf(c1104,plain,
join(composition(converse(X3),top),composition(composition(converse(X3),X),complement(zero))) = join(composition(converse(X3),top),composition(converse(composition(converse(X),X3)),complement(zero))),
inference(congruence,[status(thm)],[c1103]) ).
cnf(c1105,plain,
complement(complement(composition(converse(X),top))) = composition(converse(X),top),
inference(substitution,[status(thm)],[c450]) ).
cnf(c1106,plain,
composition(converse(X),top) = complement(complement(composition(converse(X),top))),
inference(symmetry,[status(thm)],[c1105]) ).
cnf(c1107,plain,
join(composition(converse(X3),top),composition(converse(composition(converse(X),X3)),complement(zero))) = join(complement(complement(composition(converse(X3),top))),composition(converse(composition(converse(X),X3)),complement(zero))),
inference(congruence,[status(thm)],[c1106]) ).
cnf(c1108,plain,
composition(X3,composition(X,complement(composition(converse(X),top)))) = composition(composition(X3,X),complement(composition(converse(X),top))),
inference(substitution,[status(thm)],[c998]) ).
cnf(c1109,plain,
composition(composition(X3,X),complement(composition(converse(X),top))) = composition(X3,composition(X,complement(composition(converse(X),top)))),
inference(symmetry,[status(thm)],[c1108]) ).
cnf(c1110,plain,
composition(X3,composition(X,complement(composition(converse(X),top)))) = composition(X3,zero),
inference(congruence,[status(thm)],[c771]) ).
cnf(c1111,plain,
join(composition(X,zero),zero) = composition(X,zero),
inference(substitution,[status(thm)],[c272]) ).
cnf(c1112,plain,
composition(X,zero) = join(composition(X,zero),zero),
inference(symmetry,[status(thm)],[c1111]) ).
cnf(c1113,plain,
join(zero,composition(top,zero)) = composition(top,zero),
inference(substitution,[status(thm)],[c987]) ).
cnf(c1114,plain,
composition(top,zero) = join(zero,composition(top,zero)),
inference(symmetry,[status(thm)],[c1113]) ).
cnf(c1115,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c1116,plain,
composition(top,zero) = composition(converse(top),zero),
inference(congruence,[status(thm)],[c1115]) ).
cnf(c1117,plain,
join(zero,composition(top,zero)) = join(zero,composition(converse(top),zero)),
inference(congruence,[status(thm)],[c1116]) ).
cnf(c1118,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c1119,plain,
join(zero,composition(converse(top),zero)) = join(complement(top),composition(converse(top),zero)),
inference(congruence,[status(thm)],[c1118]) ).
cnf(c1120,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c1121,plain,
composition(converse(top),zero) = composition(converse(top),complement(top)),
inference(congruence,[status(thm)],[c1120]) ).
cnf(c1122,plain,
join(complement(top),composition(converse(top),zero)) = join(complement(top),composition(converse(top),complement(top))),
inference(congruence,[status(thm)],[c1121]) ).
cnf(c1123,plain,
join(top,composition(top,top)) = composition(top,top),
inference(substitution,[status(thm)],[c987]) ).
cnf(c1124,plain,
composition(top,top) = join(top,composition(top,top)),
inference(symmetry,[status(thm)],[c1123]) ).
cnf(c1125,plain,
join(top,composition(top,top)) = top,
inference(substitution,[status(thm)],[c1045]) ).
cnf(c1126,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c1124,c1125]) ).
cnf(c1127,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c1126]) ).
cnf(c1128,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c1127]) ).
cnf(c1129,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c1128]) ).
cnf(c1130,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c1129]) ).
cnf(c1131,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c98]) ).
cnf(c1132,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c1131,c44]) ).
cnf(c1133,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c1130,c1132]) ).
cnf(c1134,plain,
join(complement(top),composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c1122,c1133]) ).
cnf(c1135,plain,
join(zero,composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c1119,c1134]) ).
cnf(c1136,plain,
join(zero,composition(top,zero)) = zero,
inference(transitivity,[status(thm)],[c1117,c1135]) ).
cnf(c1137,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c1114,c1136]) ).
cnf(c1138,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c1137]) ).
cnf(c1139,plain,
join(composition(X,zero),zero) = join(composition(X,zero),composition(top,zero)),
inference(congruence,[status(thm)],[c1138]) ).
cnf(c1140,plain,
composition(join(X,top),zero) = join(composition(X,zero),composition(top,zero)),
inference(substitution,[status(thm)],[c616]) ).
cnf(c1141,plain,
join(composition(X,zero),composition(top,zero)) = composition(join(X,top),zero),
inference(symmetry,[status(thm)],[c1140]) ).
cnf(c1142,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c1143,plain,
composition(join(X3,top),zero) = composition(join(X,top),zero),
inference(congruence,[status(thm)],[c1142]) ).
cnf(c1144,plain,
composition(join(X,top),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c192]) ).
cnf(c1145,plain,
composition(join(X,top),zero) = zero,
inference(transitivity,[status(thm)],[c1144,c1137]) ).
cnf(c1146,plain,
composition(join(X,top),zero) = zero,
inference(transitivity,[status(thm)],[c1143,c1145]) ).
cnf(c1147,plain,
join(composition(X,zero),composition(top,zero)) = zero,
inference(transitivity,[status(thm)],[c1141,c1146]) ).
cnf(c1148,plain,
join(composition(X,zero),zero) = zero,
inference(transitivity,[status(thm)],[c1139,c1147]) ).
cnf(c1149,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c1112,c1148]) ).
cnf(c1150,plain,
composition(X3,composition(X,complement(composition(converse(X),top)))) = zero,
inference(transitivity,[status(thm)],[c1110,c1149]) ).
cnf(c1151,plain,
composition(composition(X3,X),complement(composition(converse(X),top))) = zero,
inference(transitivity,[status(thm)],[c1109,c1150]) ).
cnf(c1152,plain,
composition(composition(converse(X),X3),complement(composition(converse(X3),top))) = zero,
inference(substitution,[status(thm)],[c1151]) ).
cnf(c1153,plain,
zero = composition(composition(converse(X),X3),complement(composition(converse(X3),top))),
inference(symmetry,[status(thm)],[c1152]) ).
cnf(c1154,plain,
complement(zero) = complement(composition(composition(converse(X),X3),complement(composition(converse(X3),top)))),
inference(congruence,[status(thm)],[c1153]) ).
cnf(c1155,plain,
composition(converse(composition(converse(X),X3)),complement(zero)) = composition(converse(composition(converse(X),X3)),complement(composition(composition(converse(X),X3),complement(composition(converse(X3),top))))),
inference(congruence,[status(thm)],[c1154]) ).
cnf(c1156,plain,
join(complement(complement(composition(converse(X3),top))),composition(converse(composition(converse(X),X3)),complement(zero))) = join(complement(complement(composition(converse(X3),top))),composition(converse(composition(converse(X),X3)),complement(composition(composition(converse(X),X3),complement(composition(converse(X3),top)))))),
inference(congruence,[status(thm)],[c1155]) ).
cnf(c1157,plain,
join(complement(complement(composition(converse(X3),top))),composition(converse(composition(converse(X),X3)),complement(composition(composition(converse(X),X3),complement(composition(converse(X3),top)))))) = complement(complement(composition(converse(X3),top))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c1158,plain,
complement(complement(composition(converse(X),top))) = composition(converse(X),top),
inference(substitution,[status(thm)],[c450]) ).
cnf(c1159,plain,
join(complement(complement(composition(converse(X3),top))),composition(converse(composition(converse(X),X3)),complement(composition(composition(converse(X),X3),complement(composition(converse(X3),top)))))) = composition(converse(X3),top),
inference(transitivity,[status(thm)],[c1157,c1158]) ).
cnf(c1160,plain,
join(complement(complement(composition(converse(X3),top))),composition(converse(composition(converse(X),X3)),complement(zero))) = composition(converse(X3),top),
inference(transitivity,[status(thm)],[c1156,c1159]) ).
cnf(c1161,plain,
join(composition(converse(X3),top),composition(converse(composition(converse(X),X3)),complement(zero))) = composition(converse(X3),top),
inference(transitivity,[status(thm)],[c1107,c1160]) ).
cnf(c1162,plain,
join(composition(converse(X3),top),composition(composition(converse(X3),X),complement(zero))) = composition(converse(X3),top),
inference(transitivity,[status(thm)],[c1104,c1161]) ).
cnf(c1163,plain,
join(composition(converse(X3),top),composition(composition(converse(X3),X),top)) = composition(converse(X3),top),
inference(transitivity,[status(thm)],[c1100,c1162]) ).
cnf(c1164,plain,
composition(join(converse(X3),composition(converse(X3),X)),top) = composition(converse(X3),top),
inference(transitivity,[status(thm)],[c1089,c1163]) ).
cnf(c1165,plain,
composition(join(composition(converse(X3),X),converse(X3)),top) = composition(converse(X3),top),
inference(transitivity,[status(thm)],[c1088,c1164]) ).
cnf(c1166,plain,
composition(join(composition(converse(X),X3),converse(X)),top) = composition(converse(X),top),
inference(substitution,[status(thm)],[c1165]) ).
cnf(c1167,plain,
converse(composition(join(composition(converse(X),X3),converse(X)),top)) = converse(composition(converse(X),top)),
inference(congruence,[status(thm)],[c1166]) ).
cnf(c1168,plain,
converse(composition(converse(X),top)) = composition(converse(top),converse(converse(X))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1169,plain,
composition(converse(top),converse(converse(X))) = composition(top,converse(converse(X))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c1170,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1171,plain,
composition(top,converse(converse(X))) = composition(top,X),
inference(congruence,[status(thm)],[c1170]) ).
cnf(c1172,plain,
composition(converse(top),converse(converse(X))) = composition(top,X),
inference(transitivity,[status(thm)],[c1169,c1171]) ).
cnf(c1173,plain,
converse(composition(converse(X),top)) = composition(top,X),
inference(transitivity,[status(thm)],[c1168,c1172]) ).
cnf(c1174,plain,
converse(composition(join(composition(converse(X),X3),converse(X)),top)) = composition(top,X),
inference(transitivity,[status(thm)],[c1167,c1173]) ).
cnf(c1175,plain,
composition(converse(top),converse(join(composition(converse(X),X3),converse(X)))) = composition(top,X),
inference(transitivity,[status(thm)],[c1085,c1174]) ).
cnf(c1176,plain,
composition(top,converse(join(composition(converse(X),X3),converse(X)))) = composition(top,X),
inference(transitivity,[status(thm)],[c1083,c1175]) ).
cnf(c1177,plain,
composition(top,join(converse(composition(converse(X),X3)),converse(converse(X)))) = composition(top,X),
inference(transitivity,[status(thm)],[c1081,c1176]) ).
cnf(c1178,plain,
composition(top,join(composition(converse(X3),X),converse(converse(X)))) = composition(top,X),
inference(transitivity,[status(thm)],[c1078,c1177]) ).
cnf(c1179,plain,
composition(top,join(composition(converse(X3),X),X)) = composition(top,X),
inference(transitivity,[status(thm)],[c1074,c1178]) ).
cnf(c1180,plain,
composition(top,join(composition(converse(x0),x0),x0)) = composition(top,x0),
inference(substitution,[status(thm)],[c1179]) ).
cnf(c1181,plain,
composition(top,composition(converse(x0),x0)) = composition(top,x0),
inference(transitivity,[status(thm)],[c1070,c1180]) ).
cnf(c1182,plain,
complement(composition(top,composition(converse(x0),x0))) = complement(composition(top,x0)),
inference(congruence,[status(thm)],[c1181]) ).
cnf(c1183,plain,
join(X,complement(composition(top,composition(converse(x0),x0)))) = join(X,complement(composition(top,x0))),
inference(congruence,[status(thm)],[c1182]) ).
cnf(c1184,plain,
composition(join(X,complement(composition(top,composition(converse(x0),x0)))),converse(x0)) = composition(join(X,complement(composition(top,x0))),converse(x0)),
inference(congruence,[status(thm)],[c1183]) ).
cnf(c1185,plain,
join(complement(composition(top,x0)),X) = join(X,complement(composition(top,x0))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1186,plain,
join(X,complement(composition(top,x0))) = join(complement(composition(top,x0)),X),
inference(symmetry,[status(thm)],[c1185]) ).
cnf(c1187,plain,
composition(join(X,complement(composition(top,x0))),converse(x0)) = composition(join(complement(composition(top,x0)),X),converse(x0)),
inference(congruence,[status(thm)],[c1186]) ).
cnf(c1188,plain,
composition(join(complement(composition(top,x0)),X),converse(x0)) = join(composition(complement(composition(top,x0)),converse(x0)),composition(X,converse(x0))),
inference(substitution,[status(thm)],[c616]) ).
cnf(c1189,plain,
composition(complement(composition(top,x0)),converse(x0)) = zero,
inference(substitution,[status(thm)],[c814]) ).
cnf(c1190,plain,
join(composition(complement(composition(top,x0)),converse(x0)),composition(X,converse(x0))) = join(zero,composition(X,converse(x0))),
inference(congruence,[status(thm)],[c1189]) ).
cnf(c1191,plain,
join(zero,composition(X,converse(x0))) = composition(X,converse(x0)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c1192,plain,
join(composition(complement(composition(top,x0)),converse(x0)),composition(X,converse(x0))) = composition(X,converse(x0)),
inference(transitivity,[status(thm)],[c1190,c1191]) ).
cnf(c1193,plain,
composition(join(complement(composition(top,x0)),X),converse(x0)) = composition(X,converse(x0)),
inference(transitivity,[status(thm)],[c1188,c1192]) ).
cnf(c1194,plain,
composition(join(X,complement(composition(top,x0))),converse(x0)) = composition(X,converse(x0)),
inference(transitivity,[status(thm)],[c1187,c1193]) ).
cnf(c1195,plain,
composition(join(X,complement(composition(top,composition(converse(x0),x0)))),converse(x0)) = composition(X,converse(x0)),
inference(transitivity,[status(thm)],[c1184,c1194]) ).
cnf(c1196,plain,
composition(join(complement(X),complement(composition(top,composition(converse(x0),x0)))),converse(x0)) = composition(complement(X),converse(x0)),
inference(substitution,[status(thm)],[c1195]) ).
cnf(c1197,plain,
composition(complement(meet(X,composition(top,composition(converse(x0),x0)))),converse(x0)) = composition(complement(X),converse(x0)),
inference(transitivity,[status(thm)],[c728,c1196]) ).
cnf(c1198,plain,
composition(complement(composition(X,composition(converse(x0),x0))),converse(x0)) = composition(complement(X),converse(x0)),
inference(transitivity,[status(thm)],[c725,c1197]) ).
cnf(c1199,plain,
converse(composition(complement(composition(X,composition(converse(x0),x0))),converse(x0))) = converse(composition(complement(X),converse(x0))),
inference(congruence,[status(thm)],[c1198]) ).
cnf(c1200,plain,
converse(composition(complement(X),converse(x0))) = composition(converse(converse(x0)),converse(complement(X))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1201,plain,
converse(converse(x0)) = x0,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1202,plain,
composition(converse(converse(x0)),converse(complement(X))) = composition(x0,converse(complement(X))),
inference(congruence,[status(thm)],[c1201]) ).
cnf(c1203,plain,
composition(x0,converse(complement(X))) = composition(x0,complement(converse(X))),
inference(congruence,[status(thm)],[c596]) ).
cnf(c1204,plain,
composition(converse(converse(x0)),converse(complement(X))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c1202,c1203]) ).
cnf(c1205,plain,
converse(composition(complement(X),converse(x0))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c1200,c1204]) ).
cnf(c1206,plain,
converse(composition(complement(composition(X,composition(converse(x0),x0))),converse(x0))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c1199,c1205]) ).
cnf(c1207,plain,
composition(converse(converse(x0)),converse(complement(composition(X,composition(converse(x0),x0))))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c604,c1206]) ).
cnf(c1208,plain,
composition(x0,converse(complement(composition(X,composition(converse(x0),x0))))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c602,c1207]) ).
cnf(c1209,plain,
composition(x0,complement(converse(composition(X,composition(converse(x0),x0))))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c599,c1208]) ).
cnf(c1210,plain,
composition(x0,complement(composition(converse(composition(converse(x0),x0)),converse(X)))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c436,c1209]) ).
cnf(c1211,plain,
composition(x0,complement(composition(composition(converse(x0),x0),converse(X)))) = composition(x0,complement(converse(X))),
inference(transitivity,[status(thm)],[c432,c1210]) ).
cnf(c1212,plain,
composition(x0,complement(composition(composition(converse(x0),x0),converse(converse(X))))) = composition(x0,complement(converse(converse(X)))),
inference(substitution,[status(thm)],[c1211]) ).
cnf(c1213,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1214,plain,
complement(converse(converse(X))) = complement(X),
inference(congruence,[status(thm)],[c1213]) ).
cnf(c1215,plain,
composition(x0,complement(converse(converse(X)))) = composition(x0,complement(X)),
inference(congruence,[status(thm)],[c1214]) ).
cnf(c1216,plain,
composition(x0,complement(composition(composition(converse(x0),x0),converse(converse(X))))) = composition(x0,complement(X)),
inference(transitivity,[status(thm)],[c1212,c1215]) ).
cnf(c1217,plain,
composition(x0,complement(composition(composition(converse(x0),x0),X))) = composition(x0,complement(X)),
inference(transitivity,[status(thm)],[c423,c1216]) ).
cnf(c1218,plain,
composition(x0,complement(X)) = composition(x0,complement(composition(composition(converse(x0),x0),X))),
inference(symmetry,[status(thm)],[c1217]) ).
cnf(c1219,plain,
join(complement(composition(x0,X)),composition(x0,complement(X))) = join(complement(composition(x0,X)),composition(x0,complement(composition(composition(converse(x0),x0),X)))),
inference(congruence,[status(thm)],[c1218]) ).
cnf(c1220,plain,
converse(converse(x0)) = x0,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1221,plain,
x0 = converse(converse(x0)),
inference(symmetry,[status(thm)],[c1220]) ).
cnf(c1222,plain,
composition(x0,complement(composition(composition(converse(x0),x0),X))) = composition(converse(converse(x0)),complement(composition(composition(converse(x0),x0),X))),
inference(congruence,[status(thm)],[c1221]) ).
cnf(c1223,plain,
join(complement(composition(x0,X)),composition(x0,complement(composition(composition(converse(x0),x0),X)))) = join(complement(composition(x0,X)),composition(converse(converse(x0)),complement(composition(composition(converse(x0),x0),X)))),
inference(congruence,[status(thm)],[c1222]) ).
cnf(c1224,plain,
composition(converse(x0),composition(x0,X)) = composition(composition(converse(x0),x0),X),
inference(substitution,[status(thm)],[c998]) ).
cnf(c1225,plain,
composition(composition(converse(x0),x0),X) = composition(converse(x0),composition(x0,X)),
inference(symmetry,[status(thm)],[c1224]) ).
cnf(c1226,plain,
complement(composition(composition(converse(x0),x0),X)) = complement(composition(converse(x0),composition(x0,X))),
inference(congruence,[status(thm)],[c1225]) ).
cnf(c1227,plain,
composition(converse(converse(x0)),complement(composition(composition(converse(x0),x0),X))) = composition(converse(converse(x0)),complement(composition(converse(x0),composition(x0,X)))),
inference(congruence,[status(thm)],[c1226]) ).
cnf(c1228,plain,
join(complement(composition(x0,X)),composition(converse(converse(x0)),complement(composition(composition(converse(x0),x0),X)))) = join(complement(composition(x0,X)),composition(converse(converse(x0)),complement(composition(converse(x0),composition(x0,X))))),
inference(congruence,[status(thm)],[c1227]) ).
cnf(c1229,plain,
join(complement(composition(x0,X)),composition(converse(converse(x0)),complement(composition(converse(x0),composition(x0,X))))) = complement(composition(x0,X)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c1230,plain,
join(complement(composition(x0,X)),composition(converse(converse(x0)),complement(composition(composition(converse(x0),x0),X)))) = complement(composition(x0,X)),
inference(transitivity,[status(thm)],[c1228,c1229]) ).
cnf(c1231,plain,
join(complement(composition(x0,X)),composition(x0,complement(composition(composition(converse(x0),x0),X)))) = complement(composition(x0,X)),
inference(transitivity,[status(thm)],[c1223,c1230]) ).
cnf(c1232,plain,
join(complement(composition(x0,X)),composition(x0,complement(X))) = complement(composition(x0,X)),
inference(transitivity,[status(thm)],[c1219,c1231]) ).
cnf(c1233,plain,
join(X,join(complement(composition(x0,X3)),composition(x0,complement(X3)))) = join(X,complement(composition(x0,X3))),
inference(congruence,[status(thm)],[c1232]) ).
cnf(c1234,plain,
meet(composition(x0,X3),join(X,join(complement(composition(x0,X3)),composition(x0,complement(X3))))) = meet(composition(x0,X3),join(X,complement(composition(x0,X3)))),
inference(congruence,[status(thm)],[c1233]) ).
cnf(c1235,plain,
meet(composition(x0,X3),join(X,complement(composition(x0,X3)))) = meet(composition(x0,X3),X),
inference(substitution,[status(thm)],[c413]) ).
cnf(c1236,plain,
meet(X,composition(x0,X3)) = meet(composition(x0,X3),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c1237,plain,
meet(composition(x0,X3),X) = meet(X,composition(x0,X3)),
inference(symmetry,[status(thm)],[c1236]) ).
cnf(c1238,plain,
meet(composition(x0,X3),join(X,complement(composition(x0,X3)))) = meet(X,composition(x0,X3)),
inference(transitivity,[status(thm)],[c1235,c1237]) ).
cnf(c1239,plain,
meet(composition(x0,X3),join(X,join(complement(composition(x0,X3)),composition(x0,complement(X3))))) = meet(X,composition(x0,X3)),
inference(transitivity,[status(thm)],[c1234,c1238]) ).
cnf(c1240,plain,
meet(composition(x0,X3),join(X,composition(x0,complement(X3)))) = meet(X,composition(x0,X3)),
inference(transitivity,[status(thm)],[c418,c1239]) ).
cnf(c1241,plain,
meet(composition(x0,X3),join(composition(x0,X),composition(x0,complement(X3)))) = meet(composition(x0,X),composition(x0,X3)),
inference(substitution,[status(thm)],[c1240]) ).
cnf(c1242,plain,
meet(composition(x0,X),composition(x0,X3)) = meet(composition(x0,X3),join(composition(x0,X),composition(x0,complement(X3)))),
inference(symmetry,[status(thm)],[c1241]) ).
cnf(c1243,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1244,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c1243]) ).
cnf(c1245,plain,
composition(X3,X) = composition(X3,converse(converse(X))),
inference(congruence,[status(thm)],[c1244]) ).
cnf(c1246,plain,
join(composition(X4,X3),composition(X4,X)) = join(composition(X4,X3),composition(X4,converse(converse(X)))),
inference(congruence,[status(thm)],[c1245]) ).
cnf(c1247,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1248,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c1247]) ).
cnf(c1249,plain,
composition(X3,converse(X)) = composition(converse(converse(X3)),converse(X)),
inference(congruence,[status(thm)],[c1248]) ).
cnf(c1250,plain,
join(composition(X4,X3),composition(X4,converse(X))) = join(composition(X4,X3),composition(converse(converse(X4)),converse(X))),
inference(congruence,[status(thm)],[c1249]) ).
cnf(c1251,plain,
converse(composition(X,converse(X3))) = composition(converse(converse(X3)),converse(X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1252,plain,
composition(converse(converse(X3)),converse(X)) = converse(composition(X,converse(X3))),
inference(symmetry,[status(thm)],[c1251]) ).
cnf(c1253,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = join(composition(X4,X3),converse(composition(X,converse(X4)))),
inference(congruence,[status(thm)],[c1252]) ).
cnf(c1254,plain,
converse(converse(composition(X3,X))) = composition(X3,X),
inference(substitution,[status(thm)],[c56]) ).
cnf(c1255,plain,
composition(X3,X) = converse(converse(composition(X3,X))),
inference(symmetry,[status(thm)],[c1254]) ).
cnf(c1256,plain,
join(composition(X4,X3),converse(composition(X,converse(X4)))) = join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))),
inference(congruence,[status(thm)],[c1255]) ).
cnf(c1257,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c1258,plain,
join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))) = converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))),
inference(symmetry,[status(thm)],[c1257]) ).
cnf(c1259,plain,
converse(composition(X,X3)) = composition(converse(X3),converse(X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1260,plain,
join(converse(composition(X,X3)),composition(X4,converse(X))) = join(composition(converse(X3),converse(X)),composition(X4,converse(X))),
inference(congruence,[status(thm)],[c1259]) ).
cnf(c1261,plain,
composition(join(converse(X3),X4),converse(X)) = join(composition(converse(X3),converse(X)),composition(X4,converse(X))),
inference(substitution,[status(thm)],[c616]) ).
cnf(c1262,plain,
join(composition(converse(X3),converse(X)),composition(X4,converse(X))) = composition(join(converse(X3),X4),converse(X)),
inference(symmetry,[status(thm)],[c1261]) ).
cnf(c1263,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1264,plain,
composition(join(converse(X3),X4),converse(X)) = composition(join(X4,converse(X3)),converse(X)),
inference(congruence,[status(thm)],[c1263]) ).
cnf(c1265,plain,
join(composition(converse(X3),converse(X)),composition(X4,converse(X))) = composition(join(X4,converse(X3)),converse(X)),
inference(transitivity,[status(thm)],[c1262,c1264]) ).
cnf(c1266,plain,
join(converse(composition(X,X3)),composition(X4,converse(X))) = composition(join(X4,converse(X3)),converse(X)),
inference(transitivity,[status(thm)],[c1260,c1265]) ).
cnf(c1267,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = composition(join(X,converse(X3)),converse(X4)),
inference(substitution,[status(thm)],[c1266]) ).
cnf(c1268,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = converse(composition(join(X,converse(X3)),converse(X4))),
inference(congruence,[status(thm)],[c1267]) ).
cnf(c1269,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(converse(converse(X4)),converse(join(X,converse(X3)))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c1270,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1271,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,converse(join(X,converse(X3)))),
inference(congruence,[status(thm)],[c1270]) ).
cnf(c1272,plain,
converse(join(X,converse(X3))) = join(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c1273,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(converse(X),converse(converse(X3)))),
inference(congruence,[status(thm)],[c1272]) ).
cnf(c1274,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1275,plain,
join(converse(X),converse(converse(X3))) = join(converse(X),X3),
inference(congruence,[status(thm)],[c1274]) ).
cnf(c1276,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(converse(X),X3)),
inference(congruence,[status(thm)],[c1275]) ).
cnf(c1277,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1278,plain,
composition(X4,join(converse(X),X3)) = composition(X4,join(X3,converse(X))),
inference(congruence,[status(thm)],[c1277]) ).
cnf(c1279,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1276,c1278]) ).
cnf(c1280,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1273,c1279]) ).
cnf(c1281,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1271,c1280]) ).
cnf(c1282,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1269,c1281]) ).
cnf(c1283,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1268,c1282]) ).
cnf(c1284,plain,
join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1258,c1283]) ).
cnf(c1285,plain,
join(composition(X4,X3),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1256,c1284]) ).
cnf(c1286,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1253,c1285]) ).
cnf(c1287,plain,
join(composition(X4,X3),composition(X4,converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c1250,c1286]) ).
cnf(c1288,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X3,converse(converse(X)))),
inference(substitution,[status(thm)],[c1287]) ).
cnf(c1289,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c1290,plain,
join(X3,converse(converse(X))) = join(X3,X),
inference(congruence,[status(thm)],[c1289]) ).
cnf(c1291,plain,
composition(X4,join(X3,converse(converse(X)))) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c1290]) ).
cnf(c1292,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c1288,c1291]) ).
cnf(c1293,plain,
join(composition(X4,X3),composition(X4,X)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c1246,c1292]) ).
cnf(c1294,plain,
join(composition(X4,meet(X,X3)),composition(X4,complement(X))) = composition(X4,join(meet(X,X3),complement(X))),
inference(substitution,[status(thm)],[c1293]) ).
cnf(c1295,plain,
complement(meet(X,complement(meet(X,X3)))) = join(meet(X,X3),complement(X)),
inference(substitution,[status(thm)],[c291]) ).
cnf(c1296,plain,
join(meet(X,X3),complement(X)) = complement(meet(X,complement(meet(X,X3)))),
inference(symmetry,[status(thm)],[c1295]) ).
cnf(c1297,plain,
meet(X,complement(meet(X,X3))) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c523]) ).
cnf(c1298,plain,
complement(meet(X,complement(meet(X,X3)))) = complement(meet(X,complement(X3))),
inference(congruence,[status(thm)],[c1297]) ).
cnf(c1299,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c291]) ).
cnf(c1300,plain,
complement(meet(X,complement(meet(X,X3)))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c1298,c1299]) ).
cnf(c1301,plain,
join(meet(X,X3),complement(X)) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c1296,c1300]) ).
cnf(c1302,plain,
composition(X4,join(meet(X,X3),complement(X))) = composition(X4,join(X3,complement(X))),
inference(congruence,[status(thm)],[c1301]) ).
cnf(c1303,plain,
join(composition(X4,X3),composition(X4,complement(X))) = composition(X4,join(X3,complement(X))),
inference(substitution,[status(thm)],[c1293]) ).
cnf(c1304,plain,
composition(X4,join(X3,complement(X))) = join(composition(X4,X3),composition(X4,complement(X))),
inference(symmetry,[status(thm)],[c1303]) ).
cnf(c1305,plain,
composition(X4,join(meet(X,X3),complement(X))) = join(composition(X4,X3),composition(X4,complement(X))),
inference(transitivity,[status(thm)],[c1302,c1304]) ).
cnf(c1306,plain,
join(composition(X4,meet(X,X3)),composition(X4,complement(X))) = join(composition(X4,X3),composition(X4,complement(X))),
inference(transitivity,[status(thm)],[c1294,c1305]) ).
cnf(c1307,plain,
join(composition(x0,meet(X3,X)),composition(x0,complement(X3))) = join(composition(x0,X),composition(x0,complement(X3))),
inference(substitution,[status(thm)],[c1306]) ).
cnf(c1308,plain,
join(composition(x0,X),composition(x0,complement(X3))) = join(composition(x0,meet(X3,X)),composition(x0,complement(X3))),
inference(symmetry,[status(thm)],[c1307]) ).
cnf(c1309,plain,
meet(composition(x0,X3),join(composition(x0,X),composition(x0,complement(X3)))) = meet(composition(x0,X3),join(composition(x0,meet(X3,X)),composition(x0,complement(X3)))),
inference(congruence,[status(thm)],[c1308]) ).
cnf(c1310,plain,
meet(composition(x0,X3),join(composition(x0,meet(X3,X)),composition(x0,complement(X3)))) = meet(composition(x0,meet(X3,X)),composition(x0,X3)),
inference(substitution,[status(thm)],[c1240]) ).
cnf(c1311,plain,
join(composition(X4,X3),composition(X4,meet(X3,X))) = join(composition(X4,meet(X3,X)),composition(X4,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1312,plain,
join(composition(X4,meet(X3,X)),composition(X4,X3)) = join(composition(X4,X3),composition(X4,meet(X3,X))),
inference(symmetry,[status(thm)],[c1311]) ).
cnf(c1313,plain,
join(composition(X4,X),composition(X4,X3)) = composition(X4,join(X,X3)),
inference(substitution,[status(thm)],[c1293]) ).
cnf(c1314,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1315,plain,
composition(X4,join(X,X3)) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c1314]) ).
cnf(c1316,plain,
join(composition(X4,X),composition(X4,X3)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c1313,c1315]) ).
cnf(c1317,plain,
join(composition(X4,X3),composition(X4,meet(X3,X))) = composition(X4,join(meet(X3,X),X3)),
inference(substitution,[status(thm)],[c1316]) ).
cnf(c1318,plain,
join(X3,meet(X3,X)) = join(meet(X3,X),X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1319,plain,
join(meet(X3,X),X3) = join(X3,meet(X3,X)),
inference(symmetry,[status(thm)],[c1318]) ).
cnf(c1320,plain,
join(meet(X3,X),X3) = X3,
inference(transitivity,[status(thm)],[c1319,c514]) ).
cnf(c1321,plain,
composition(X4,join(meet(X3,X),X3)) = composition(X4,X3),
inference(congruence,[status(thm)],[c1320]) ).
cnf(c1322,plain,
join(composition(X4,X3),composition(X4,meet(X3,X))) = composition(X4,X3),
inference(transitivity,[status(thm)],[c1317,c1321]) ).
cnf(c1323,plain,
join(composition(X4,meet(X3,X)),composition(X4,X3)) = composition(X4,X3),
inference(transitivity,[status(thm)],[c1312,c1322]) ).
cnf(c1324,plain,
composition(X4,X3) = join(composition(X4,meet(X3,X)),composition(X4,X3)),
inference(symmetry,[status(thm)],[c1323]) ).
cnf(c1325,plain,
meet(composition(X4,meet(X3,X)),composition(X4,X3)) = meet(composition(X4,meet(X3,X)),join(composition(X4,meet(X3,X)),composition(X4,X3))),
inference(congruence,[status(thm)],[c1324]) ).
cnf(c1326,plain,
meet(composition(X4,meet(X3,X)),join(composition(X4,meet(X3,X)),composition(X4,X3))) = composition(X4,meet(X3,X)),
inference(substitution,[status(thm)],[c714]) ).
cnf(c1327,plain,
meet(composition(X4,meet(X3,X)),composition(X4,X3)) = composition(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c1325,c1326]) ).
cnf(c1328,plain,
meet(composition(x0,meet(X3,X)),composition(x0,X3)) = composition(x0,meet(X3,X)),
inference(substitution,[status(thm)],[c1327]) ).
cnf(c1329,plain,
meet(composition(x0,X3),join(composition(x0,meet(X3,X)),composition(x0,complement(X3)))) = composition(x0,meet(X3,X)),
inference(transitivity,[status(thm)],[c1310,c1328]) ).
cnf(c1330,plain,
meet(composition(x0,X3),join(composition(x0,X),composition(x0,complement(X3)))) = composition(x0,meet(X3,X)),
inference(transitivity,[status(thm)],[c1309,c1329]) ).
cnf(c1331,plain,
meet(composition(x0,X),composition(x0,X3)) = composition(x0,meet(X3,X)),
inference(transitivity,[status(thm)],[c1242,c1330]) ).
cnf(c1332,plain,
meet(composition(x0,X3),composition(x0,X)) = composition(x0,meet(X3,X)),
inference(transitivity,[status(thm)],[c15,c1331]) ).
cnf(c1333,plain,
meet(composition(x0,x1),composition(x0,x2)) = composition(x0,meet(x1,x2)),
inference(substitution,[status(thm)],[c1332]) ).
cnf(c1334,plain,
composition(x0,meet(x1,x2)) = meet(composition(x0,x1),composition(x0,x2)),
inference(symmetry,[status(thm)],[c1333]) ).
cnf(c1335,plain,
$false,
inference(resolution,[status(thm)],[c4,c1334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL040+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n012.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sun Sep 27 22:55:19 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 139.34/17.91 Command-line arguments: --flatten --complete-subsets
% 139.34/17.91
% 139.34/17.91 % SZS status Theorem
% 139.34/17.91
% 139.34/17.96 % SZS output start CNFRefutation
% See solution above
% 142.49/18.37
% 142.49/18.37 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------