%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL030+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:33:20 PM UTC 2026
% Result : Theorem 33.96s 4.72s
% Output : CNFRefutation 36.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 109
% Number of leaves : 16
% Syntax : Number of formulae : 1069 (1063 unt; 0 def)
% Number of atoms : 1075 (1074 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 : 1486 ( 103 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0,X1,X2] :
( join(X0,one) = one
=> meet(composition(X0,X1),complement(X2)) = meet(composition(X0,X1),complement(composition(X0,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( join(X0_2,one) = one
=> meet(composition(X0_2,X1_2),complement(X2_2)) = meet(composition(X0_2,X1_2),complement(composition(X0_2,X2_2))) ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( meet(composition(x0,x1),complement(x2)) != meet(composition(x0,x1),complement(composition(x0,x2)))
& join(x0,one) = one ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
meet(composition(x0,x1),complement(x2)) != meet(composition(x0,x1),complement(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(complement(X3),X) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
join(meet(X3,X),meet(complement(X3),X)) = join(meet(X3,X),meet(X,complement(X3))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c18,plain,
join(meet(X3,X),meet(X,complement(X3))) = join(meet(X,X3),meet(X,complement(X3))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,X),meet(X3,complement(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c20,plain,
join(meet(X3,X),meet(X3,complement(X))) = join(meet(X3,complement(X)),meet(X3,X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c22,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c24,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)],[c23]) ).
cnf(c25,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(c26,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c24,c27]) ).
cnf(c29,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c22,c29]) ).
cnf(c31,plain,
join(meet(X3,X),meet(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c20,c30]) ).
cnf(c32,plain,
join(meet(X,X3),meet(X,complement(X3))) = X,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
join(meet(X3,X),meet(X,complement(X3))) = X,
inference(transitivity,[status(thm)],[c18,c32]) ).
cnf(c34,plain,
join(meet(X3,X),meet(complement(X3),X)) = X,
inference(transitivity,[status(thm)],[c16,c33]) ).
cnf(c35,plain,
join(meet(X,meet(composition(x0,X3),complement(composition(x0,X)))),meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X))))) = meet(composition(x0,X3),complement(composition(x0,X))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(composition(x0,X3),complement(composition(x0,X))) = join(meet(X,meet(composition(x0,X3),complement(composition(x0,X)))),meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X))))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c38,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c7]) ).
cnf(c40,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c42,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c44,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c28]) ).
cnf(c47,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c42,c47]) ).
cnf(c49,plain,
X = join(zero,meet(X,X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
join(zero,X) = join(zero,join(zero,meet(X,X))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c52,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
join(zero,join(zero,X)) = join(zero,join(X,zero)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c7]) ).
cnf(c55,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
join(zero,join(X,zero)) = join(zero,join(zero,X)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,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(c58,plain,
join(zero,join(zero,X)) = join(join(zero,zero),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c60,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c63,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c65,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c61,c66]) ).
cnf(c68,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
join(zero,zero) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c71,plain,
join(zero,complement(top)) = join(complement(top),complement(top)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c73,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c75,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c73,c76]) ).
cnf(c78,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c81,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c84,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c79,c84]) ).
cnf(c86,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c90,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,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(c92,plain,
composition(X3,composition(one,X)) = composition(composition(X3,one),X),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c80]) ).
cnf(c94,plain,
composition(composition(X3,one),X) = composition(X3,X),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
composition(X3,composition(one,X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c92,c94]) ).
cnf(c96,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c96,c85]) ).
cnf(c98,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c90,c97]) ).
cnf(c99,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,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(c104,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)],[c103]) ).
cnf(c105,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(c106,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c102,c108]) ).
cnf(c110,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c88,c109]) ).
cnf(c111,plain,
join(complement(top),complement(top)) = complement(top),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
join(complement(top),complement(top)) = zero,
inference(transitivity,[status(thm)],[c111,c67]) ).
cnf(c113,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c71,c112]) ).
cnf(c114,plain,
join(zero,zero) = zero,
inference(transitivity,[status(thm)],[c69,c113]) ).
cnf(c115,plain,
join(join(zero,zero),X) = join(zero,X),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c7]) ).
cnf(c117,plain,
join(join(zero,zero),X) = join(X,zero),
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c58,c117]) ).
cnf(c119,plain,
join(zero,join(X,zero)) = join(X,zero),
inference(transitivity,[status(thm)],[c56,c118]) ).
cnf(c120,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c53,c119]) ).
cnf(c121,plain,
join(zero,join(zero,meet(X,X))) = join(meet(X,X),zero),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c123,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c124,plain,
meet(X,X) = complement(complement(X)),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
join(meet(X,X),zero) = join(complement(complement(X)),zero),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
join(complement(complement(X)),zero) = join(zero,complement(complement(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c127,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c128,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c130,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c28]) ).
cnf(c133,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c128,c133]) ).
cnf(c135,plain,
join(complement(complement(X)),zero) = X,
inference(transitivity,[status(thm)],[c126,c134]) ).
cnf(c136,plain,
join(meet(X,X),zero) = X,
inference(transitivity,[status(thm)],[c125,c135]) ).
cnf(c137,plain,
join(zero,join(zero,meet(X,X))) = X,
inference(transitivity,[status(thm)],[c121,c136]) ).
cnf(c138,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c50,c137]) ).
cnf(c139,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c40,c138]) ).
cnf(c140,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c38,c139]) ).
cnf(c141,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c142,c134]) ).
cnf(c144,plain,
complement(complement(meet(composition(x0,X),complement(composition(x0,X3))))) = meet(composition(x0,X),complement(composition(x0,X3))),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
meet(composition(x0,X),complement(composition(x0,X3))) = complement(complement(meet(composition(x0,X),complement(composition(x0,X3))))),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
meet(X3,meet(composition(x0,X),complement(composition(x0,X3)))) = meet(X3,complement(complement(meet(composition(x0,X),complement(composition(x0,X3)))))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c148,plain,
meet(X3,complement(complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = meet(complement(complement(X3)),complement(complement(meet(composition(x0,X),complement(composition(x0,X3)))))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c150,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c153,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c155,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c153,c155]) ).
cnf(c157,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c151,c156]) ).
cnf(c158,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c140]) ).
cnf(c160,plain,
complement(join(zero,complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c160,c143]) ).
cnf(c162,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c158,c161]) ).
cnf(c163,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
join(X3,X) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
complement(join(X3,X)) = complement(join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c167,plain,
join(X3,meet(X,top)) = join(X3,complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
complement(join(X3,meet(X,top))) = complement(join(X3,complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c170,plain,
join(X3,complement(X)) = join(complement(complement(X3)),complement(X)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
complement(join(X3,complement(X))) = complement(join(complement(complement(X3)),complement(X))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
meet(complement(X3),X) = complement(join(complement(complement(X3)),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c173,plain,
complement(join(complement(complement(X3)),complement(X))) = meet(complement(X3),X),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
meet(X,complement(X3)) = meet(complement(X3),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c175,plain,
meet(complement(X3),X) = meet(X,complement(X3)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
complement(join(complement(complement(X3)),complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c173,c175]) ).
cnf(c177,plain,
complement(join(X3,complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c171,c176]) ).
cnf(c178,plain,
complement(join(X3,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c140]) ).
cnf(c180,plain,
meet(join(zero,complement(X)),complement(X3)) = meet(complement(X),complement(X3)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
meet(complement(X3),complement(X)) = meet(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c182,plain,
meet(complement(X),complement(X3)) = meet(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
meet(join(zero,complement(X)),complement(X3)) = meet(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c180,c182]) ).
cnf(c184,plain,
complement(join(X3,complement(join(zero,complement(X))))) = meet(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c178,c183]) ).
cnf(c185,plain,
complement(join(X3,meet(X,top))) = meet(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c168,c184]) ).
cnf(c186,plain,
complement(join(X3,X)) = meet(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c165,c185]) ).
cnf(c187,plain,
complement(join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = meet(complement(complement(X3)),complement(complement(meet(composition(x0,X),complement(composition(x0,X3)))))),
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
meet(complement(complement(X3)),complement(complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = complement(join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3)))))),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c190,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
join(meet(X,X3),zero) = meet(X,X3),
inference(substitution,[status(thm)],[c139]) ).
cnf(c192,plain,
meet(X,X3) = join(meet(X,X3),zero),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
complement(meet(X,X3)) = complement(join(meet(X,X3),zero)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c195,plain,
join(meet(X,X3),zero) = join(meet(X,X3),complement(top)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
complement(join(meet(X,X3),zero)) = complement(join(meet(X,X3),complement(top))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c198,plain,
join(meet(X3,X),complement(X4)) = join(complement(join(complement(X3),complement(X))),complement(X4)),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
complement(join(meet(X4,X3),complement(X))) = complement(join(complement(join(complement(X4),complement(X3))),complement(X))),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
meet(join(complement(X4),complement(X3)),X) = complement(join(complement(join(complement(X4),complement(X3))),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c201,plain,
complement(join(complement(join(complement(X4),complement(X3))),complement(X))) = meet(join(complement(X4),complement(X3)),X),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
meet(X,join(complement(X4),complement(X3))) = meet(join(complement(X4),complement(X3)),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c203,plain,
meet(join(complement(X4),complement(X3)),X) = meet(X,join(complement(X4),complement(X3))),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
complement(join(complement(join(complement(X4),complement(X3))),complement(X))) = meet(X,join(complement(X4),complement(X3))),
inference(transitivity,[status(thm)],[c201,c203]) ).
cnf(c205,plain,
complement(join(meet(X4,X3),complement(X))) = meet(X,join(complement(X4),complement(X3))),
inference(transitivity,[status(thm)],[c199,c204]) ).
cnf(c206,plain,
complement(join(meet(X,X3),complement(top))) = meet(top,join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c208,plain,
meet(top,X) = meet(top,complement(complement(X))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c210,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c157]) ).
cnf(c211,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c134]) ).
cnf(c213,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c211,c212]) ).
cnf(c214,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c209,c213]) ).
cnf(c215,plain,
meet(top,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
meet(top,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c215,c143]) ).
cnf(c217,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c208,c216]) ).
cnf(c218,plain,
meet(top,join(complement(X),complement(X3))) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c220,plain,
meet(top,join(complement(X),complement(X3))) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c218,c219]) ).
cnf(c221,plain,
complement(join(meet(X,X3),complement(top))) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c206,c220]) ).
cnf(c222,plain,
complement(join(meet(X,X3),zero)) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c196,c221]) ).
cnf(c223,plain,
complement(meet(X,X3)) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c193,c222]) ).
cnf(c224,plain,
complement(meet(X3,X)) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c190,c223]) ).
cnf(c225,plain,
complement(meet(X,complement(X3))) = join(complement(X),complement(complement(X3))),
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
join(complement(X),complement(complement(X3))) = join(complement(X),X3),
inference(congruence,[status(thm)],[c143]) ).
cnf(c227,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c228,plain,
join(complement(X),complement(complement(X3))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c226,c227]) ).
cnf(c229,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c225,c228]) ).
cnf(c230,plain,
complement(meet(composition(x0,X),complement(composition(x0,X3)))) = join(composition(x0,X3),complement(composition(x0,X))),
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = join(complement(X3),join(composition(x0,X3),complement(composition(x0,X)))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
join(complement(composition(x0,X)),composition(x0,X3)) = join(composition(x0,X3),complement(composition(x0,X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c233,plain,
join(composition(x0,X3),complement(composition(x0,X))) = join(complement(composition(x0,X)),composition(x0,X3)),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
join(complement(X3),join(composition(x0,X3),complement(composition(x0,X)))) = join(complement(X3),join(complement(composition(x0,X)),composition(x0,X3))),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
join(join(X3,X),X4) = join(X4,join(X3,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c236,plain,
join(X4,join(X3,X)) = join(join(X3,X),X4),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
join(X3,join(X,X4)) = join(join(X3,X),X4),
inference(substitution,[status(thm)],[c57]) ).
cnf(c238,plain,
join(join(X3,X),X4) = join(X3,join(X,X4)),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c240,plain,
join(X3,join(X,X4)) = join(X3,join(X4,X)),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
join(join(X3,X),X4) = join(X3,join(X4,X)),
inference(transitivity,[status(thm)],[c238,c240]) ).
cnf(c242,plain,
join(X4,join(X3,X)) = join(X3,join(X4,X)),
inference(transitivity,[status(thm)],[c236,c241]) ).
cnf(c243,plain,
join(complement(composition(x0,X)),join(complement(X3),composition(x0,X3))) = join(complement(X3),join(complement(composition(x0,X)),composition(x0,X3))),
inference(substitution,[status(thm)],[c242]) ).
cnf(c244,plain,
join(complement(X3),join(complement(composition(x0,X)),composition(x0,X3))) = join(complement(composition(x0,X)),join(complement(X3),composition(x0,X3))),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
join(converse(x0),x0) = join(x0,converse(x0)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c246,plain,
join(x0,converse(x0)) = join(converse(x0),x0),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
meet(x0,composition(converse(x0),x0)) = meet(composition(converse(x0),x0),x0),
inference(substitution,[status(thm)],[c14]) ).
cnf(c248,plain,
meet(one,composition(converse(x0),x0)) = meet(composition(converse(x0),x0),one),
inference(substitution,[status(thm)],[c14]) ).
cnf(c249,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c250,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
composition(join(X3,X),x0) = composition(join(X,X3),x0),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
join(X3,composition(join(X3,X),x0)) = join(X3,composition(join(X,X3),x0)),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,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(c254,plain,
composition(join(X,X3),x0) = join(composition(X,x0),composition(X3,x0)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
join(X3,composition(join(X,X3),x0)) = join(X3,join(composition(X,x0),composition(X3,x0))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c257,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
composition(X3,X) = composition(X3,converse(converse(X))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
join(X3,composition(X3,X)) = join(X3,composition(X3,converse(converse(X)))),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
converse(composition(X3,converse(X))) = composition(converse(converse(X)),converse(X3)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c261,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c262,plain,
composition(converse(converse(X)),converse(X3)) = composition(X,converse(X3)),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
converse(composition(X3,converse(X))) = composition(X,converse(X3)),
inference(transitivity,[status(thm)],[c260,c262]) ).
cnf(c264,plain,
converse(composition(X,converse(X3))) = composition(X3,converse(X)),
inference(substitution,[status(thm)],[c263]) ).
cnf(c265,plain,
composition(X3,converse(X)) = converse(composition(X,converse(X3))),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
join(X3,composition(X3,converse(X))) = join(X3,converse(composition(X,converse(X3)))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
join(X,converse(X3)) = join(converse(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c268,plain,
join(converse(X3),X) = join(X,converse(X3)),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
converse(join(converse(X3),X)) = converse(join(X,converse(X3))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c271,plain,
join(X3,converse(X)) = join(converse(X),X3),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
converse(join(X3,converse(X))) = converse(join(converse(X),X3)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c274,plain,
converse(join(converse(X),X3)) = join(converse(converse(X)),converse(X3)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c275,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c276,plain,
join(converse(converse(X)),converse(X3)) = join(X,converse(X3)),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
converse(join(converse(X),X3)) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c274,c276]) ).
cnf(c278,plain,
converse(join(X3,converse(X))) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c272,c277]) ).
cnf(c279,plain,
converse(join(X,converse(X3))) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c278]) ).
cnf(c280,plain,
converse(join(converse(X3),X)) = join(X3,converse(X)),
inference(transitivity,[status(thm)],[c269,c279]) ).
cnf(c281,plain,
converse(join(converse(X3),composition(X,converse(X3)))) = join(X3,converse(composition(X,converse(X3)))),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
join(X3,converse(composition(X,converse(X3)))) = converse(join(converse(X3),composition(X,converse(X3)))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c284,plain,
join(X3,composition(X,X3)) = join(composition(one,X3),composition(X,X3)),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
composition(join(one,X),X3) = join(composition(one,X3),composition(X,X3)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c286,plain,
join(composition(one,X3),composition(X,X3)) = composition(join(one,X),X3),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c288,plain,
composition(join(one,X),X3) = composition(join(X,one),X3),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
join(composition(one,X3),composition(X,X3)) = composition(join(X,one),X3),
inference(transitivity,[status(thm)],[c286,c288]) ).
cnf(c290,plain,
join(X3,composition(X,X3)) = composition(join(X,one),X3),
inference(transitivity,[status(thm)],[c284,c289]) ).
cnf(c291,plain,
join(converse(X3),composition(X,converse(X3))) = composition(join(X,one),converse(X3)),
inference(substitution,[status(thm)],[c290]) ).
cnf(c292,plain,
converse(join(converse(X3),composition(X,converse(X3)))) = converse(composition(join(X,one),converse(X3))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
converse(composition(join(X,one),converse(X3))) = composition(X3,converse(join(X,one))),
inference(substitution,[status(thm)],[c263]) ).
cnf(c294,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c295,plain,
join(X,one) = join(one,X),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
converse(join(X,one)) = converse(join(one,X)),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
converse(join(one,X)) = join(converse(one),converse(X)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c298,plain,
composition(converse(one),one) = converse(one),
inference(substitution,[status(thm)],[c80]) ).
cnf(c299,plain,
converse(one) = composition(converse(one),one),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
composition(converse(one),one) = one,
inference(substitution,[status(thm)],[c85]) ).
cnf(c301,plain,
converse(one) = one,
inference(transitivity,[status(thm)],[c299,c300]) ).
cnf(c302,plain,
join(converse(one),converse(X)) = join(one,converse(X)),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
converse(join(one,X)) = join(one,converse(X)),
inference(transitivity,[status(thm)],[c297,c302]) ).
cnf(c304,plain,
converse(join(X,one)) = join(one,converse(X)),
inference(transitivity,[status(thm)],[c296,c303]) ).
cnf(c305,plain,
composition(X3,converse(join(X,one))) = composition(X3,join(one,converse(X))),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
converse(composition(join(X,one),converse(X3))) = composition(X3,join(one,converse(X))),
inference(transitivity,[status(thm)],[c293,c305]) ).
cnf(c307,plain,
converse(join(converse(X3),composition(X,converse(X3)))) = composition(X3,join(one,converse(X))),
inference(transitivity,[status(thm)],[c292,c306]) ).
cnf(c308,plain,
join(X3,converse(composition(X,converse(X3)))) = composition(X3,join(one,converse(X))),
inference(transitivity,[status(thm)],[c282,c307]) ).
cnf(c309,plain,
join(X3,composition(X3,converse(X))) = composition(X3,join(one,converse(X))),
inference(transitivity,[status(thm)],[c266,c308]) ).
cnf(c310,plain,
join(X3,composition(X3,converse(converse(X)))) = composition(X3,join(one,converse(converse(X)))),
inference(substitution,[status(thm)],[c309]) ).
cnf(c311,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c312,plain,
join(one,converse(converse(X))) = join(one,X),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
composition(X3,join(one,converse(converse(X)))) = composition(X3,join(one,X)),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c315,plain,
composition(X3,join(one,X)) = composition(X3,join(X,one)),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
composition(X3,join(one,converse(converse(X)))) = composition(X3,join(X,one)),
inference(transitivity,[status(thm)],[c313,c315]) ).
cnf(c317,plain,
join(X3,composition(X3,converse(converse(X)))) = composition(X3,join(X,one)),
inference(transitivity,[status(thm)],[c310,c316]) ).
cnf(c318,plain,
join(X3,composition(X3,X)) = composition(X3,join(X,one)),
inference(transitivity,[status(thm)],[c259,c317]) ).
cnf(c319,plain,
composition(X3,join(X,one)) = join(X3,composition(X3,X)),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
join(composition(X4,join(X,one)),X3) = join(join(X4,composition(X4,X)),X3),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
join(X4,join(composition(X4,X),X3)) = join(join(X4,composition(X4,X)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c322,plain,
join(join(X4,composition(X4,X)),X3) = join(X4,join(composition(X4,X),X3)),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c323,plain,
join(composition(X4,X),X3) = join(X3,composition(X4,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c324,plain,
join(X4,join(composition(X4,X),X3)) = join(X4,join(X3,composition(X4,X))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
join(join(X4,composition(X4,X)),X3) = join(X4,join(X3,composition(X4,X))),
inference(transitivity,[status(thm)],[c322,c324]) ).
cnf(c326,plain,
join(composition(X4,join(X,one)),X3) = join(X4,join(X3,composition(X4,X))),
inference(transitivity,[status(thm)],[c320,c325]) ).
cnf(c327,plain,
join(composition(X3,join(x0,one)),X) = join(X3,join(X,composition(X3,x0))),
inference(substitution,[status(thm)],[c326]) ).
cnf(c328,plain,
join(X3,join(X,composition(X3,x0))) = join(composition(X3,join(x0,one)),X),
inference(symmetry,[status(thm)],[c327]) ).
fof(c329,conjecture,
! [X0_2,X1_2,X2_2] :
( join(X0_2,one) = one
=> meet(composition(X0_2,X1_2),complement(X2_2)) = meet(composition(X0_2,X1_2),complement(composition(X0_2,X2_2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c330,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( join(X0_2,one) = one
=> meet(composition(X0_2,X1_2),complement(X2_2)) = meet(composition(X0_2,X1_2),complement(composition(X0_2,X2_2))) ),
inference(negate_conjecture,[status(cth)],[c329]) ).
fof(c331,plain,
( meet(composition(x0,x1),complement(x2)) != meet(composition(x0,x1),complement(composition(x0,x2)))
& join(x0,one) = one ),
inference(clausify,[status(esa)],[c330]) ).
cnf(c332,plain,
join(x0,one) = one,
inference(clausify,[status(thm)],[c331]) ).
cnf(c333,plain,
composition(X,join(x0,one)) = composition(X,one),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
join(composition(X3,join(x0,one)),X) = join(composition(X3,one),X),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c80]) ).
cnf(c336,plain,
join(composition(X3,one),X) = join(X3,X),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
join(composition(X3,join(x0,one)),X) = join(X3,X),
inference(transitivity,[status(thm)],[c334,c336]) ).
cnf(c338,plain,
join(X3,join(X,composition(X3,x0))) = join(X3,X),
inference(transitivity,[status(thm)],[c328,c337]) ).
cnf(c339,plain,
join(X3,join(composition(X,x0),composition(X3,x0))) = join(X3,composition(X,x0)),
inference(substitution,[status(thm)],[c338]) ).
cnf(c340,plain,
join(X3,composition(join(X,X3),x0)) = join(X3,composition(X,x0)),
inference(transitivity,[status(thm)],[c255,c339]) ).
cnf(c341,plain,
join(X3,composition(join(X3,X),x0)) = join(X3,composition(X,x0)),
inference(transitivity,[status(thm)],[c252,c340]) ).
cnf(c342,plain,
join(one,composition(join(one,converse(x0)),x0)) = join(one,composition(converse(x0),x0)),
inference(substitution,[status(thm)],[c341]) ).
cnf(c343,plain,
join(one,composition(converse(x0),x0)) = join(one,composition(join(one,converse(x0)),x0)),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
converse(join(x0,one)) = join(one,converse(x0)),
inference(substitution,[status(thm)],[c304]) ).
cnf(c345,plain,
join(one,converse(x0)) = converse(join(x0,one)),
inference(symmetry,[status(thm)],[c344]) ).
cnf(c346,plain,
converse(join(x0,one)) = converse(one),
inference(congruence,[status(thm)],[c332]) ).
cnf(c347,plain,
converse(join(x0,one)) = one,
inference(transitivity,[status(thm)],[c346,c301]) ).
cnf(c348,plain,
join(one,converse(x0)) = one,
inference(transitivity,[status(thm)],[c345,c347]) ).
cnf(c349,plain,
composition(join(one,converse(x0)),x0) = composition(one,x0),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
join(one,composition(join(one,converse(x0)),x0)) = join(one,composition(one,x0)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
join(one,composition(one,x0)) = composition(one,join(x0,one)),
inference(substitution,[status(thm)],[c318]) ).
cnf(c352,plain,
composition(one,join(x0,one)) = join(x0,one),
inference(substitution,[status(thm)],[c98]) ).
cnf(c353,plain,
composition(one,join(x0,one)) = one,
inference(transitivity,[status(thm)],[c352,c332]) ).
cnf(c354,plain,
join(one,composition(one,x0)) = one,
inference(transitivity,[status(thm)],[c351,c353]) ).
cnf(c355,plain,
join(one,composition(join(one,converse(x0)),x0)) = one,
inference(transitivity,[status(thm)],[c350,c354]) ).
cnf(c356,plain,
join(one,composition(converse(x0),x0)) = one,
inference(transitivity,[status(thm)],[c343,c355]) ).
cnf(c357,plain,
one = join(one,composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c356]) ).
cnf(c358,plain,
meet(composition(converse(x0),x0),one) = meet(composition(converse(x0),x0),join(one,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c360,plain,
join(X,X3) = join(X3,X),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
meet(X3,join(X,X3)) = meet(X3,join(X3,X)),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c363,plain,
join(X3,X) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
meet(X3,join(X3,X)) = meet(X3,join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c366,plain,
join(X3,meet(X,top)) = join(X3,complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
meet(X3,join(X3,meet(X,top))) = meet(X3,join(X3,complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c369,plain,
join(X3,complement(X)) = join(complement(complement(X3)),complement(X)),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
meet(X3,join(X3,complement(X))) = meet(X3,join(complement(complement(X3)),complement(X))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c372,plain,
join(complement(X4),meet(X3,X)) = join(complement(X4),meet(X,X3)),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
complement(join(complement(X4),meet(X3,X))) = complement(join(complement(X4),meet(X,X3))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c375,plain,
join(complement(X4),meet(X,X3)) = join(complement(X4),complement(join(complement(X),complement(X3)))),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
complement(join(complement(X4),meet(X,X3))) = complement(join(complement(X4),complement(join(complement(X),complement(X3))))),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
meet(X4,join(complement(X),complement(X3))) = complement(join(complement(X4),complement(join(complement(X),complement(X3))))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c378,plain,
complement(join(complement(X4),complement(join(complement(X),complement(X3))))) = meet(X4,join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c380,plain,
meet(X4,join(complement(X),complement(X3))) = meet(X4,join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
complement(join(complement(X4),complement(join(complement(X),complement(X3))))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c378,c380]) ).
cnf(c382,plain,
complement(join(complement(X4),meet(X,X3))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c376,c381]) ).
cnf(c383,plain,
complement(join(complement(X4),meet(X3,X))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c373,c382]) ).
cnf(c384,plain,
complement(join(complement(X3),meet(complement(X3),X))) = meet(X3,join(complement(complement(X3)),complement(X))),
inference(substitution,[status(thm)],[c383]) ).
cnf(c385,plain,
meet(X3,join(complement(complement(X3)),complement(X))) = complement(join(complement(X3),meet(complement(X3),X))),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
join(meet(X3,X),X3) = join(X3,meet(X3,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c387,plain,
join(X3,meet(X3,X)) = join(meet(X3,X),X3),
inference(symmetry,[status(thm)],[c386]) ).
cnf(c388,plain,
X3 = join(meet(X3,X),complement(join(complement(X3),X))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c389,plain,
join(meet(X3,X),X3) = join(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c391,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c390]) ).
cnf(c392,plain,
join(X3,join(X3,X)) = join(X3,join(X,X3)),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c394,plain,
join(X,X3) = join(X,meet(X3,top)),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
join(X3,join(X,X3)) = join(X3,join(X,meet(X3,top))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c397,plain,
join(X,meet(X3,top)) = join(X,complement(join(zero,complement(X3)))),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
join(X3,join(X,meet(X3,top))) = join(X3,join(X,complement(join(zero,complement(X3))))),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c400,plain,
join(X3,join(X,complement(join(zero,complement(X3))))) = join(meet(X3,top),join(X,complement(join(zero,complement(X3))))),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c402,plain,
join(meet(X3,top),join(X,complement(join(zero,complement(X3))))) = join(complement(join(zero,complement(X3))),join(X,complement(join(zero,complement(X3))))),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c404,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c403]) ).
cnf(c405,plain,
join(complement(X3),join(X,complement(X3))) = join(complement(X3),join(complement(X3),X)),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
join(complement(X3),join(complement(X3),X)) = join(join(complement(X3),complement(X3)),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c407,plain,
join(join(complement(X3),complement(X3)),X) = join(complement(X3),X),
inference(congruence,[status(thm)],[c110]) ).
cnf(c408,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c409,plain,
join(join(complement(X3),complement(X3)),X) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c407,c408]) ).
cnf(c410,plain,
join(complement(X3),join(complement(X3),X)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c406,c409]) ).
cnf(c411,plain,
join(complement(X3),join(X,complement(X3))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c405,c410]) ).
cnf(c412,plain,
join(complement(join(zero,complement(X3))),join(X,complement(join(zero,complement(X3))))) = join(X,complement(join(zero,complement(X3)))),
inference(substitution,[status(thm)],[c411]) ).
cnf(c413,plain,
join(X,complement(join(zero,complement(X3)))) = join(X,meet(X3,top)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c414,plain,
join(X,meet(X3,top)) = join(X,X3),
inference(congruence,[status(thm)],[c162]) ).
cnf(c415,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c416,plain,
join(X,meet(X3,top)) = join(X3,X),
inference(transitivity,[status(thm)],[c414,c415]) ).
cnf(c417,plain,
join(X,complement(join(zero,complement(X3)))) = join(X3,X),
inference(transitivity,[status(thm)],[c413,c416]) ).
cnf(c418,plain,
join(complement(join(zero,complement(X3))),join(X,complement(join(zero,complement(X3))))) = join(X3,X),
inference(transitivity,[status(thm)],[c412,c417]) ).
cnf(c419,plain,
join(meet(X3,top),join(X,complement(join(zero,complement(X3))))) = join(X3,X),
inference(transitivity,[status(thm)],[c402,c418]) ).
cnf(c420,plain,
join(X3,join(X,complement(join(zero,complement(X3))))) = join(X3,X),
inference(transitivity,[status(thm)],[c400,c419]) ).
cnf(c421,plain,
join(X3,join(X,meet(X3,top))) = join(X3,X),
inference(transitivity,[status(thm)],[c398,c420]) ).
cnf(c422,plain,
join(X3,join(X,X3)) = join(X3,X),
inference(transitivity,[status(thm)],[c395,c421]) ).
cnf(c423,plain,
join(X3,join(X3,X)) = join(X3,X),
inference(transitivity,[status(thm)],[c392,c422]) ).
cnf(c424,plain,
join(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))) = join(meet(X3,X),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c423]) ).
cnf(c425,plain,
join(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))) = X3,
inference(transitivity,[status(thm)],[c424,c28]) ).
cnf(c426,plain,
join(meet(X3,X),X3) = X3,
inference(transitivity,[status(thm)],[c389,c425]) ).
cnf(c427,plain,
join(X3,meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c387,c426]) ).
cnf(c428,plain,
join(complement(X3),meet(complement(X3),X)) = complement(X3),
inference(substitution,[status(thm)],[c427]) ).
cnf(c429,plain,
complement(join(complement(X3),meet(complement(X3),X))) = complement(complement(X3)),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
complement(join(complement(X3),meet(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c429,c143]) ).
cnf(c431,plain,
meet(X3,join(complement(complement(X3)),complement(X))) = X3,
inference(transitivity,[status(thm)],[c385,c430]) ).
cnf(c432,plain,
meet(X3,join(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c370,c431]) ).
cnf(c433,plain,
meet(X3,join(X3,complement(join(zero,complement(X))))) = X3,
inference(substitution,[status(thm)],[c432]) ).
cnf(c434,plain,
meet(X3,join(X3,meet(X,top))) = X3,
inference(transitivity,[status(thm)],[c367,c433]) ).
cnf(c435,plain,
meet(X3,join(X3,X)) = X3,
inference(transitivity,[status(thm)],[c364,c434]) ).
cnf(c436,plain,
meet(X3,join(X,X3)) = X3,
inference(transitivity,[status(thm)],[c361,c435]) ).
cnf(c437,plain,
meet(composition(converse(x0),x0),join(one,composition(converse(x0),x0))) = composition(converse(x0),x0),
inference(substitution,[status(thm)],[c436]) ).
cnf(c438,plain,
meet(composition(converse(x0),x0),one) = composition(converse(x0),x0),
inference(transitivity,[status(thm)],[c358,c437]) ).
cnf(c439,plain,
meet(one,composition(converse(x0),x0)) = composition(converse(x0),x0),
inference(transitivity,[status(thm)],[c248,c438]) ).
cnf(c440,plain,
composition(converse(x0),x0) = meet(one,composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
composition(x0,composition(converse(x0),x0)) = composition(x0,meet(one,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
complement(complement(x0)) = x0,
inference(substitution,[status(thm)],[c143]) ).
cnf(c443,plain,
x0 = complement(complement(x0)),
inference(symmetry,[status(thm)],[c442]) ).
cnf(c444,plain,
composition(x0,meet(one,composition(converse(x0),x0))) = composition(complement(complement(x0)),meet(one,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
meet(x0,x0) = complement(complement(x0)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c446,plain,
complement(complement(x0)) = meet(x0,x0),
inference(symmetry,[status(thm)],[c445]) ).
cnf(c447,plain,
composition(complement(complement(x0)),meet(one,composition(converse(x0),x0))) = composition(meet(x0,x0),meet(one,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
composition(x0,one) = x0,
inference(substitution,[status(thm)],[c80]) ).
cnf(c449,plain,
x0 = composition(x0,one),
inference(symmetry,[status(thm)],[c448]) ).
cnf(c450,plain,
meet(x0,x0) = meet(x0,composition(x0,one)),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
composition(meet(x0,x0),meet(one,composition(converse(x0),x0))) = composition(meet(x0,composition(x0,one)),meet(one,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c453,plain,
composition(x0,one) = composition(x0,converse(one)),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
meet(x0,composition(x0,one)) = meet(x0,composition(x0,converse(one))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
composition(meet(x0,composition(x0,one)),meet(one,composition(converse(x0),x0))) = composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,axiom,
join(meet(composition(X0_2,X1_2),X2_2),composition(meet(X0_2,composition(X2_2,converse(X1_2))),meet(X1_2,composition(converse(X0_2),X2_2)))) = composition(meet(X0_2,composition(X2_2,converse(X1_2))),meet(X1_2,composition(converse(X0_2),X2_2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law) ).
cnf(c457,plain,
join(meet(composition(x0,one),x0),composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0)))) = composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c456]) ).
cnf(c458,plain,
composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0))) = join(meet(composition(x0,one),x0),composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0)))),
inference(symmetry,[status(thm)],[c457]) ).
cnf(c459,plain,
composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0))) = composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0)),
inference(congruence,[status(thm)],[c439]) ).
cnf(c460,plain,
join(meet(composition(x0,one),x0),composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0)))) = join(meet(composition(x0,one),x0),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
composition(x0,one) = x0,
inference(substitution,[status(thm)],[c80]) ).
cnf(c462,plain,
meet(composition(x0,one),x0) = meet(x0,x0),
inference(congruence,[status(thm)],[c461]) ).
cnf(c463,plain,
join(meet(composition(x0,one),x0),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = join(meet(x0,x0),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
meet(x0,x0) = complement(complement(x0)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c465,plain,
join(meet(x0,x0),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = join(complement(complement(x0)),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
complement(complement(x0)) = x0,
inference(substitution,[status(thm)],[c143]) ).
cnf(c467,plain,
join(complement(complement(x0)),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = join(x0,composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
composition(X3,composition(X,X4)) = composition(composition(X3,X),X4),
inference(substitution,[status(thm)],[c91]) ).
cnf(c469,plain,
join(X4,composition(X3,composition(X,X4))) = join(X4,composition(composition(X3,X),X4)),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
join(X4,composition(composition(X3,X),X4)) = composition(join(composition(X3,X),one),X4),
inference(substitution,[status(thm)],[c290]) ).
cnf(c471,plain,
join(composition(X3,X),one) = join(one,composition(X3,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c472,plain,
composition(join(composition(X3,X),one),X4) = composition(join(one,composition(X3,X)),X4),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
join(X4,composition(composition(X3,X),X4)) = composition(join(one,composition(X3,X)),X4),
inference(transitivity,[status(thm)],[c470,c472]) ).
cnf(c474,plain,
join(X4,composition(X3,composition(X,X4))) = composition(join(one,composition(X3,X)),X4),
inference(transitivity,[status(thm)],[c469,c473]) ).
cnf(c475,plain,
join(x0,composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = composition(join(one,composition(meet(x0,composition(x0,converse(one))),converse(x0))),x0),
inference(substitution,[status(thm)],[c474]) ).
cnf(c476,plain,
composition(x0,converse(one)) = composition(x0,one),
inference(congruence,[status(thm)],[c301]) ).
cnf(c477,plain,
meet(x0,composition(x0,converse(one))) = meet(x0,composition(x0,one)),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
composition(meet(x0,composition(x0,converse(one))),converse(x0)) = composition(meet(x0,composition(x0,one)),converse(x0)),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
join(one,composition(meet(x0,composition(x0,converse(one))),converse(x0))) = join(one,composition(meet(x0,composition(x0,one)),converse(x0))),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,plain,
composition(join(one,composition(meet(x0,composition(x0,converse(one))),converse(x0))),x0) = composition(join(one,composition(meet(x0,composition(x0,one)),converse(x0))),x0),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
composition(x0,one) = x0,
inference(substitution,[status(thm)],[c80]) ).
cnf(c482,plain,
meet(x0,composition(x0,one)) = meet(x0,x0),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
composition(meet(x0,composition(x0,one)),converse(x0)) = composition(meet(x0,x0),converse(x0)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
join(one,composition(meet(x0,composition(x0,one)),converse(x0))) = join(one,composition(meet(x0,x0),converse(x0))),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
composition(join(one,composition(meet(x0,composition(x0,one)),converse(x0))),x0) = composition(join(one,composition(meet(x0,x0),converse(x0))),x0),
inference(congruence,[status(thm)],[c484]) ).
cnf(c486,plain,
meet(x0,x0) = complement(complement(x0)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c487,plain,
composition(meet(x0,x0),converse(x0)) = composition(complement(complement(x0)),converse(x0)),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
join(one,composition(meet(x0,x0),converse(x0))) = join(one,composition(complement(complement(x0)),converse(x0))),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
composition(join(one,composition(meet(x0,x0),converse(x0))),x0) = composition(join(one,composition(complement(complement(x0)),converse(x0))),x0),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
complement(complement(x0)) = x0,
inference(substitution,[status(thm)],[c143]) ).
cnf(c491,plain,
composition(complement(complement(x0)),converse(x0)) = composition(x0,converse(x0)),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
join(one,composition(complement(complement(x0)),converse(x0))) = join(one,composition(x0,converse(x0))),
inference(congruence,[status(thm)],[c491]) ).
cnf(c493,plain,
composition(join(one,composition(complement(complement(x0)),converse(x0))),x0) = composition(join(one,composition(x0,converse(x0))),x0),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
join(X3,composition(X3,composition(X,X3))) = composition(join(one,composition(X3,X)),X3),
inference(substitution,[status(thm)],[c474]) ).
cnf(c495,plain,
composition(join(one,composition(X3,X)),X3) = join(X3,composition(X3,composition(X,X3))),
inference(symmetry,[status(thm)],[c494]) ).
cnf(c496,plain,
join(X3,composition(X3,composition(X,X3))) = composition(X3,join(composition(X,X3),one)),
inference(substitution,[status(thm)],[c318]) ).
cnf(c497,plain,
join(composition(X,X3),one) = join(one,composition(X,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c498,plain,
composition(X3,join(composition(X,X3),one)) = composition(X3,join(one,composition(X,X3))),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
join(X3,composition(X3,composition(X,X3))) = composition(X3,join(one,composition(X,X3))),
inference(transitivity,[status(thm)],[c496,c498]) ).
cnf(c500,plain,
composition(join(one,composition(X3,X)),X3) = composition(X3,join(one,composition(X,X3))),
inference(transitivity,[status(thm)],[c495,c499]) ).
cnf(c501,plain,
composition(join(one,composition(x0,converse(x0))),x0) = composition(x0,join(one,composition(converse(x0),x0))),
inference(substitution,[status(thm)],[c500]) ).
cnf(c502,plain,
composition(x0,join(one,composition(converse(x0),x0))) = composition(x0,one),
inference(congruence,[status(thm)],[c356]) ).
cnf(c503,plain,
composition(x0,one) = x0,
inference(substitution,[status(thm)],[c80]) ).
cnf(c504,plain,
composition(x0,join(one,composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c502,c503]) ).
cnf(c505,plain,
composition(join(one,composition(x0,converse(x0))),x0) = x0,
inference(transitivity,[status(thm)],[c501,c504]) ).
cnf(c506,plain,
composition(join(one,composition(complement(complement(x0)),converse(x0))),x0) = x0,
inference(transitivity,[status(thm)],[c493,c505]) ).
cnf(c507,plain,
composition(join(one,composition(meet(x0,x0),converse(x0))),x0) = x0,
inference(transitivity,[status(thm)],[c489,c506]) ).
cnf(c508,plain,
composition(join(one,composition(meet(x0,composition(x0,one)),converse(x0))),x0) = x0,
inference(transitivity,[status(thm)],[c485,c507]) ).
cnf(c509,plain,
composition(join(one,composition(meet(x0,composition(x0,converse(one))),converse(x0))),x0) = x0,
inference(transitivity,[status(thm)],[c480,c508]) ).
cnf(c510,plain,
join(x0,composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c475,c509]) ).
cnf(c511,plain,
join(complement(complement(x0)),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c467,c510]) ).
cnf(c512,plain,
join(meet(x0,x0),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c465,c511]) ).
cnf(c513,plain,
join(meet(composition(x0,one),x0),composition(meet(x0,composition(x0,converse(one))),composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c463,c512]) ).
cnf(c514,plain,
join(meet(composition(x0,one),x0),composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0)))) = x0,
inference(transitivity,[status(thm)],[c460,c513]) ).
cnf(c515,plain,
composition(meet(x0,composition(x0,converse(one))),meet(one,composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c458,c514]) ).
cnf(c516,plain,
composition(meet(x0,composition(x0,one)),meet(one,composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c455,c515]) ).
cnf(c517,plain,
composition(meet(x0,x0),meet(one,composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c451,c516]) ).
cnf(c518,plain,
composition(complement(complement(x0)),meet(one,composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c447,c517]) ).
cnf(c519,plain,
composition(x0,meet(one,composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c444,c518]) ).
cnf(c520,plain,
composition(x0,composition(converse(x0),x0)) = x0,
inference(transitivity,[status(thm)],[c441,c519]) ).
cnf(c521,plain,
x0 = composition(x0,composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c522,plain,
meet(composition(converse(x0),x0),x0) = meet(composition(converse(x0),x0),composition(x0,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
meet(X,composition(x0,X)) = meet(composition(x0,X),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c524,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c525,plain,
composition(x0,X) = composition(x0,complement(complement(X))),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
meet(composition(x0,X),X) = meet(composition(x0,complement(complement(X))),X),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
join(meet(composition(x0,complement(complement(X))),X),zero) = meet(composition(x0,complement(complement(X))),X),
inference(substitution,[status(thm)],[c139]) ).
cnf(c528,plain,
meet(composition(x0,complement(complement(X))),X) = join(meet(composition(x0,complement(complement(X))),X),zero),
inference(symmetry,[status(thm)],[c527]) ).
cnf(c529,plain,
meet(X,composition(x0,complement(X))) = complement(join(complement(X),complement(composition(x0,complement(X))))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c530,plain,
join(X,composition(x0,X3)) = join(composition(x0,X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c531,plain,
join(composition(x0,X3),X) = join(X,composition(x0,X3)),
inference(symmetry,[status(thm)],[c530]) ).
cnf(c532,plain,
join(X3,join(composition(x0,X3),X)) = join(X3,join(X,composition(x0,X3))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
composition(join(X,one),X3) = join(X3,composition(X,X3)),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c534,plain,
join(composition(join(X,one),X4),X3) = join(join(X4,composition(X,X4)),X3),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
join(X4,join(composition(X,X4),X3)) = join(join(X4,composition(X,X4)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c536,plain,
join(join(X4,composition(X,X4)),X3) = join(X4,join(composition(X,X4),X3)),
inference(symmetry,[status(thm)],[c535]) ).
cnf(c537,plain,
join(composition(X,X4),X3) = join(X3,composition(X,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c538,plain,
join(X4,join(composition(X,X4),X3)) = join(X4,join(X3,composition(X,X4))),
inference(congruence,[status(thm)],[c537]) ).
cnf(c539,plain,
join(join(X4,composition(X,X4)),X3) = join(X4,join(X3,composition(X,X4))),
inference(transitivity,[status(thm)],[c536,c538]) ).
cnf(c540,plain,
join(composition(join(X,one),X4),X3) = join(X4,join(X3,composition(X,X4))),
inference(transitivity,[status(thm)],[c534,c539]) ).
cnf(c541,plain,
join(composition(join(x0,one),X3),X) = join(X3,join(X,composition(x0,X3))),
inference(substitution,[status(thm)],[c540]) ).
cnf(c542,plain,
join(X3,join(X,composition(x0,X3))) = join(composition(join(x0,one),X3),X),
inference(symmetry,[status(thm)],[c541]) ).
cnf(c543,plain,
composition(join(x0,one),X) = composition(one,X),
inference(congruence,[status(thm)],[c332]) ).
cnf(c544,plain,
join(composition(join(x0,one),X3),X) = join(composition(one,X3),X),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
join(composition(one,X3),X) = join(X3,X),
inference(congruence,[status(thm)],[c98]) ).
cnf(c546,plain,
join(composition(join(x0,one),X3),X) = join(X3,X),
inference(transitivity,[status(thm)],[c544,c545]) ).
cnf(c547,plain,
join(X3,join(X,composition(x0,X3))) = join(X3,X),
inference(transitivity,[status(thm)],[c542,c546]) ).
cnf(c548,plain,
join(X3,join(composition(x0,X3),X)) = join(X3,X),
inference(transitivity,[status(thm)],[c532,c547]) ).
cnf(c549,plain,
join(X,join(composition(x0,X),complement(composition(x0,X)))) = join(X,complement(composition(x0,X))),
inference(substitution,[status(thm)],[c548]) ).
cnf(c550,plain,
join(X,complement(composition(x0,X))) = join(X,join(composition(x0,X),complement(composition(x0,X)))),
inference(symmetry,[status(thm)],[c549]) ).
cnf(c551,plain,
top = join(composition(x0,X),complement(composition(x0,X))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c552,plain,
join(composition(x0,X),complement(composition(x0,X))) = top,
inference(symmetry,[status(thm)],[c551]) ).
cnf(c553,plain,
join(X,join(composition(x0,X),complement(composition(x0,X)))) = join(X,top),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c555,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c554]) ).
cnf(c556,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c557,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c556]) ).
cnf(c558,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c560,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c561,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c7]) ).
cnf(c564,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c562,c563]) ).
cnf(c565,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c559,c564]) ).
cnf(c566,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c558,c565]) ).
cnf(c567,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c566]) ).
cnf(c568,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c567]) ).
cnf(c569,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c570,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c571,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c570]) ).
cnf(c572,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c569,c571]) ).
cnf(c573,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c568,c572]) ).
cnf(c574,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c555,c573]) ).
cnf(c575,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c574]) ).
cnf(c576,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c566]) ).
cnf(c578,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c566]) ).
cnf(c579,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c578]) ).
cnf(c580,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c574]) ).
cnf(c581,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c579,c580]) ).
cnf(c582,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c577,c581]) ).
cnf(c583,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c576,c582]) ).
cnf(c584,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c585,plain,
join(X3,top) = join(complement(X),top),
inference(substitution,[status(thm)],[c583]) ).
cnf(c586,plain,
join(top,complement(X)) = join(complement(X),top),
inference(substitution,[status(thm)],[c7]) ).
cnf(c587,plain,
join(complement(X),top) = join(top,complement(X)),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c587,c574]) ).
cnf(c589,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c585,c588]) ).
cnf(c590,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c584,c589]) ).
cnf(c591,plain,
join(X,join(composition(x0,X),complement(composition(x0,X)))) = top,
inference(transitivity,[status(thm)],[c553,c590]) ).
cnf(c592,plain,
join(X,complement(composition(x0,X))) = top,
inference(transitivity,[status(thm)],[c550,c591]) ).
cnf(c593,plain,
join(complement(X),complement(composition(x0,complement(X)))) = top,
inference(substitution,[status(thm)],[c592]) ).
cnf(c594,plain,
complement(join(complement(X),complement(composition(x0,complement(X))))) = complement(top),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
complement(join(complement(X),complement(composition(x0,complement(X))))) = zero,
inference(transitivity,[status(thm)],[c594,c67]) ).
cnf(c596,plain,
meet(X,composition(x0,complement(X))) = zero,
inference(transitivity,[status(thm)],[c529,c595]) ).
cnf(c597,plain,
meet(complement(X),composition(x0,complement(complement(X)))) = zero,
inference(substitution,[status(thm)],[c596]) ).
cnf(c598,plain,
zero = meet(complement(X),composition(x0,complement(complement(X)))),
inference(symmetry,[status(thm)],[c597]) ).
cnf(c599,plain,
join(meet(composition(x0,complement(complement(X))),X),zero) = join(meet(composition(x0,complement(complement(X))),X),meet(complement(X),composition(x0,complement(complement(X))))),
inference(congruence,[status(thm)],[c598]) ).
cnf(c600,plain,
meet(complement(X),X3) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c601,plain,
join(meet(X3,X),meet(complement(X),X3)) = join(meet(X3,X),meet(X3,complement(X))),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
join(meet(X3,X),meet(complement(X),X3)) = X3,
inference(transitivity,[status(thm)],[c601,c31]) ).
cnf(c603,plain,
join(meet(composition(x0,complement(complement(X))),X),meet(complement(X),composition(x0,complement(complement(X))))) = composition(x0,complement(complement(X))),
inference(substitution,[status(thm)],[c602]) ).
cnf(c604,plain,
composition(x0,complement(complement(X))) = composition(x0,X),
inference(congruence,[status(thm)],[c143]) ).
cnf(c605,plain,
join(meet(composition(x0,complement(complement(X))),X),meet(complement(X),composition(x0,complement(complement(X))))) = composition(x0,X),
inference(transitivity,[status(thm)],[c603,c604]) ).
cnf(c606,plain,
join(meet(composition(x0,complement(complement(X))),X),zero) = composition(x0,X),
inference(transitivity,[status(thm)],[c599,c605]) ).
cnf(c607,plain,
meet(composition(x0,complement(complement(X))),X) = composition(x0,X),
inference(transitivity,[status(thm)],[c528,c606]) ).
cnf(c608,plain,
meet(composition(x0,X),X) = composition(x0,X),
inference(transitivity,[status(thm)],[c526,c607]) ).
cnf(c609,plain,
meet(X,composition(x0,X)) = composition(x0,X),
inference(transitivity,[status(thm)],[c523,c608]) ).
cnf(c610,plain,
meet(composition(converse(x0),x0),composition(x0,composition(converse(x0),x0))) = composition(x0,composition(converse(x0),x0)),
inference(substitution,[status(thm)],[c609]) ).
cnf(c611,plain,
meet(composition(converse(x0),x0),composition(x0,composition(converse(x0),x0))) = x0,
inference(transitivity,[status(thm)],[c610,c520]) ).
cnf(c612,plain,
meet(composition(converse(x0),x0),x0) = x0,
inference(transitivity,[status(thm)],[c522,c611]) ).
cnf(c613,plain,
meet(x0,composition(converse(x0),x0)) = x0,
inference(transitivity,[status(thm)],[c247,c612]) ).
cnf(c614,plain,
x0 = meet(x0,composition(converse(x0),x0)),
inference(symmetry,[status(thm)],[c613]) ).
cnf(c615,plain,
join(converse(x0),x0) = join(converse(x0),meet(x0,composition(converse(x0),x0))),
inference(congruence,[status(thm)],[c614]) ).
cnf(c616,plain,
join(X,composition(X3,x0)) = join(composition(X3,x0),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c617,plain,
join(composition(X3,x0),X) = join(X,composition(X3,x0)),
inference(symmetry,[status(thm)],[c616]) ).
cnf(c618,plain,
join(X3,join(composition(X3,x0),X)) = join(X3,join(X,composition(X3,x0))),
inference(congruence,[status(thm)],[c617]) ).
cnf(c619,plain,
join(X3,join(composition(X3,x0),X)) = join(X3,X),
inference(transitivity,[status(thm)],[c618,c338]) ).
cnf(c620,plain,
join(X3,join(composition(X3,x0),meet(X,composition(X3,x0)))) = join(X3,meet(X,composition(X3,x0))),
inference(substitution,[status(thm)],[c619]) ).
cnf(c621,plain,
join(X3,meet(X,composition(X3,x0))) = join(X3,join(composition(X3,x0),meet(X,composition(X3,x0)))),
inference(symmetry,[status(thm)],[c620]) ).
cnf(c622,plain,
join(X3,meet(X,X3)) = join(X3,meet(X3,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c623,plain,
join(X3,meet(X,X3)) = X3,
inference(transitivity,[status(thm)],[c622,c427]) ).
cnf(c624,plain,
join(composition(X3,x0),meet(X,composition(X3,x0))) = composition(X3,x0),
inference(substitution,[status(thm)],[c623]) ).
cnf(c625,plain,
join(X3,join(composition(X3,x0),meet(X,composition(X3,x0)))) = join(X3,composition(X3,x0)),
inference(congruence,[status(thm)],[c624]) ).
cnf(c626,plain,
join(X,composition(X,x0)) = composition(X,join(x0,one)),
inference(substitution,[status(thm)],[c318]) ).
cnf(c627,plain,
composition(X,join(x0,one)) = composition(X,one),
inference(congruence,[status(thm)],[c332]) ).
cnf(c628,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c80]) ).
cnf(c629,plain,
composition(X,join(x0,one)) = X,
inference(transitivity,[status(thm)],[c627,c628]) ).
cnf(c630,plain,
join(X,composition(X,x0)) = X,
inference(transitivity,[status(thm)],[c626,c629]) ).
cnf(c631,plain,
join(X3,join(composition(X3,x0),meet(X,composition(X3,x0)))) = X3,
inference(transitivity,[status(thm)],[c625,c630]) ).
cnf(c632,plain,
join(X3,meet(X,composition(X3,x0))) = X3,
inference(transitivity,[status(thm)],[c621,c631]) ).
cnf(c633,plain,
join(converse(x0),meet(x0,composition(converse(x0),x0))) = converse(x0),
inference(substitution,[status(thm)],[c632]) ).
cnf(c634,plain,
join(converse(x0),x0) = converse(x0),
inference(transitivity,[status(thm)],[c615,c633]) ).
cnf(c635,plain,
join(x0,converse(x0)) = converse(x0),
inference(transitivity,[status(thm)],[c246,c634]) ).
cnf(c636,plain,
converse(x0) = join(x0,converse(x0)),
inference(symmetry,[status(thm)],[c635]) ).
cnf(c637,plain,
converse(join(x0,converse(x0))) = join(x0,converse(x0)),
inference(substitution,[status(thm)],[c278]) ).
cnf(c638,plain,
join(x0,converse(x0)) = converse(join(x0,converse(x0))),
inference(symmetry,[status(thm)],[c637]) ).
cnf(c639,plain,
converse(join(x0,converse(x0))) = converse(converse(x0)),
inference(congruence,[status(thm)],[c635]) ).
cnf(c640,plain,
converse(converse(x0)) = x0,
inference(substitution,[status(thm)],[c74]) ).
cnf(c641,plain,
converse(join(x0,converse(x0))) = x0,
inference(transitivity,[status(thm)],[c639,c640]) ).
cnf(c642,plain,
join(x0,converse(x0)) = x0,
inference(transitivity,[status(thm)],[c638,c641]) ).
cnf(c643,plain,
converse(x0) = x0,
inference(transitivity,[status(thm)],[c636,c642]) ).
cnf(c644,plain,
x0 = converse(x0),
inference(symmetry,[status(thm)],[c643]) ).
cnf(c645,plain,
composition(x0,top) = composition(converse(x0),top),
inference(congruence,[status(thm)],[c644]) ).
cnf(c646,plain,
join(complement(X),composition(x0,top)) = join(complement(X),composition(converse(x0),top)),
inference(congruence,[status(thm)],[c645]) ).
cnf(c647,plain,
converse(composition(top,X)) = composition(converse(X),converse(top)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c648,plain,
converse(join(top,converse(X))) = join(X,converse(top)),
inference(substitution,[status(thm)],[c278]) ).
cnf(c649,plain,
join(X,converse(top)) = converse(join(top,converse(X))),
inference(symmetry,[status(thm)],[c648]) ).
cnf(c650,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c651,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c650]) ).
cnf(c652,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c653,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c652,c589]) ).
cnf(c654,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c651,c653]) ).
cnf(c655,plain,
join(top,converse(X)) = top,
inference(substitution,[status(thm)],[c654]) ).
cnf(c656,plain,
converse(join(top,converse(X))) = converse(top),
inference(congruence,[status(thm)],[c655]) ).
cnf(c657,plain,
join(X,converse(top)) = converse(top),
inference(transitivity,[status(thm)],[c649,c656]) ).
cnf(c658,plain,
converse(top) = join(X,converse(top)),
inference(symmetry,[status(thm)],[c657]) ).
cnf(c659,plain,
join(complement(X),converse(top)) = converse(top),
inference(substitution,[status(thm)],[c657]) ).
cnf(c660,plain,
converse(top) = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c659]) ).
cnf(c661,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c663,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c662]) ).
cnf(c664,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c664,c566]) ).
cnf(c666,plain,
join(X,join(complement(X),converse(top))) = join(converse(top),top),
inference(substitution,[status(thm)],[c665]) ).
cnf(c667,plain,
join(converse(top),top) = top,
inference(substitution,[status(thm)],[c589]) ).
cnf(c668,plain,
join(X,join(complement(X),converse(top))) = top,
inference(transitivity,[status(thm)],[c666,c667]) ).
cnf(c669,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c661,c668]) ).
cnf(c670,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c658,c669]) ).
cnf(c671,plain,
composition(converse(X),converse(top)) = composition(converse(X),top),
inference(congruence,[status(thm)],[c670]) ).
cnf(c672,plain,
converse(composition(top,X)) = composition(converse(X),top),
inference(transitivity,[status(thm)],[c647,c671]) ).
cnf(c673,plain,
converse(composition(top,x0)) = composition(converse(x0),top),
inference(substitution,[status(thm)],[c672]) ).
cnf(c674,plain,
composition(converse(x0),top) = converse(composition(top,x0)),
inference(symmetry,[status(thm)],[c673]) ).
cnf(c675,plain,
join(complement(X),composition(converse(x0),top)) = join(complement(X),converse(composition(top,x0))),
inference(congruence,[status(thm)],[c674]) ).
cnf(c676,plain,
converse(join(converse(complement(X)),composition(top,x0))) = join(complement(X),converse(composition(top,x0))),
inference(substitution,[status(thm)],[c280]) ).
cnf(c677,plain,
join(complement(X),converse(composition(top,x0))) = converse(join(converse(complement(X)),composition(top,x0))),
inference(symmetry,[status(thm)],[c676]) ).
cnf(c678,plain,
converse(join(complement(X),composition(x0,X))) = join(converse(complement(X)),converse(composition(x0,X))),
inference(substitution,[status(thm)],[c273]) ).
cnf(c679,plain,
converse(composition(x0,X)) = composition(converse(X),converse(x0)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c680,plain,
converse(x0) = join(x0,converse(x0)),
inference(symmetry,[status(thm)],[c635]) ).
cnf(c681,plain,
composition(converse(X),converse(x0)) = composition(converse(X),join(x0,converse(x0))),
inference(congruence,[status(thm)],[c680]) ).
cnf(c682,plain,
converse(composition(join(X4,converse(X3)),X)) = composition(converse(X),converse(join(X4,converse(X3)))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c683,plain,
composition(converse(X),converse(join(X4,converse(X3)))) = composition(converse(X),join(X3,converse(X4))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c684,plain,
converse(composition(join(X4,converse(X3)),X)) = composition(converse(X),join(X3,converse(X4))),
inference(transitivity,[status(thm)],[c682,c683]) ).
cnf(c685,plain,
converse(composition(join(x0,converse(x0)),X)) = composition(converse(X),join(x0,converse(x0))),
inference(substitution,[status(thm)],[c684]) ).
cnf(c686,plain,
composition(converse(X),join(x0,converse(x0))) = converse(composition(join(x0,converse(x0)),X)),
inference(symmetry,[status(thm)],[c685]) ).
cnf(c687,plain,
composition(join(x0,converse(x0)),X) = composition(converse(x0),X),
inference(congruence,[status(thm)],[c635]) ).
cnf(c688,plain,
converse(composition(join(x0,converse(x0)),X)) = converse(composition(converse(x0),X)),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
converse(composition(converse(x0),X)) = composition(converse(X),x0),
inference(substitution,[status(thm)],[c77]) ).
cnf(c690,plain,
converse(composition(join(x0,converse(x0)),X)) = composition(converse(X),x0),
inference(transitivity,[status(thm)],[c688,c689]) ).
cnf(c691,plain,
composition(converse(X),join(x0,converse(x0))) = composition(converse(X),x0),
inference(transitivity,[status(thm)],[c686,c690]) ).
cnf(c692,plain,
composition(converse(X),converse(x0)) = composition(converse(X),x0),
inference(transitivity,[status(thm)],[c681,c691]) ).
cnf(c693,plain,
converse(composition(x0,X)) = composition(converse(X),x0),
inference(transitivity,[status(thm)],[c679,c692]) ).
cnf(c694,plain,
join(converse(complement(X)),converse(composition(x0,X))) = join(converse(complement(X)),composition(converse(X),x0)),
inference(congruence,[status(thm)],[c693]) ).
cnf(c695,plain,
converse(converse(complement(converse(complement(X))))) = complement(converse(complement(X))),
inference(substitution,[status(thm)],[c74]) ).
cnf(c696,plain,
complement(converse(complement(X))) = converse(converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c695]) ).
cnf(c697,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = converse(complement(converse(complement(X)))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c698,plain,
converse(complement(converse(complement(X)))) = join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c697]) ).
cnf(c699,plain,
converse(converse(meet(X,converse(complement(converse(X)))))) = meet(X,converse(complement(converse(X)))),
inference(substitution,[status(thm)],[c74]) ).
cnf(c700,plain,
meet(X,converse(complement(converse(X)))) = converse(converse(meet(X,converse(complement(converse(X)))))),
inference(symmetry,[status(thm)],[c699]) ).
cnf(c701,plain,
meet(converse(X3),converse(meet(X3,X))) = meet(converse(meet(X3,X)),converse(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c702,plain,
X3 = join(meet(X3,X),complement(join(complement(X3),X))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c703,plain,
converse(X3) = converse(join(meet(X3,X),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c702]) ).
cnf(c704,plain,
meet(converse(meet(X3,X)),converse(X3)) = meet(converse(meet(X3,X)),converse(join(meet(X3,X),complement(join(complement(X3),X))))),
inference(congruence,[status(thm)],[c703]) ).
cnf(c705,plain,
join(meet(converse(X3),converse(join(X3,X))),zero) = meet(converse(X3),converse(join(X3,X))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c706,plain,
meet(converse(X3),converse(join(X3,X))) = join(meet(converse(X3),converse(join(X3,X))),zero),
inference(symmetry,[status(thm)],[c705]) ).
cnf(c707,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c708,plain,
join(meet(converse(X3),converse(join(X3,X))),zero) = join(meet(converse(X3),converse(join(X3,X))),complement(top)),
inference(congruence,[status(thm)],[c707]) ).
cnf(c709,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c710,plain,
join(X3,converse(X)) = join(converse(X),X3),
inference(symmetry,[status(thm)],[c709]) ).
cnf(c711,plain,
join(converse(X4),join(X3,converse(X))) = join(converse(X4),join(converse(X),X3)),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
join(converse(X),join(converse(X4),X3)) = join(converse(X4),join(converse(X),X3)),
inference(substitution,[status(thm)],[c242]) ).
cnf(c713,plain,
join(converse(X4),join(converse(X),X3)) = join(converse(X),join(converse(X4),X3)),
inference(symmetry,[status(thm)],[c712]) ).
cnf(c714,plain,
join(converse(X),join(converse(X4),X3)) = join(join(converse(X),converse(X4)),X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c715,plain,
converse(join(X,X3)) = join(converse(X),converse(X3)),
inference(substitution,[status(thm)],[c273]) ).
cnf(c716,plain,
join(converse(X),converse(X3)) = converse(join(X,X3)),
inference(symmetry,[status(thm)],[c715]) ).
cnf(c717,plain,
join(join(converse(X),converse(X4)),X3) = join(converse(join(X,X4)),X3),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
join(converse(join(X,X4)),X3) = join(X3,converse(join(X,X4))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c719,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c720,plain,
converse(join(X,X3)) = converse(join(X3,X)),
inference(congruence,[status(thm)],[c719]) ).
cnf(c721,plain,
join(X3,converse(join(X,X4))) = join(X3,converse(join(X4,X))),
inference(congruence,[status(thm)],[c720]) ).
cnf(c722,plain,
join(converse(join(X,X4)),X3) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c718,c721]) ).
cnf(c723,plain,
join(join(converse(X),converse(X4)),X3) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c717,c722]) ).
cnf(c724,plain,
join(converse(X),join(converse(X4),X3)) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c714,c723]) ).
cnf(c725,plain,
join(converse(X4),join(converse(X),X3)) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c713,c724]) ).
cnf(c726,plain,
join(converse(X4),join(X3,converse(X))) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c711,c725]) ).
cnf(c727,plain,
join(converse(X3),join(complement(converse(X3)),converse(X))) = join(complement(converse(X3)),converse(join(X3,X))),
inference(substitution,[status(thm)],[c726]) ).
cnf(c728,plain,
join(complement(converse(X3)),converse(join(X3,X))) = join(converse(X3),join(complement(converse(X3)),converse(X))),
inference(symmetry,[status(thm)],[c727]) ).
cnf(c729,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c730,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c729]) ).
cnf(c731,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c730]) ).
cnf(c732,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c733,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c732,c589]) ).
cnf(c734,plain,
join(X3,join(X,complement(X3))) = top,
inference(transitivity,[status(thm)],[c566,c733]) ).
cnf(c735,plain,
join(X3,join(complement(X3),X)) = top,
inference(transitivity,[status(thm)],[c731,c734]) ).
cnf(c736,plain,
join(converse(X3),join(complement(converse(X3)),converse(X))) = top,
inference(substitution,[status(thm)],[c735]) ).
cnf(c737,plain,
join(complement(converse(X3)),converse(join(X3,X))) = top,
inference(transitivity,[status(thm)],[c728,c736]) ).
cnf(c738,plain,
top = join(complement(converse(X3)),converse(join(X3,X))),
inference(symmetry,[status(thm)],[c737]) ).
cnf(c739,plain,
complement(top) = complement(join(complement(converse(X3)),converse(join(X3,X)))),
inference(congruence,[status(thm)],[c738]) ).
cnf(c740,plain,
join(meet(converse(X3),converse(join(X3,X))),complement(top)) = join(meet(converse(X3),converse(join(X3,X))),complement(join(complement(converse(X3)),converse(join(X3,X))))),
inference(congruence,[status(thm)],[c739]) ).
cnf(c741,plain,
join(meet(converse(X3),converse(join(X3,X))),complement(join(complement(converse(X3)),converse(join(X3,X))))) = converse(X3),
inference(substitution,[status(thm)],[c28]) ).
cnf(c742,plain,
join(meet(converse(X3),converse(join(X3,X))),complement(top)) = converse(X3),
inference(transitivity,[status(thm)],[c740,c741]) ).
cnf(c743,plain,
join(meet(converse(X3),converse(join(X3,X))),zero) = converse(X3),
inference(transitivity,[status(thm)],[c708,c742]) ).
cnf(c744,plain,
meet(converse(X3),converse(join(X3,X))) = converse(X3),
inference(transitivity,[status(thm)],[c706,c743]) ).
cnf(c745,plain,
meet(converse(meet(X3,X)),converse(join(meet(X3,X),complement(join(complement(X3),X))))) = converse(meet(X3,X)),
inference(substitution,[status(thm)],[c744]) ).
cnf(c746,plain,
meet(converse(meet(X3,X)),converse(X3)) = converse(meet(X3,X)),
inference(transitivity,[status(thm)],[c704,c745]) ).
cnf(c747,plain,
meet(converse(X3),converse(meet(X3,X))) = converse(meet(X3,X)),
inference(transitivity,[status(thm)],[c701,c746]) ).
cnf(c748,plain,
meet(converse(X),converse(meet(X,converse(complement(converse(X)))))) = converse(meet(X,converse(complement(converse(X))))),
inference(substitution,[status(thm)],[c747]) ).
cnf(c749,plain,
converse(meet(X,converse(complement(converse(X))))) = meet(converse(X),converse(meet(X,converse(complement(converse(X)))))),
inference(symmetry,[status(thm)],[c748]) ).
cnf(c750,plain,
meet(meet(X3,converse(meet(X,converse(complement(X3))))),top) = meet(X3,converse(meet(X,converse(complement(X3))))),
inference(substitution,[status(thm)],[c162]) ).
cnf(c751,plain,
meet(X3,converse(meet(X,converse(complement(X3))))) = meet(meet(X3,converse(meet(X,converse(complement(X3))))),top),
inference(symmetry,[status(thm)],[c750]) ).
cnf(c752,plain,
meet(X,converse(X3)) = meet(converse(X3),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c753,plain,
converse(meet(X,converse(X3))) = converse(meet(converse(X3),X)),
inference(congruence,[status(thm)],[c752]) ).
cnf(c754,plain,
complement(converse(meet(X,converse(X3)))) = complement(converse(meet(converse(X3),X))),
inference(congruence,[status(thm)],[c753]) ).
cnf(c755,plain,
join(X3,complement(converse(meet(X,converse(X3))))) = join(X3,complement(converse(meet(converse(X3),X)))),
inference(congruence,[status(thm)],[c754]) ).
cnf(c756,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c757,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c756]) ).
cnf(c758,plain,
join(X3,complement(converse(meet(converse(X3),X)))) = join(converse(converse(X3)),complement(converse(meet(converse(X3),X)))),
inference(congruence,[status(thm)],[c757]) ).
cnf(c759,plain,
join(complement(converse(meet(X3,X))),converse(X3)) = join(converse(X3),complement(converse(meet(X3,X)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c760,plain,
join(converse(X3),complement(converse(meet(X3,X)))) = join(complement(converse(meet(X3,X))),converse(X3)),
inference(symmetry,[status(thm)],[c759]) ).
cnf(c761,plain,
X3 = join(meet(X3,X),meet(X3,complement(X))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c762,plain,
converse(X3) = converse(join(meet(X3,X),meet(X3,complement(X)))),
inference(congruence,[status(thm)],[c761]) ).
cnf(c763,plain,
join(complement(converse(meet(X3,X))),converse(X3)) = join(complement(converse(meet(X3,X))),converse(join(meet(X3,X),meet(X3,complement(X))))),
inference(congruence,[status(thm)],[c762]) ).
cnf(c764,plain,
join(complement(converse(meet(X3,X))),converse(join(meet(X3,X),meet(X3,complement(X))))) = top,
inference(substitution,[status(thm)],[c737]) ).
cnf(c765,plain,
join(complement(converse(meet(X3,X))),converse(X3)) = top,
inference(transitivity,[status(thm)],[c763,c764]) ).
cnf(c766,plain,
join(converse(X3),complement(converse(meet(X3,X)))) = top,
inference(transitivity,[status(thm)],[c760,c765]) ).
cnf(c767,plain,
join(converse(converse(X3)),complement(converse(meet(converse(X3),X)))) = top,
inference(substitution,[status(thm)],[c766]) ).
cnf(c768,plain,
join(X3,complement(converse(meet(converse(X3),X)))) = top,
inference(transitivity,[status(thm)],[c758,c767]) ).
cnf(c769,plain,
join(X3,complement(converse(meet(X,converse(X3))))) = top,
inference(transitivity,[status(thm)],[c755,c768]) ).
cnf(c770,plain,
join(complement(X3),complement(converse(meet(X,converse(complement(X3)))))) = top,
inference(substitution,[status(thm)],[c769]) ).
cnf(c771,plain,
top = join(complement(X3),complement(converse(meet(X,converse(complement(X3)))))),
inference(symmetry,[status(thm)],[c770]) ).
cnf(c772,plain,
meet(meet(X3,converse(meet(X,converse(complement(X3))))),top) = meet(meet(X3,converse(meet(X,converse(complement(X3))))),join(complement(X3),complement(converse(meet(X,converse(complement(X3))))))),
inference(congruence,[status(thm)],[c771]) ).
cnf(c773,plain,
join(complement(X3),complement(X)) = complement(meet(X3,X)),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c774,plain,
meet(meet(X3,X),join(complement(X3),complement(X))) = meet(meet(X3,X),complement(meet(X3,X))),
inference(congruence,[status(thm)],[c773]) ).
cnf(c775,plain,
zero = meet(meet(X3,X),complement(meet(X3,X))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c776,plain,
meet(meet(X3,X),complement(meet(X3,X))) = zero,
inference(symmetry,[status(thm)],[c775]) ).
cnf(c777,plain,
meet(meet(X3,X),join(complement(X3),complement(X))) = zero,
inference(transitivity,[status(thm)],[c774,c776]) ).
cnf(c778,plain,
meet(meet(X3,converse(meet(X,converse(complement(X3))))),join(complement(X3),complement(converse(meet(X,converse(complement(X3))))))) = zero,
inference(substitution,[status(thm)],[c777]) ).
cnf(c779,plain,
meet(meet(X3,converse(meet(X,converse(complement(X3))))),top) = zero,
inference(transitivity,[status(thm)],[c772,c778]) ).
cnf(c780,plain,
meet(X3,converse(meet(X,converse(complement(X3))))) = zero,
inference(transitivity,[status(thm)],[c751,c779]) ).
cnf(c781,plain,
meet(converse(X),converse(meet(X,converse(complement(converse(X)))))) = zero,
inference(substitution,[status(thm)],[c780]) ).
cnf(c782,plain,
converse(meet(X,converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c749,c781]) ).
cnf(c783,plain,
converse(converse(meet(X,converse(complement(converse(X)))))) = converse(zero),
inference(congruence,[status(thm)],[c782]) ).
cnf(c784,plain,
join(converse(zero),zero) = converse(zero),
inference(substitution,[status(thm)],[c139]) ).
cnf(c785,plain,
converse(zero) = join(converse(zero),zero),
inference(symmetry,[status(thm)],[c784]) ).
cnf(c786,plain,
join(zero,join(zero,converse(zero))) = join(converse(zero),zero),
inference(substitution,[status(thm)],[c120]) ).
cnf(c787,plain,
join(converse(zero),zero) = join(zero,join(zero,converse(zero))),
inference(symmetry,[status(thm)],[c786]) ).
cnf(c788,plain,
converse(join(converse(X),zero)) = join(X,converse(zero)),
inference(substitution,[status(thm)],[c280]) ).
cnf(c789,plain,
join(X,converse(zero)) = converse(join(converse(X),zero)),
inference(symmetry,[status(thm)],[c788]) ).
cnf(c790,plain,
join(converse(X),zero) = converse(X),
inference(substitution,[status(thm)],[c139]) ).
cnf(c791,plain,
converse(join(converse(X),zero)) = converse(converse(X)),
inference(congruence,[status(thm)],[c790]) ).
cnf(c792,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c793,plain,
converse(join(converse(X),zero)) = X,
inference(transitivity,[status(thm)],[c791,c792]) ).
cnf(c794,plain,
join(X,converse(zero)) = X,
inference(transitivity,[status(thm)],[c789,c793]) ).
cnf(c795,plain,
join(zero,converse(zero)) = zero,
inference(substitution,[status(thm)],[c794]) ).
cnf(c796,plain,
join(zero,join(zero,converse(zero))) = join(zero,zero),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
join(zero,join(zero,converse(zero))) = zero,
inference(transitivity,[status(thm)],[c796,c114]) ).
cnf(c798,plain,
join(converse(zero),zero) = zero,
inference(transitivity,[status(thm)],[c787,c797]) ).
cnf(c799,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c785,c798]) ).
cnf(c800,plain,
converse(converse(meet(X,converse(complement(converse(X)))))) = zero,
inference(transitivity,[status(thm)],[c783,c799]) ).
cnf(c801,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c700,c800]) ).
cnf(c802,plain,
meet(complement(X),converse(complement(converse(complement(X))))) = zero,
inference(substitution,[status(thm)],[c801]) ).
cnf(c803,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = join(meet(X,converse(complement(converse(complement(X))))),zero),
inference(congruence,[status(thm)],[c802]) ).
cnf(c804,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = meet(X,converse(complement(converse(complement(X))))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c805,plain,
complement(complement(converse(complement(converse(complement(X)))))) = converse(complement(converse(complement(X)))),
inference(substitution,[status(thm)],[c143]) ).
cnf(c806,plain,
converse(complement(converse(complement(X)))) = complement(complement(converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c805]) ).
cnf(c807,plain,
meet(X,converse(complement(converse(complement(X))))) = meet(X,complement(complement(converse(complement(converse(complement(X))))))),
inference(congruence,[status(thm)],[c806]) ).
cnf(c808,plain,
join(zero,meet(X,complement(complement(converse(complement(converse(complement(X)))))))) = meet(X,complement(complement(converse(complement(converse(complement(X))))))),
inference(substitution,[status(thm)],[c140]) ).
cnf(c809,plain,
meet(X,complement(complement(converse(complement(converse(complement(X))))))) = join(zero,meet(X,complement(complement(converse(complement(converse(complement(X)))))))),
inference(symmetry,[status(thm)],[c808]) ).
cnf(c810,plain,
meet(meet(X,complement(converse(complement(converse(complement(X)))))),top) = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(substitution,[status(thm)],[c162]) ).
cnf(c811,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = meet(meet(X,complement(converse(complement(converse(complement(X)))))),top),
inference(symmetry,[status(thm)],[c810]) ).
cnf(c812,plain,
converse(join(converse(X),complement(converse(X)))) = join(X,converse(complement(converse(X)))),
inference(substitution,[status(thm)],[c280]) ).
cnf(c813,plain,
join(X,converse(complement(converse(X)))) = converse(join(converse(X),complement(converse(X)))),
inference(symmetry,[status(thm)],[c812]) ).
cnf(c814,plain,
top = join(converse(X),complement(converse(X))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c815,plain,
join(converse(X),complement(converse(X))) = top,
inference(symmetry,[status(thm)],[c814]) ).
cnf(c816,plain,
converse(join(converse(X),complement(converse(X)))) = converse(top),
inference(congruence,[status(thm)],[c815]) ).
cnf(c817,plain,
converse(join(converse(X),complement(converse(X)))) = top,
inference(transitivity,[status(thm)],[c816,c670]) ).
cnf(c818,plain,
join(X,converse(complement(converse(X)))) = top,
inference(transitivity,[status(thm)],[c813,c817]) ).
cnf(c819,plain,
join(complement(X),converse(complement(converse(complement(X))))) = top,
inference(substitution,[status(thm)],[c818]) ).
cnf(c820,plain,
top = join(complement(X),converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c819]) ).
cnf(c821,plain,
meet(meet(X,complement(converse(complement(converse(complement(X)))))),top) = meet(meet(X,complement(converse(complement(converse(complement(X)))))),join(complement(X),converse(complement(converse(complement(X)))))),
inference(congruence,[status(thm)],[c820]) ).
cnf(c822,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c823,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c822]) ).
cnf(c824,plain,
meet(meet(X3,complement(X)),join(complement(X3),X)) = meet(meet(X3,complement(X)),join(X,complement(X3))),
inference(congruence,[status(thm)],[c823]) ).
cnf(c825,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c826,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c825]) ).
cnf(c827,plain,
meet(meet(X3,complement(X)),join(X,complement(X3))) = meet(meet(X3,complement(X)),join(complement(X3),X)),
inference(congruence,[status(thm)],[c826]) ).
cnf(c828,plain,
meet(X3,complement(X)) = meet(complement(X),X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c829,plain,
meet(meet(X3,complement(X)),join(complement(X3),X)) = meet(meet(complement(X),X3),join(complement(X3),X)),
inference(congruence,[status(thm)],[c828]) ).
cnf(c830,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c831,plain,
join(complement(X3),X) = join(complement(X3),meet(X,top)),
inference(congruence,[status(thm)],[c830]) ).
cnf(c832,plain,
meet(meet(complement(X),X3),join(complement(X3),X)) = meet(meet(complement(X),X3),join(complement(X3),meet(X,top))),
inference(congruence,[status(thm)],[c831]) ).
cnf(c833,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c140]) ).
cnf(c834,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c833]) ).
cnf(c835,plain,
meet(complement(X),X3) = meet(join(zero,complement(X)),X3),
inference(congruence,[status(thm)],[c834]) ).
cnf(c836,plain,
meet(meet(complement(X),X3),join(complement(X3),meet(X,top))) = meet(meet(join(zero,complement(X)),X3),join(complement(X3),meet(X,top))),
inference(congruence,[status(thm)],[c835]) ).
cnf(c837,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c838,plain,
join(complement(X3),meet(X,top)) = join(complement(X3),complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c837]) ).
cnf(c839,plain,
meet(meet(join(zero,complement(X)),X3),join(complement(X3),meet(X,top))) = meet(meet(join(zero,complement(X)),X3),join(complement(X3),complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c838]) ).
cnf(c840,plain,
meet(meet(X3,X),join(complement(X),complement(X3))) = meet(join(complement(X),complement(X3)),meet(X3,X)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c841,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c842,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c841]) ).
cnf(c843,plain,
meet(X3,X) = meet(X,X3),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c844,plain,
complement(join(complement(X3),complement(X))) = meet(X,X3),
inference(transitivity,[status(thm)],[c842,c843]) ).
cnf(c845,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(substitution,[status(thm)],[c844]) ).
cnf(c846,plain,
meet(X3,X) = complement(join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c845]) ).
cnf(c847,plain,
meet(join(complement(X),complement(X3)),meet(X3,X)) = meet(join(complement(X),complement(X3)),complement(join(complement(X),complement(X3)))),
inference(congruence,[status(thm)],[c846]) ).
cnf(c848,plain,
zero = meet(join(complement(X),complement(X3)),complement(join(complement(X),complement(X3)))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c849,plain,
meet(join(complement(X),complement(X3)),complement(join(complement(X),complement(X3)))) = zero,
inference(symmetry,[status(thm)],[c848]) ).
cnf(c850,plain,
meet(join(complement(X),complement(X3)),meet(X3,X)) = zero,
inference(transitivity,[status(thm)],[c847,c849]) ).
cnf(c851,plain,
meet(meet(X3,X),join(complement(X),complement(X3))) = zero,
inference(transitivity,[status(thm)],[c840,c850]) ).
cnf(c852,plain,
meet(meet(join(zero,complement(X)),X3),join(complement(X3),complement(join(zero,complement(X))))) = zero,
inference(substitution,[status(thm)],[c851]) ).
cnf(c853,plain,
meet(meet(join(zero,complement(X)),X3),join(complement(X3),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c839,c852]) ).
cnf(c854,plain,
meet(meet(complement(X),X3),join(complement(X3),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c836,c853]) ).
cnf(c855,plain,
meet(meet(complement(X),X3),join(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c832,c854]) ).
cnf(c856,plain,
meet(meet(X3,complement(X)),join(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c829,c855]) ).
cnf(c857,plain,
meet(meet(X3,complement(X)),join(X,complement(X3))) = zero,
inference(transitivity,[status(thm)],[c827,c856]) ).
cnf(c858,plain,
meet(meet(X3,complement(X)),join(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c824,c857]) ).
cnf(c859,plain,
meet(meet(X,complement(converse(complement(converse(complement(X)))))),join(complement(X),converse(complement(converse(complement(X)))))) = zero,
inference(substitution,[status(thm)],[c858]) ).
cnf(c860,plain,
meet(meet(X,complement(converse(complement(converse(complement(X)))))),top) = zero,
inference(transitivity,[status(thm)],[c821,c859]) ).
cnf(c861,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c811,c860]) ).
cnf(c862,plain,
zero = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c861]) ).
cnf(c863,plain,
join(zero,meet(X,complement(complement(converse(complement(converse(complement(X)))))))) = join(meet(X,complement(converse(complement(converse(complement(X)))))),meet(X,complement(complement(converse(complement(converse(complement(X)))))))),
inference(congruence,[status(thm)],[c862]) ).
cnf(c864,plain,
join(meet(X,complement(converse(complement(converse(complement(X)))))),meet(X,complement(complement(converse(complement(converse(complement(X)))))))) = X,
inference(substitution,[status(thm)],[c31]) ).
cnf(c865,plain,
join(zero,meet(X,complement(complement(converse(complement(converse(complement(X)))))))) = X,
inference(transitivity,[status(thm)],[c863,c864]) ).
cnf(c866,plain,
meet(X,complement(complement(converse(complement(converse(complement(X))))))) = X,
inference(transitivity,[status(thm)],[c809,c865]) ).
cnf(c867,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(transitivity,[status(thm)],[c807,c866]) ).
cnf(c868,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = X,
inference(transitivity,[status(thm)],[c804,c867]) ).
cnf(c869,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = X,
inference(transitivity,[status(thm)],[c803,c868]) ).
cnf(c870,plain,
converse(complement(converse(complement(X)))) = X,
inference(transitivity,[status(thm)],[c698,c869]) ).
cnf(c871,plain,
converse(converse(complement(converse(complement(X))))) = converse(X),
inference(congruence,[status(thm)],[c870]) ).
cnf(c872,plain,
complement(converse(complement(X))) = converse(X),
inference(transitivity,[status(thm)],[c696,c871]) ).
cnf(c873,plain,
converse(X) = complement(converse(complement(X))),
inference(symmetry,[status(thm)],[c872]) ).
cnf(c874,plain,
composition(converse(X),x0) = composition(complement(converse(complement(X))),x0),
inference(congruence,[status(thm)],[c873]) ).
cnf(c875,plain,
join(converse(complement(X)),composition(converse(X),x0)) = join(converse(complement(X)),composition(complement(converse(complement(X))),x0)),
inference(congruence,[status(thm)],[c874]) ).
cnf(c876,plain,
join(X,composition(join(X,complement(X)),x0)) = join(X,composition(complement(X),x0)),
inference(substitution,[status(thm)],[c341]) ).
cnf(c877,plain,
join(X,composition(complement(X),x0)) = join(X,composition(join(X,complement(X)),x0)),
inference(symmetry,[status(thm)],[c876]) ).
cnf(c878,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c879,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c878]) ).
cnf(c880,plain,
composition(join(X,complement(X)),x0) = composition(top,x0),
inference(congruence,[status(thm)],[c879]) ).
cnf(c881,plain,
join(X,composition(join(X,complement(X)),x0)) = join(X,composition(top,x0)),
inference(congruence,[status(thm)],[c880]) ).
cnf(c882,plain,
join(X,composition(complement(X),x0)) = join(X,composition(top,x0)),
inference(transitivity,[status(thm)],[c877,c881]) ).
cnf(c883,plain,
join(converse(complement(X)),composition(complement(converse(complement(X))),x0)) = join(converse(complement(X)),composition(top,x0)),
inference(substitution,[status(thm)],[c882]) ).
cnf(c884,plain,
join(converse(complement(X)),composition(converse(X),x0)) = join(converse(complement(X)),composition(top,x0)),
inference(transitivity,[status(thm)],[c875,c883]) ).
cnf(c885,plain,
join(converse(complement(X)),converse(composition(x0,X))) = join(converse(complement(X)),composition(top,x0)),
inference(transitivity,[status(thm)],[c694,c884]) ).
cnf(c886,plain,
converse(join(complement(X),composition(x0,X))) = join(converse(complement(X)),composition(top,x0)),
inference(transitivity,[status(thm)],[c678,c885]) ).
cnf(c887,plain,
join(converse(complement(X)),composition(top,x0)) = converse(join(complement(X),composition(x0,X))),
inference(symmetry,[status(thm)],[c886]) ).
cnf(c888,plain,
converse(join(converse(complement(X)),composition(top,x0))) = converse(converse(join(complement(X),composition(x0,X)))),
inference(congruence,[status(thm)],[c887]) ).
cnf(c889,plain,
converse(converse(join(complement(X),composition(x0,X)))) = join(complement(X),composition(x0,X)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c890,plain,
converse(join(converse(complement(X)),composition(top,x0))) = join(complement(X),composition(x0,X)),
inference(transitivity,[status(thm)],[c888,c889]) ).
cnf(c891,plain,
join(complement(X),converse(composition(top,x0))) = join(complement(X),composition(x0,X)),
inference(transitivity,[status(thm)],[c677,c890]) ).
cnf(c892,plain,
join(complement(X),composition(converse(x0),top)) = join(complement(X),composition(x0,X)),
inference(transitivity,[status(thm)],[c675,c891]) ).
cnf(c893,plain,
join(complement(X),composition(x0,top)) = join(complement(X),composition(x0,X)),
inference(transitivity,[status(thm)],[c646,c892]) ).
cnf(c894,plain,
join(complement(X),composition(x0,X)) = join(complement(X),composition(x0,top)),
inference(symmetry,[status(thm)],[c893]) ).
cnf(c895,plain,
join(complement(composition(x0,X)),join(complement(X3),composition(x0,X3))) = join(complement(composition(x0,X)),join(complement(X3),composition(x0,top))),
inference(congruence,[status(thm)],[c894]) ).
cnf(c896,plain,
join(composition(X3,top),X) = join(X,composition(X3,top)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c897,plain,
join(X,composition(X3,top)) = join(composition(X3,top),X),
inference(symmetry,[status(thm)],[c896]) ).
cnf(c898,plain,
join(complement(composition(X4,X3)),join(X,composition(X4,top))) = join(complement(composition(X4,X3)),join(composition(X4,top),X)),
inference(congruence,[status(thm)],[c897]) ).
cnf(c899,plain,
join(complement(composition(X4,X3)),join(composition(X4,top),X)) = join(join(complement(composition(X4,X3)),composition(X4,top)),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c900,plain,
complement(complement(composition(X,top))) = composition(X,top),
inference(substitution,[status(thm)],[c143]) ).
cnf(c901,plain,
composition(X,top) = complement(complement(composition(X,top))),
inference(symmetry,[status(thm)],[c900]) ).
cnf(c902,plain,
join(complement(composition(X3,X)),composition(X3,top)) = join(complement(composition(X3,X)),complement(complement(composition(X3,top)))),
inference(congruence,[status(thm)],[c901]) ).
cnf(c903,plain,
complement(meet(composition(X3,X),complement(composition(X3,top)))) = join(complement(composition(X3,X)),complement(complement(composition(X3,top)))),
inference(substitution,[status(thm)],[c224]) ).
cnf(c904,plain,
join(complement(composition(X3,X)),complement(complement(composition(X3,top)))) = complement(meet(composition(X3,X),complement(composition(X3,top)))),
inference(symmetry,[status(thm)],[c903]) ).
cnf(c905,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),zero) = meet(composition(X3,X),complement(composition(X3,top))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c906,plain,
meet(composition(X3,X),complement(composition(X3,top))) = join(meet(composition(X3,X),complement(composition(X3,top))),zero),
inference(symmetry,[status(thm)],[c905]) ).
cnf(c907,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c140]) ).
cnf(c908,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c907]) ).
cnf(c909,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c910,plain,
composition(top,zero) = composition(top,complement(top)),
inference(congruence,[status(thm)],[c909]) ).
cnf(c911,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c654]) ).
cnf(c912,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c911]) ).
cnf(c913,plain,
composition(top,complement(top)) = composition(join(top,one),complement(top)),
inference(congruence,[status(thm)],[c912]) ).
cnf(c914,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c670]) ).
cnf(c915,plain,
join(top,one) = join(converse(top),one),
inference(congruence,[status(thm)],[c914]) ).
cnf(c916,plain,
composition(join(top,one),complement(top)) = composition(join(converse(top),one),complement(top)),
inference(congruence,[status(thm)],[c915]) ).
cnf(c917,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(join(converse(top),one),complement(top)),
inference(substitution,[status(thm)],[c290]) ).
cnf(c918,plain,
composition(join(converse(top),one),complement(top)) = join(complement(top),composition(converse(top),complement(top))),
inference(symmetry,[status(thm)],[c917]) ).
cnf(c919,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c654]) ).
cnf(c920,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c919]) ).
cnf(c921,plain,
composition(top,top) = composition(join(top,one),top),
inference(congruence,[status(thm)],[c920]) ).
cnf(c922,plain,
join(top,composition(X,top)) = composition(join(X,one),top),
inference(substitution,[status(thm)],[c290]) ).
cnf(c923,plain,
composition(join(X,one),top) = join(top,composition(X,top)),
inference(symmetry,[status(thm)],[c922]) ).
cnf(c924,plain,
join(top,composition(X,top)) = top,
inference(substitution,[status(thm)],[c654]) ).
cnf(c925,plain,
composition(join(X,one),top) = top,
inference(transitivity,[status(thm)],[c923,c924]) ).
cnf(c926,plain,
composition(join(top,one),top) = top,
inference(substitution,[status(thm)],[c925]) ).
cnf(c927,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c921,c926]) ).
cnf(c928,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c927]) ).
cnf(c929,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c928]) ).
cnf(c930,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c929]) ).
cnf(c931,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c930]) ).
cnf(c932,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c107]) ).
cnf(c933,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c932,c67]) ).
cnf(c934,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c931,c933]) ).
cnf(c935,plain,
composition(join(converse(top),one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c918,c934]) ).
cnf(c936,plain,
composition(join(top,one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c916,c935]) ).
cnf(c937,plain,
composition(top,complement(top)) = zero,
inference(transitivity,[status(thm)],[c913,c936]) ).
cnf(c938,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c910,c937]) ).
cnf(c939,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c938]) ).
cnf(c940,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c939]) ).
cnf(c941,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c942,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c941]) ).
cnf(c943,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c654]) ).
cnf(c944,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c943,c938]) ).
cnf(c945,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c942,c944]) ).
cnf(c946,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c940,c945]) ).
cnf(c947,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c908,c946]) ).
cnf(c948,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero) = zero,
inference(substitution,[status(thm)],[c947]) ).
cnf(c949,plain,
zero = composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero),
inference(symmetry,[status(thm)],[c948]) ).
cnf(c950,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),zero) = join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero)),
inference(congruence,[status(thm)],[c949]) ).
cnf(c951,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c952,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c953,plain,
join(zero,complement(zero)) = complement(zero),
inference(substitution,[status(thm)],[c140]) ).
cnf(c954,plain,
complement(zero) = join(zero,complement(zero)),
inference(symmetry,[status(thm)],[c953]) ).
cnf(c955,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c956,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c955]) ).
cnf(c957,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c954,c956]) ).
cnf(c958,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c957]) ).
cnf(c959,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c958]) ).
cnf(c960,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c574]) ).
cnf(c961,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c960,c67]) ).
cnf(c962,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c959,c961]) ).
cnf(c963,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c952,c962]) ).
cnf(c964,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c951,c963]) ).
cnf(c965,plain,
zero = meet(X,zero),
inference(symmetry,[status(thm)],[c964]) ).
cnf(c966,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero) = composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero)),
inference(congruence,[status(thm)],[c965]) ).
cnf(c967,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero)) = join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero))),
inference(congruence,[status(thm)],[c966]) ).
cnf(c968,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = composition(converse(X),complement(composition(X,top))),
inference(substitution,[status(thm)],[c140]) ).
cnf(c969,plain,
composition(converse(X),complement(composition(X,top))) = join(zero,composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c968]) ).
cnf(c970,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c971,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = join(complement(top),composition(converse(X),complement(composition(X,top)))),
inference(congruence,[status(thm)],[c970]) ).
cnf(c972,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = complement(top),
inference(substitution,[status(thm)],[c107]) ).
cnf(c973,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c972,c67]) ).
cnf(c974,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c971,c973]) ).
cnf(c975,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c969,c974]) ).
cnf(c976,plain,
zero = composition(converse(X),complement(composition(X,top))),
inference(symmetry,[status(thm)],[c975]) ).
cnf(c977,plain,
meet(X,zero) = meet(X,composition(converse(X3),complement(composition(X3,top)))),
inference(congruence,[status(thm)],[c976]) ).
cnf(c978,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero)) = composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,composition(converse(X3),complement(composition(X3,top))))),
inference(congruence,[status(thm)],[c977]) ).
cnf(c979,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero))) = join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,composition(converse(X3),complement(composition(X3,top)))))),
inference(congruence,[status(thm)],[c978]) ).
cnf(c980,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,composition(converse(X3),complement(composition(X3,top)))))) = composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,composition(converse(X3),complement(composition(X3,top))))),
inference(substitution,[status(thm)],[c456]) ).
cnf(c981,plain,
meet(X,composition(converse(X3),complement(composition(X3,top)))) = meet(X,zero),
inference(congruence,[status(thm)],[c975]) ).
cnf(c982,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,composition(converse(X3),complement(composition(X3,top))))) = composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero)),
inference(congruence,[status(thm)],[c981]) ).
cnf(c983,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero)) = composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero),
inference(congruence,[status(thm)],[c964]) ).
cnf(c984,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero) = zero,
inference(substitution,[status(thm)],[c947]) ).
cnf(c985,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero)) = zero,
inference(transitivity,[status(thm)],[c983,c984]) ).
cnf(c986,plain,
composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,composition(converse(X3),complement(composition(X3,top))))) = zero,
inference(transitivity,[status(thm)],[c982,c985]) ).
cnf(c987,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,composition(converse(X3),complement(composition(X3,top)))))) = zero,
inference(transitivity,[status(thm)],[c980,c986]) ).
cnf(c988,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),meet(X,zero))) = zero,
inference(transitivity,[status(thm)],[c979,c987]) ).
cnf(c989,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),composition(meet(X3,composition(complement(composition(X3,top)),converse(X))),zero)) = zero,
inference(transitivity,[status(thm)],[c967,c988]) ).
cnf(c990,plain,
join(meet(composition(X3,X),complement(composition(X3,top))),zero) = zero,
inference(transitivity,[status(thm)],[c950,c989]) ).
cnf(c991,plain,
meet(composition(X3,X),complement(composition(X3,top))) = zero,
inference(transitivity,[status(thm)],[c906,c990]) ).
cnf(c992,plain,
complement(meet(composition(X3,X),complement(composition(X3,top)))) = complement(zero),
inference(congruence,[status(thm)],[c991]) ).
cnf(c993,plain,
complement(meet(composition(X3,X),complement(composition(X3,top)))) = top,
inference(transitivity,[status(thm)],[c992,c957]) ).
cnf(c994,plain,
join(complement(composition(X3,X)),complement(complement(composition(X3,top)))) = top,
inference(transitivity,[status(thm)],[c904,c993]) ).
cnf(c995,plain,
join(complement(composition(X3,X)),composition(X3,top)) = top,
inference(transitivity,[status(thm)],[c902,c994]) ).
cnf(c996,plain,
join(join(complement(composition(X4,X3)),composition(X4,top)),X) = join(top,X),
inference(congruence,[status(thm)],[c995]) ).
cnf(c997,plain,
join(join(complement(composition(X4,X3)),composition(X4,top)),X) = top,
inference(transitivity,[status(thm)],[c996,c654]) ).
cnf(c998,plain,
join(complement(composition(X4,X3)),join(composition(X4,top),X)) = top,
inference(transitivity,[status(thm)],[c899,c997]) ).
cnf(c999,plain,
join(complement(composition(X4,X3)),join(X,composition(X4,top))) = top,
inference(transitivity,[status(thm)],[c898,c998]) ).
cnf(c1000,plain,
join(complement(composition(x0,X)),join(complement(X3),composition(x0,top))) = top,
inference(substitution,[status(thm)],[c999]) ).
cnf(c1001,plain,
join(complement(composition(x0,X)),join(complement(X3),composition(x0,X3))) = top,
inference(transitivity,[status(thm)],[c895,c1000]) ).
cnf(c1002,plain,
join(complement(X3),join(complement(composition(x0,X)),composition(x0,X3))) = top,
inference(transitivity,[status(thm)],[c244,c1001]) ).
cnf(c1003,plain,
join(complement(X3),join(composition(x0,X3),complement(composition(x0,X)))) = top,
inference(transitivity,[status(thm)],[c234,c1002]) ).
cnf(c1004,plain,
join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = top,
inference(transitivity,[status(thm)],[c231,c1003]) ).
cnf(c1005,plain,
complement(join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = complement(top),
inference(congruence,[status(thm)],[c1004]) ).
cnf(c1006,plain,
complement(join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = zero,
inference(transitivity,[status(thm)],[c1005,c67]) ).
cnf(c1007,plain,
meet(complement(complement(X3)),complement(complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = zero,
inference(transitivity,[status(thm)],[c188,c1006]) ).
cnf(c1008,plain,
meet(X3,complement(complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = zero,
inference(transitivity,[status(thm)],[c148,c1007]) ).
cnf(c1009,plain,
meet(X3,meet(composition(x0,X),complement(composition(x0,X3)))) = zero,
inference(transitivity,[status(thm)],[c146,c1008]) ).
cnf(c1010,plain,
meet(X,meet(composition(x0,X3),complement(composition(x0,X)))) = zero,
inference(substitution,[status(thm)],[c1009]) ).
cnf(c1011,plain,
join(meet(X,meet(composition(x0,X3),complement(composition(x0,X)))),meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X))))) = join(zero,meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X))))),
inference(congruence,[status(thm)],[c1010]) ).
cnf(c1012,plain,
join(zero,meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X))))) = meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X)))),
inference(substitution,[status(thm)],[c140]) ).
cnf(c1013,plain,
meet(complement(X3),meet(X,complement(composition(x0,X3)))) = meet(meet(X,complement(composition(x0,X3))),complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c1014,plain,
complement(join(X3,complement(meet(X,complement(composition(x0,X3)))))) = meet(meet(X,complement(composition(x0,X3))),complement(X3)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c1015,plain,
meet(meet(X,complement(composition(x0,X3))),complement(X3)) = complement(join(X3,complement(meet(X,complement(composition(x0,X3)))))),
inference(symmetry,[status(thm)],[c1014]) ).
cnf(c1016,plain,
complement(meet(X,complement(composition(x0,X3)))) = join(composition(x0,X3),complement(X)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c1017,plain,
join(X3,complement(meet(X,complement(composition(x0,X3))))) = join(X3,join(composition(x0,X3),complement(X))),
inference(congruence,[status(thm)],[c1016]) ).
cnf(c1018,plain,
join(X,composition(x0,X3)) = join(composition(x0,X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1019,plain,
join(composition(x0,X3),X) = join(X,composition(x0,X3)),
inference(symmetry,[status(thm)],[c1018]) ).
cnf(c1020,plain,
join(X3,join(composition(x0,X3),X)) = join(X3,join(X,composition(x0,X3))),
inference(congruence,[status(thm)],[c1019]) ).
cnf(c1021,plain,
join(composition(x0,X3),X) = join(X,composition(x0,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1022,plain,
join(X,composition(x0,X3)) = join(composition(x0,X3),X),
inference(symmetry,[status(thm)],[c1021]) ).
cnf(c1023,plain,
join(X3,join(X,composition(x0,X3))) = join(X3,join(composition(x0,X3),X)),
inference(congruence,[status(thm)],[c1022]) ).
cnf(c1024,plain,
join(X3,join(composition(x0,X3),X)) = join(join(X3,composition(x0,X3)),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c1025,plain,
join(composition(x0,X),X) = join(X,composition(x0,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1026,plain,
join(X,composition(x0,X)) = join(composition(x0,X),X),
inference(symmetry,[status(thm)],[c1025]) ).
cnf(c1027,plain,
X = composition(converse(one),X),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c1028,plain,
join(composition(x0,X),X) = join(composition(x0,X),composition(converse(one),X)),
inference(congruence,[status(thm)],[c1027]) ).
cnf(c1029,plain,
composition(join(X4,X),X3) = join(composition(X4,X3),composition(X,X3)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c1030,plain,
join(composition(X4,X3),composition(X,X3)) = composition(join(X4,X),X3),
inference(symmetry,[status(thm)],[c1029]) ).
cnf(c1031,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1032,plain,
composition(join(X4,X),X3) = composition(join(X,X4),X3),
inference(congruence,[status(thm)],[c1031]) ).
cnf(c1033,plain,
join(composition(X4,X3),composition(X,X3)) = composition(join(X,X4),X3),
inference(transitivity,[status(thm)],[c1030,c1032]) ).
cnf(c1034,plain,
join(composition(x0,X),composition(converse(one),X)) = composition(join(converse(one),x0),X),
inference(substitution,[status(thm)],[c1033]) ).
cnf(c1035,plain,
join(converse(one),x0) = join(one,x0),
inference(congruence,[status(thm)],[c301]) ).
cnf(c1036,plain,
composition(join(converse(one),x0),X) = composition(join(one,x0),X),
inference(congruence,[status(thm)],[c1035]) ).
cnf(c1037,plain,
join(one,x0) = join(x0,one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1038,plain,
composition(join(one,x0),X) = composition(join(x0,one),X),
inference(congruence,[status(thm)],[c1037]) ).
cnf(c1039,plain,
composition(join(x0,one),X) = composition(one,X),
inference(congruence,[status(thm)],[c332]) ).
cnf(c1040,plain,
composition(join(x0,one),X) = X,
inference(transitivity,[status(thm)],[c1039,c98]) ).
cnf(c1041,plain,
composition(join(one,x0),X) = X,
inference(transitivity,[status(thm)],[c1038,c1040]) ).
cnf(c1042,plain,
composition(join(converse(one),x0),X) = X,
inference(transitivity,[status(thm)],[c1036,c1041]) ).
cnf(c1043,plain,
join(composition(x0,X),composition(converse(one),X)) = X,
inference(transitivity,[status(thm)],[c1034,c1042]) ).
cnf(c1044,plain,
join(composition(x0,X),X) = X,
inference(transitivity,[status(thm)],[c1028,c1043]) ).
cnf(c1045,plain,
join(X,composition(x0,X)) = X,
inference(transitivity,[status(thm)],[c1026,c1044]) ).
cnf(c1046,plain,
join(join(X3,composition(x0,X3)),X) = join(X3,X),
inference(congruence,[status(thm)],[c1045]) ).
cnf(c1047,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1048,plain,
join(join(X3,composition(x0,X3)),X) = join(X,X3),
inference(transitivity,[status(thm)],[c1046,c1047]) ).
cnf(c1049,plain,
join(X3,join(composition(x0,X3),X)) = join(X,X3),
inference(transitivity,[status(thm)],[c1024,c1048]) ).
cnf(c1050,plain,
join(X3,join(X,composition(x0,X3))) = join(X,X3),
inference(transitivity,[status(thm)],[c1023,c1049]) ).
cnf(c1051,plain,
join(X3,join(composition(x0,X3),X)) = join(X,X3),
inference(transitivity,[status(thm)],[c1020,c1050]) ).
cnf(c1052,plain,
join(X3,join(composition(x0,X3),complement(X))) = join(complement(X),X3),
inference(substitution,[status(thm)],[c1051]) ).
cnf(c1053,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c1054,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c1055,plain,
join(complement(X),X3) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c1053,c1054]) ).
cnf(c1056,plain,
join(X3,join(composition(x0,X3),complement(X))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c1052,c1055]) ).
cnf(c1057,plain,
join(X3,complement(meet(X,complement(composition(x0,X3))))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c1017,c1056]) ).
cnf(c1058,plain,
complement(join(X3,complement(meet(X,complement(composition(x0,X3)))))) = complement(complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c1057]) ).
cnf(c1059,plain,
complement(complement(meet(X,complement(X3)))) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c1060,plain,
complement(join(X3,complement(meet(X,complement(composition(x0,X3)))))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c1058,c1059]) ).
cnf(c1061,plain,
meet(meet(X,complement(composition(x0,X3))),complement(X3)) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c1015,c1060]) ).
cnf(c1062,plain,
meet(complement(X3),meet(X,complement(composition(x0,X3)))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c1013,c1061]) ).
cnf(c1063,plain,
meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X)))) = meet(composition(x0,X3),complement(X)),
inference(substitution,[status(thm)],[c1062]) ).
cnf(c1064,plain,
join(zero,meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X))))) = meet(composition(x0,X3),complement(X)),
inference(transitivity,[status(thm)],[c1012,c1063]) ).
cnf(c1065,plain,
join(meet(X,meet(composition(x0,X3),complement(composition(x0,X)))),meet(complement(X),meet(composition(x0,X3),complement(composition(x0,X))))) = meet(composition(x0,X3),complement(X)),
inference(transitivity,[status(thm)],[c1011,c1064]) ).
cnf(c1066,plain,
meet(composition(x0,X3),complement(composition(x0,X))) = meet(composition(x0,X3),complement(X)),
inference(transitivity,[status(thm)],[c36,c1065]) ).
cnf(c1067,plain,
meet(composition(x0,x1),complement(composition(x0,x2))) = meet(composition(x0,x1),complement(x2)),
inference(substitution,[status(thm)],[c1066]) ).
cnf(c1068,plain,
meet(composition(x0,x1),complement(x2)) = meet(composition(x0,x1),complement(composition(x0,x2))),
inference(symmetry,[status(thm)],[c1067]) ).
cnf(c1069,plain,
$false,
inference(resolution,[status(thm)],[c4,c1068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL030+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 22:54:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.96/4.72 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 33.96/4.72
% 33.96/4.72 % SZS status Theorem
% 33.96/4.72
% 33.96/4.75 % SZS output start CNFRefutation
% See solution above
% 36.72/5.12
% 36.72/5.12 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------