%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL030+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 33.21s 4.77s
% Output : CNFRefutation 35.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 93
% Number of leaves : 15
% Syntax : Number of formulae : 691 ( 685 unt; 0 def)
% Number of atoms : 697 ( 696 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 : 8 ( 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 : 1246 ( 74 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/sandbox2/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/sandbox2/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/sandbox2/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(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
cnf(c17,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c20,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
cnf(c22,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c20,c23]) ).
cnf(c25,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c18,c24]) ).
cnf(c26,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c30,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c32,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c28,c33]) ).
cnf(c35,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c38,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c40,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c42,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c40,c43]) ).
cnf(c45,plain,
converse(composition(converse(X),join(x0,one))) = composition(converse(join(x0,one)),X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
composition(converse(join(x0,one)),X) = converse(composition(converse(X),join(x0,one))),
inference(symmetry,[status(thm)],[c45]) ).
fof(c47,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c48,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)],[c47]) ).
fof(c49,plain,
( meet(composition(x0,x1),complement(x2)) != meet(composition(x0,x1),complement(composition(x0,x2)))
& join(x0,one) = one ),
inference(clausify,[status(esa)],[c48]) ).
cnf(c50,plain,
join(x0,one) = one,
inference(clausify,[status(thm)],[c49]) ).
cnf(c51,plain,
composition(X,join(x0,one)) = composition(X,one),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
cnf(c53,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
composition(X,join(x0,one)) = X,
inference(transitivity,[status(thm)],[c51,c53]) ).
cnf(c55,plain,
composition(converse(X),join(x0,one)) = converse(X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
converse(composition(converse(X),join(x0,one))) = converse(converse(X)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c58,plain,
converse(composition(converse(X),join(x0,one))) = X,
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
composition(converse(join(x0,one)),X) = X,
inference(transitivity,[status(thm)],[c46,c58]) ).
cnf(c60,plain,
composition(converse(join(x0,one)),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
complement(X) = composition(converse(join(x0,one)),complement(X)),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(join(x0,one)),complement(X))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
composition(converse(join(x0,one)),composition(join(x0,one),X)) = composition(join(x0,one),X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c64,plain,
composition(join(x0,one),X) = composition(converse(join(x0,one)),composition(join(x0,one),X)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,axiom,
composition(X0_2,composition(X1_2,X2_2)) = composition(composition(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c66,plain,
composition(X3,composition(join(x0,one),X)) = composition(composition(X3,join(x0,one)),X),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
composition(composition(X3,join(x0,one)),X) = composition(X3,X),
inference(congruence,[status(thm)],[c54]) ).
cnf(c68,plain,
composition(X3,composition(join(x0,one),X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
composition(converse(join(x0,one)),composition(join(x0,one),X)) = composition(converse(join(x0,one)),X),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
composition(converse(join(x0,one)),composition(join(x0,one),X)) = X,
inference(transitivity,[status(thm)],[c69,c59]) ).
cnf(c71,plain,
composition(join(x0,one),X) = X,
inference(transitivity,[status(thm)],[c64,c70]) ).
cnf(c72,plain,
X = composition(join(x0,one),X),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
complement(X) = complement(composition(join(x0,one),X)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
composition(converse(join(x0,one)),complement(X)) = composition(converse(join(x0,one)),complement(composition(join(x0,one),X))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
join(complement(X),composition(converse(join(x0,one)),complement(X))) = join(complement(X),composition(converse(join(x0,one)),complement(composition(join(x0,one),X)))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,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(c77,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)],[c76]) ).
cnf(c78,axiom,
join(composition(converse(X0_2),complement(composition(X0_2,X1_2))),complement(X1_2)) = complement(X1_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
cnf(c79,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c77,c79]) ).
cnf(c81,plain,
join(complement(X),composition(converse(join(x0,one)),complement(composition(join(x0,one),X)))) = complement(X),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
join(complement(X),composition(converse(join(x0,one)),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c75,c81]) ).
cnf(c83,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c62,c82]) ).
cnf(c84,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c88,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)],[c87]) ).
cnf(c89,axiom,
X0_2 = join(complement(join(complement(X0_2),complement(X1_2))),complement(join(complement(X0_2),X1_2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
cnf(c90,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c88,c91]) ).
cnf(c93,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c86,c93]) ).
cnf(c95,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c38,c94]) ).
cnf(c96,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c36,c96]) ).
cnf(c98,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c15,c97]) ).
cnf(c99,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c102,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(zero,X) = meet(X,zero),
inference(substitution,[status(thm)],[c14]) ).
cnf(c104,plain,
join(meet(X,top),meet(zero,X)) = join(meet(X,top),meet(X,zero)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c106,plain,
meet(X,zero) = meet(X,complement(top)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
join(meet(X,top),meet(X,zero)) = join(meet(X,top),meet(X,complement(top))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,X),meet(X3,complement(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c109,plain,
join(meet(X3,X),meet(X3,complement(X))) = join(meet(X3,complement(X)),meet(X3,X)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c111,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c92]) ).
cnf(c113,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c111,c112]) ).
cnf(c114,plain,
join(meet(X3,X),meet(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c109,c113]) ).
cnf(c115,plain,
join(meet(X,top),meet(X,complement(top))) = X,
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
join(meet(X,top),meet(X,zero)) = X,
inference(transitivity,[status(thm)],[c107,c115]) ).
cnf(c117,plain,
join(meet(X,top),meet(zero,X)) = X,
inference(transitivity,[status(thm)],[c104,c116]) ).
cnf(c118,plain,
join(meet(complement(zero),top),meet(zero,complement(zero))) = complement(zero),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
complement(zero) = join(meet(complement(zero),top),meet(zero,complement(zero))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
zero = meet(zero,complement(zero)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c121,plain,
meet(zero,complement(zero)) = zero,
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
join(meet(complement(zero),top),meet(zero,complement(zero))) = join(meet(complement(zero),top),zero),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
join(meet(complement(zero),top),zero) = join(zero,meet(complement(zero),top)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c124,plain,
meet(top,complement(zero)) = meet(complement(zero),top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c125,plain,
meet(complement(zero),top) = meet(top,complement(zero)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
join(zero,meet(complement(zero),top)) = join(zero,meet(top,complement(zero))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
meet(top,complement(zero)) = complement(zero),
inference(substitution,[status(thm)],[c98]) ).
cnf(c128,plain,
join(zero,meet(top,complement(zero))) = join(zero,complement(zero)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c130,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
join(zero,meet(top,complement(zero))) = top,
inference(transitivity,[status(thm)],[c128,c130]) ).
cnf(c132,plain,
join(zero,meet(complement(zero),top)) = top,
inference(transitivity,[status(thm)],[c126,c131]) ).
cnf(c133,plain,
join(meet(complement(zero),top),zero) = top,
inference(transitivity,[status(thm)],[c123,c132]) ).
cnf(c134,plain,
join(meet(complement(zero),top),meet(zero,complement(zero))) = top,
inference(transitivity,[status(thm)],[c122,c133]) ).
cnf(c135,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c119,c134]) ).
cnf(c136,plain,
top = complement(zero),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
meet(X,top) = meet(X,complement(zero)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
join(zero,meet(X,top)) = join(zero,meet(X,complement(zero))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c140,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c141,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c142,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c144,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c146,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,axiom,
join(X0_2,join(X1_2,X2_2)) = join(join(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c149,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c151,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c7]) ).
cnf(c154,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c149,c154]) ).
cnf(c156,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c147,c155]) ).
cnf(c157,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c160,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c161,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c159,c161]) ).
cnf(c163,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c158,c162]) ).
cnf(c164,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c144,c163]) ).
cnf(c165,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c165,c25]) ).
cnf(c167,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c142,c166]) ).
cnf(c168,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c140,c167]) ).
cnf(c169,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c139,c168]) ).
cnf(c170,plain,
zero = meet(X,zero),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
join(zero,meet(X,complement(zero))) = join(meet(X,zero),meet(X,complement(zero))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
join(meet(X,zero),meet(X,complement(zero))) = X,
inference(substitution,[status(thm)],[c114]) ).
cnf(c173,plain,
join(zero,meet(X,complement(zero))) = X,
inference(transitivity,[status(thm)],[c171,c172]) ).
cnf(c174,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c138,c173]) ).
cnf(c175,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c102,c174]) ).
cnf(c176,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c100,c176]) ).
cnf(c178,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c179,c95]) ).
cnf(c181,plain,
complement(complement(meet(composition(x0,X3),complement(composition(x0,X))))) = meet(composition(x0,X3),complement(composition(x0,X))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
meet(composition(x0,X3),complement(composition(x0,X))) = complement(complement(meet(composition(x0,X3),complement(composition(x0,X))))),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c184,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
meet(join(X3,complement(X)),join(complement(X3),complement(X))) = meet(join(X3,complement(X)),join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c187,plain,
join(X3,complement(X)) = join(complement(X),X3),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
meet(join(X3,complement(X)),join(complement(X),complement(X3))) = meet(join(complement(X),X3),join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c190,plain,
join(meet(X3,X),complement(X4)) = join(complement(join(complement(X3),complement(X))),complement(X4)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
complement(join(meet(X4,X3),complement(X))) = complement(join(complement(join(complement(X4),complement(X3))),complement(X))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
meet(join(complement(X4),complement(X3)),X) = complement(join(complement(join(complement(X4),complement(X3))),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c193,plain,
complement(join(complement(join(complement(X4),complement(X3))),complement(X))) = meet(join(complement(X4),complement(X3)),X),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
meet(X,join(complement(X4),complement(X3))) = meet(join(complement(X4),complement(X3)),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c195,plain,
meet(join(complement(X4),complement(X3)),X) = meet(X,join(complement(X4),complement(X3))),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
complement(join(complement(join(complement(X4),complement(X3))),complement(X))) = meet(X,join(complement(X4),complement(X3))),
inference(transitivity,[status(thm)],[c193,c195]) ).
cnf(c197,plain,
complement(join(meet(X4,X3),complement(X))) = meet(X,join(complement(X4),complement(X3))),
inference(transitivity,[status(thm)],[c191,c196]) ).
cnf(c198,plain,
complement(join(meet(X,X3),complement(join(complement(X),X3)))) = meet(join(complement(X),X3),join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,plain,
meet(join(complement(X),X3),join(complement(X),complement(X3))) = complement(join(meet(X,X3),complement(join(complement(X),X3)))),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
join(meet(X,X3),complement(join(complement(X),X3))) = X,
inference(substitution,[status(thm)],[c92]) ).
cnf(c201,plain,
complement(join(meet(X,X3),complement(join(complement(X),X3)))) = complement(X),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
meet(join(complement(X),X3),join(complement(X),complement(X3))) = complement(X),
inference(transitivity,[status(thm)],[c199,c201]) ).
cnf(c203,plain,
meet(join(X3,complement(X)),join(complement(X),complement(X3))) = complement(X),
inference(transitivity,[status(thm)],[c188,c202]) ).
cnf(c204,plain,
meet(join(X3,complement(X)),join(complement(X3),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c185,c203]) ).
cnf(c205,plain,
meet(join(complement(X),complement(meet(composition(x0,X3),complement(composition(x0,X))))),join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X)))))) = complement(meet(composition(x0,X3),complement(composition(x0,X)))),
inference(substitution,[status(thm)],[c204]) ).
cnf(c206,plain,
complement(meet(composition(x0,X3),complement(composition(x0,X)))) = meet(join(complement(X),complement(meet(composition(x0,X3),complement(composition(x0,X))))),join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X)))))),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c208,plain,
join(X3,complement(meet(X,complement(X3)))) = join(complement(complement(X3)),complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c210,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c212,plain,
join(X,zero) = join(X,complement(top)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c214,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c156]) ).
cnf(c216,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c156]) ).
cnf(c217,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c164]) ).
cnf(c219,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c217,c218]) ).
cnf(c220,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c215,c219]) ).
cnf(c221,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c214,c220]) ).
cnf(c222,plain,
join(X,top) = join(complement(top),top),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
join(X,complement(X)) = join(complement(X),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c224,plain,
join(complement(X),X) = join(X,complement(X)),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c226,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
join(complement(X),X) = top,
inference(transitivity,[status(thm)],[c224,c226]) ).
cnf(c228,plain,
join(complement(top),top) = top,
inference(substitution,[status(thm)],[c227]) ).
cnf(c229,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c222,c228]) ).
cnf(c230,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
top = join(complement(X),top),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
complement(top) = complement(join(complement(X),top)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
join(X,complement(top)) = join(X,complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c235,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c236,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c238,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c237,c174]) ).
cnf(c239,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c236,c238]) ).
cnf(c240,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c234,c239]) ).
cnf(c241,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
join(X,complement(join(complement(X),top))) = join(meet(X,top),complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
join(meet(X,top),complement(join(complement(X),top))) = X,
inference(substitution,[status(thm)],[c92]) ).
cnf(c244,plain,
join(X,complement(join(complement(X),top))) = X,
inference(transitivity,[status(thm)],[c242,c243]) ).
cnf(c245,plain,
join(X,complement(top)) = X,
inference(transitivity,[status(thm)],[c233,c244]) ).
cnf(c246,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c212,c245]) ).
cnf(c247,plain,
join(meet(X,X3),zero) = meet(X,X3),
inference(substitution,[status(thm)],[c246]) ).
cnf(c248,plain,
meet(X,X3) = join(meet(X,X3),zero),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
complement(meet(X,X3)) = complement(join(meet(X,X3),zero)),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c251,plain,
join(meet(X,X3),zero) = join(meet(X,X3),complement(top)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
complement(join(meet(X,X3),zero)) = complement(join(meet(X,X3),complement(top))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
complement(join(meet(X,X3),complement(top))) = meet(top,join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c197]) ).
cnf(c254,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c255,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c254,c240]) ).
cnf(c256,plain,
meet(top,join(complement(X),complement(X3))) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c255]) ).
cnf(c257,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c258,plain,
meet(top,join(complement(X),complement(X3))) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c256,c257]) ).
cnf(c259,plain,
complement(join(meet(X,X3),complement(top))) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c253,c258]) ).
cnf(c260,plain,
complement(join(meet(X,X3),zero)) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c252,c259]) ).
cnf(c261,plain,
complement(meet(X,X3)) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c249,c260]) ).
cnf(c262,plain,
complement(meet(X3,X)) = join(complement(X3),complement(X)),
inference(transitivity,[status(thm)],[c210,c261]) ).
cnf(c263,plain,
complement(meet(complement(X3),meet(X,complement(X3)))) = join(complement(complement(X3)),complement(meet(X,complement(X3)))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c264,plain,
join(complement(complement(X3)),complement(meet(X,complement(X3)))) = complement(meet(complement(X3),meet(X,complement(X3)))),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
meet(complement(X3),meet(X,complement(X3))) = meet(meet(X,complement(X3)),complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c266,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c267,plain,
join(zero,X) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c267,c95]) ).
cnf(c269,plain,
join(zero,meet(meet(X,complement(X3)),complement(X3))) = meet(meet(X,complement(X3)),complement(X3)),
inference(substitution,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(meet(X,complement(X3)),complement(X3)) = join(zero,meet(meet(X,complement(X3)),complement(X3))),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c272,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
meet(X3,X) = meet(X,X3),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c274,plain,
complement(join(complement(X3),complement(X))) = meet(X,X3),
inference(transitivity,[status(thm)],[c272,c273]) ).
cnf(c275,plain,
complement(join(complement(X),complement(meet(X3,complement(X))))) = meet(meet(X3,complement(X)),X),
inference(substitution,[status(thm)],[c274]) ).
cnf(c276,plain,
meet(meet(X3,complement(X)),X) = complement(join(complement(X),complement(meet(X3,complement(X))))),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,plain,
complement(meet(X,complement(X3))) = join(complement(X),complement(complement(X3))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c278,plain,
join(complement(X),complement(complement(X3))) = join(complement(X),X3),
inference(congruence,[status(thm)],[c180]) ).
cnf(c279,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c280,plain,
join(complement(X),complement(complement(X3))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c278,c279]) ).
cnf(c281,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c277,c280]) ).
cnf(c282,plain,
join(complement(X3),complement(meet(X,complement(X3)))) = join(complement(X3),join(X3,complement(X))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c284,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
join(complement(X3),join(X3,X)) = join(complement(X3),join(X,X3)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c287,plain,
join(X,X3) = join(X3,X),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
join(complement(X3),join(X,X3)) = join(complement(X3),join(X3,X)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
join(complement(X3),join(X3,X)) = join(join(complement(X3),X3),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c290,plain,
join(join(complement(X3),X3),X) = join(top,X),
inference(congruence,[status(thm)],[c227]) ).
cnf(c291,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c7]) ).
cnf(c292,plain,
join(join(complement(X3),X3),X) = join(X,top),
inference(transitivity,[status(thm)],[c290,c291]) ).
cnf(c293,plain,
join(complement(X3),join(X3,X)) = join(X,top),
inference(transitivity,[status(thm)],[c289,c292]) ).
cnf(c294,plain,
join(complement(X3),join(X,X3)) = join(X,top),
inference(transitivity,[status(thm)],[c288,c293]) ).
cnf(c295,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c296,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c295,c229]) ).
cnf(c297,plain,
join(complement(X3),join(X,X3)) = top,
inference(transitivity,[status(thm)],[c294,c296]) ).
cnf(c298,plain,
join(complement(X3),join(X3,X)) = top,
inference(transitivity,[status(thm)],[c285,c297]) ).
cnf(c299,plain,
join(complement(X3),join(X3,complement(X))) = top,
inference(substitution,[status(thm)],[c298]) ).
cnf(c300,plain,
join(complement(X3),complement(meet(X,complement(X3)))) = top,
inference(transitivity,[status(thm)],[c282,c299]) ).
cnf(c301,plain,
join(complement(X),complement(meet(X3,complement(X)))) = top,
inference(substitution,[status(thm)],[c300]) ).
cnf(c302,plain,
complement(join(complement(X),complement(meet(X3,complement(X))))) = complement(top),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
complement(join(complement(X),complement(meet(X3,complement(X))))) = zero,
inference(transitivity,[status(thm)],[c302,c25]) ).
cnf(c304,plain,
meet(meet(X3,complement(X)),X) = zero,
inference(transitivity,[status(thm)],[c276,c303]) ).
cnf(c305,plain,
meet(meet(X,complement(X3)),X3) = zero,
inference(substitution,[status(thm)],[c304]) ).
cnf(c306,plain,
zero = meet(meet(X,complement(X3)),X3),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
join(zero,meet(meet(X,complement(X3)),complement(X3))) = join(meet(meet(X,complement(X3)),X3),meet(meet(X,complement(X3)),complement(X3))),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
join(meet(meet(X,complement(X3)),X3),meet(meet(X,complement(X3)),complement(X3))) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c309,plain,
join(zero,meet(meet(X,complement(X3)),complement(X3))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c307,c308]) ).
cnf(c310,plain,
meet(meet(X,complement(X3)),complement(X3)) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c270,c309]) ).
cnf(c311,plain,
meet(complement(X3),meet(X,complement(X3))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c265,c310]) ).
cnf(c312,plain,
complement(meet(complement(X3),meet(X,complement(X3)))) = complement(meet(X,complement(X3))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
join(complement(complement(X3)),complement(meet(X,complement(X3)))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c264,c312]) ).
cnf(c314,plain,
join(X3,complement(meet(X,complement(X3)))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c208,c313]) ).
cnf(c315,plain,
join(composition(x0,X3),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = complement(meet(composition(x0,X),complement(composition(x0,X3)))),
inference(substitution,[status(thm)],[c314]) ).
cnf(c316,plain,
complement(meet(composition(x0,X),complement(composition(x0,X3)))) = join(composition(x0,X3),complement(meet(composition(x0,X),complement(composition(x0,X3))))),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = join(complement(X3),join(composition(x0,X3),complement(meet(composition(x0,X),complement(composition(x0,X3)))))),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
join(complement(X3),join(composition(x0,X3),complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = join(join(complement(X3),composition(x0,X3)),complement(meet(composition(x0,X),complement(composition(x0,X3))))),
inference(substitution,[status(thm)],[c148]) ).
cnf(c319,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c320,plain,
join(complement(meet(X4,complement(X3))),meet(X4,X)) = join(complement(meet(X4,complement(X3))),meet(X,X4)),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
join(complement(meet(X4,complement(X3))),meet(X,X4)) = join(complement(meet(X4,complement(X3))),meet(X4,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c322,plain,
join(meet(X4,X),complement(meet(X4,complement(X3)))) = join(complement(meet(X4,complement(X3))),meet(X4,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c323,plain,
join(complement(meet(X4,complement(X3))),meet(X4,X)) = join(meet(X4,X),complement(meet(X4,complement(X3)))),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
join(complement(meet(X,complement(X4))),X3) = join(X3,complement(meet(X,complement(X4)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c325,plain,
join(X3,complement(meet(X,complement(X4)))) = join(complement(meet(X,complement(X4))),X3),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
join(complement(meet(X,complement(X4))),X3) = join(join(X4,complement(X)),X3),
inference(congruence,[status(thm)],[c281]) ).
cnf(c327,plain,
join(X4,join(complement(X),X3)) = join(join(X4,complement(X)),X3),
inference(substitution,[status(thm)],[c148]) ).
cnf(c328,plain,
join(join(X4,complement(X)),X3) = join(X4,join(complement(X),X3)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c330,plain,
join(X4,join(complement(X),X3)) = join(X4,join(X3,complement(X))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
join(join(X4,complement(X)),X3) = join(X4,join(X3,complement(X))),
inference(transitivity,[status(thm)],[c328,c330]) ).
cnf(c332,plain,
join(complement(meet(X,complement(X4))),X3) = join(X4,join(X3,complement(X))),
inference(transitivity,[status(thm)],[c326,c331]) ).
cnf(c333,plain,
join(X3,complement(meet(X,complement(X4)))) = join(X4,join(X3,complement(X))),
inference(transitivity,[status(thm)],[c325,c332]) ).
cnf(c334,plain,
join(X,complement(meet(X3,complement(X4)))) = join(X4,join(X,complement(X3))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c336,plain,
join(X4,join(X,complement(X3))) = join(X4,join(complement(X3),X)),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
join(X,complement(meet(X3,complement(X4)))) = join(X4,join(complement(X3),X)),
inference(transitivity,[status(thm)],[c334,c336]) ).
cnf(c338,plain,
join(meet(X4,X),complement(meet(X4,complement(X3)))) = join(X3,join(complement(X4),meet(X4,X))),
inference(substitution,[status(thm)],[c337]) ).
cnf(c339,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c340,plain,
join(complement(X3),meet(X3,X)) = join(complement(X3),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
complement(meet(X3,join(complement(X3),complement(X)))) = join(complement(X3),complement(join(complement(X3),complement(X)))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c342,plain,
join(complement(X3),complement(join(complement(X3),complement(X)))) = complement(meet(X3,join(complement(X3),complement(X)))),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
join(X3,meet(X,X3)) = join(X3,meet(X3,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c344,plain,
join(meet(X3,X),X3) = join(X3,meet(X3,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c345,plain,
join(X3,meet(X3,X)) = join(meet(X3,X),X3),
inference(symmetry,[status(thm)],[c344]) ).
cnf(c346,plain,
X3 = join(meet(X3,X),complement(join(complement(X3),X))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c347,plain,
join(meet(X3,X),X3) = join(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c349,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c348]) ).
cnf(c350,plain,
join(X3,join(X3,X)) = join(X3,join(X,X3)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c352,plain,
join(X,X3) = join(X,meet(X3,top)),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
join(X3,join(X,X3)) = join(X3,join(X,meet(X3,top))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c355,plain,
join(X,meet(X3,top)) = join(X,complement(join(zero,complement(X3)))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
join(X3,join(X,meet(X3,top))) = join(X3,join(X,complement(join(zero,complement(X3))))),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c358,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)],[c357]) ).
cnf(c359,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c360,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)],[c359]) ).
cnf(c361,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c362,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
join(complement(X3),join(X,complement(X3))) = join(complement(X3),join(complement(X3),X)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
join(complement(X3),join(complement(X3),X)) = join(join(complement(X3),complement(X3)),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c365,plain,
join(join(complement(X3),complement(X3)),X) = join(complement(X3),X),
inference(congruence,[status(thm)],[c83]) ).
cnf(c366,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c367,plain,
join(join(complement(X3),complement(X3)),X) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c365,c366]) ).
cnf(c368,plain,
join(complement(X3),join(complement(X3),X)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c364,c367]) ).
cnf(c369,plain,
join(complement(X3),join(X,complement(X3))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c363,c368]) ).
cnf(c370,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)],[c369]) ).
cnf(c371,plain,
join(X,complement(join(zero,complement(X3)))) = join(X,meet(X3,top)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c372,plain,
join(X,meet(X3,top)) = join(X,X3),
inference(congruence,[status(thm)],[c240]) ).
cnf(c373,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c374,plain,
join(X,meet(X3,top)) = join(X3,X),
inference(transitivity,[status(thm)],[c372,c373]) ).
cnf(c375,plain,
join(X,complement(join(zero,complement(X3)))) = join(X3,X),
inference(transitivity,[status(thm)],[c371,c374]) ).
cnf(c376,plain,
join(complement(join(zero,complement(X3))),join(X,complement(join(zero,complement(X3))))) = join(X3,X),
inference(transitivity,[status(thm)],[c370,c375]) ).
cnf(c377,plain,
join(meet(X3,top),join(X,complement(join(zero,complement(X3))))) = join(X3,X),
inference(transitivity,[status(thm)],[c360,c376]) ).
cnf(c378,plain,
join(X3,join(X,complement(join(zero,complement(X3))))) = join(X3,X),
inference(transitivity,[status(thm)],[c358,c377]) ).
cnf(c379,plain,
join(X3,join(X,meet(X3,top))) = join(X3,X),
inference(transitivity,[status(thm)],[c356,c378]) ).
cnf(c380,plain,
join(X3,join(X,X3)) = join(X3,X),
inference(transitivity,[status(thm)],[c353,c379]) ).
cnf(c381,plain,
join(X3,join(X3,X)) = join(X3,X),
inference(transitivity,[status(thm)],[c350,c380]) ).
cnf(c382,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)],[c381]) ).
cnf(c383,plain,
join(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))) = X3,
inference(transitivity,[status(thm)],[c382,c92]) ).
cnf(c384,plain,
join(meet(X3,X),X3) = X3,
inference(transitivity,[status(thm)],[c347,c383]) ).
cnf(c385,plain,
join(X3,meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c345,c384]) ).
cnf(c386,plain,
join(X3,meet(X,X3)) = X3,
inference(transitivity,[status(thm)],[c343,c385]) ).
cnf(c387,plain,
join(complement(X),meet(X3,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c386]) ).
cnf(c388,plain,
complement(X) = join(complement(X),meet(X3,complement(X))),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
join(complement(X3),complement(X)) = join(complement(X3),join(complement(X),meet(X3,complement(X)))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
meet(X3,join(complement(X3),complement(X))) = meet(X3,join(complement(X3),join(complement(X),meet(X3,complement(X))))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c392,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
complement(join(complement(X3),X)) = complement(join(X,complement(X3))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c395,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c396,plain,
complement(join(complement(X),complement(X))) = X,
inference(transitivity,[status(thm)],[c395,c180]) ).
cnf(c397,plain,
meet(X,X) = X,
inference(transitivity,[status(thm)],[c394,c396]) ).
cnf(c398,plain,
X = meet(X,X),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
join(X3,complement(X)) = join(meet(X3,X3),complement(X)),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
complement(join(X3,complement(X))) = complement(join(meet(X3,X3),complement(X))),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
complement(join(meet(X3,X3),complement(X))) = meet(X,join(complement(X3),complement(X3))),
inference(substitution,[status(thm)],[c197]) ).
cnf(c402,plain,
meet(X,join(complement(X3),complement(X3))) = meet(X,complement(X3)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c403,plain,
complement(join(meet(X3,X3),complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c401,c402]) ).
cnf(c404,plain,
complement(join(X3,complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c400,c403]) ).
cnf(c405,plain,
complement(join(X,complement(X3))) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c404]) ).
cnf(c406,plain,
complement(join(complement(X3),X)) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c393,c405]) ).
cnf(c407,plain,
meet(X3,complement(X)) = complement(join(complement(X3),X)),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
join(complement(X),meet(X3,complement(X))) = join(complement(X),complement(join(complement(X3),X))),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
join(complement(X3),join(complement(X),meet(X3,complement(X)))) = join(complement(X3),join(complement(X),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
meet(X3,join(complement(X3),join(complement(X),meet(X3,complement(X))))) = meet(X3,join(complement(X3),join(complement(X),complement(join(complement(X3),X))))),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
join(complement(X3),join(complement(X),complement(join(complement(X3),X)))) = join(join(complement(X3),complement(X)),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c148]) ).
cnf(c412,plain,
meet(X3,join(complement(X3),join(complement(X),complement(join(complement(X3),X))))) = meet(X3,join(join(complement(X3),complement(X)),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
join(complement(X3),complement(X)) = complement(meet(X3,X)),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c414,plain,
join(join(complement(X3),complement(X)),complement(join(complement(X3),X))) = join(complement(meet(X3,X)),complement(join(complement(X3),X))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
meet(X3,join(join(complement(X3),complement(X)),complement(join(complement(X3),X)))) = meet(X3,join(complement(meet(X3,X)),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
X3 = join(meet(X3,X),complement(join(complement(X3),X))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c417,plain,
meet(X3,join(complement(meet(X3,X)),complement(join(complement(X3),X)))) = meet(join(meet(X3,X),complement(join(complement(X3),X))),join(complement(meet(X3,X)),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
meet(join(meet(X3,X),complement(join(complement(X3),X))),join(complement(meet(X3,X)),complement(join(complement(X3),X)))) = complement(join(complement(X3),X)),
inference(substitution,[status(thm)],[c204]) ).
cnf(c419,plain,
meet(join(meet(X3,X),complement(join(complement(X3),X))),join(complement(meet(X3,X)),complement(join(complement(X3),X)))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c418,c406]) ).
cnf(c420,plain,
meet(X3,join(complement(meet(X3,X)),complement(join(complement(X3),X)))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c417,c419]) ).
cnf(c421,plain,
meet(X3,join(join(complement(X3),complement(X)),complement(join(complement(X3),X)))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c415,c420]) ).
cnf(c422,plain,
meet(X3,join(complement(X3),join(complement(X),complement(join(complement(X3),X))))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c412,c421]) ).
cnf(c423,plain,
meet(X3,join(complement(X3),join(complement(X),meet(X3,complement(X))))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c410,c422]) ).
cnf(c424,plain,
meet(X3,join(complement(X3),complement(X))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c390,c423]) ).
cnf(c425,plain,
complement(meet(X3,join(complement(X3),complement(X)))) = complement(meet(X3,complement(X))),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
complement(meet(X3,complement(X))) = join(complement(X3),complement(complement(X))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c427,plain,
join(complement(X3),complement(complement(X))) = join(complement(X3),X),
inference(congruence,[status(thm)],[c180]) ).
cnf(c428,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c429,plain,
join(complement(X3),complement(complement(X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c427,c428]) ).
cnf(c430,plain,
complement(meet(X3,complement(X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c426,c429]) ).
cnf(c431,plain,
complement(meet(X3,join(complement(X3),complement(X)))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c425,c430]) ).
cnf(c432,plain,
join(complement(X3),complement(join(complement(X3),complement(X)))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c342,c431]) ).
cnf(c433,plain,
join(complement(X3),meet(X3,X)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c340,c432]) ).
cnf(c434,plain,
join(X3,join(complement(X4),meet(X4,X))) = join(X3,join(X,complement(X4))),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
join(X,complement(meet(X4,complement(X3)))) = join(X3,join(X,complement(X4))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c436,plain,
join(X3,join(X,complement(X4))) = join(X,complement(meet(X4,complement(X3)))),
inference(symmetry,[status(thm)],[c435]) ).
cnf(c437,plain,
join(X3,join(complement(X4),meet(X4,X))) = join(X,complement(meet(X4,complement(X3)))),
inference(transitivity,[status(thm)],[c434,c436]) ).
cnf(c438,plain,
join(meet(X4,X),complement(meet(X4,complement(X3)))) = join(X,complement(meet(X4,complement(X3)))),
inference(transitivity,[status(thm)],[c338,c437]) ).
cnf(c439,plain,
join(complement(meet(X4,complement(X3))),meet(X4,X)) = join(X,complement(meet(X4,complement(X3)))),
inference(transitivity,[status(thm)],[c323,c438]) ).
cnf(c440,plain,
join(complement(meet(X4,complement(X3))),meet(X,X4)) = join(X,complement(meet(X4,complement(X3)))),
inference(transitivity,[status(thm)],[c321,c439]) ).
cnf(c441,plain,
join(complement(meet(X4,complement(X3))),meet(X4,X)) = join(X,complement(meet(X4,complement(X3)))),
inference(transitivity,[status(thm)],[c320,c440]) ).
cnf(c442,plain,
join(complement(meet(composition(x0,X),complement(composition(x0,X3)))),meet(composition(x0,X),join(complement(X3),composition(x0,X3)))) = join(join(complement(X3),composition(x0,X3)),complement(meet(composition(x0,X),complement(composition(x0,X3))))),
inference(substitution,[status(thm)],[c441]) ).
cnf(c443,plain,
join(join(complement(X3),composition(x0,X3)),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = join(complement(meet(composition(x0,X),complement(composition(x0,X3)))),meet(composition(x0,X),join(complement(X3),composition(x0,X3)))),
inference(symmetry,[status(thm)],[c442]) ).
cnf(c444,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c445,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c444]) ).
cnf(c446,plain,
composition(X3,X) = composition(X3,converse(converse(X))),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
join(composition(X4,X),composition(X4,X3)) = join(composition(X4,X),composition(X4,converse(converse(X3)))),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
converse(converse(join(composition(X4,X3),composition(X4,converse(X))))) = join(composition(X4,X3),composition(X4,converse(X))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c449,plain,
join(composition(X4,X3),composition(X4,converse(X))) = converse(converse(join(composition(X4,X3),composition(X4,converse(X))))),
inference(symmetry,[status(thm)],[c448]) ).
cnf(c450,plain,
join(composition(X3,converse(X)),converse(X4)) = join(converse(X4),composition(X3,converse(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c451,plain,
join(converse(X4),composition(X3,converse(X))) = join(composition(X3,converse(X)),converse(X4)),
inference(symmetry,[status(thm)],[c450]) ).
cnf(c452,plain,
converse(composition(X3,converse(X))) = composition(converse(converse(X)),converse(X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c453,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c454,plain,
composition(converse(converse(X)),converse(X3)) = composition(X,converse(X3)),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
converse(composition(X3,converse(X))) = composition(X,converse(X3)),
inference(transitivity,[status(thm)],[c452,c454]) ).
cnf(c456,plain,
converse(composition(X,converse(X3))) = composition(X3,converse(X)),
inference(substitution,[status(thm)],[c455]) ).
cnf(c457,plain,
composition(X3,converse(X)) = converse(composition(X,converse(X3))),
inference(symmetry,[status(thm)],[c456]) ).
cnf(c458,plain,
join(composition(X3,converse(X)),converse(X4)) = join(converse(composition(X,converse(X3))),converse(X4)),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c460,plain,
converse(join(composition(X,converse(X3)),X4)) = join(converse(composition(X,converse(X3))),converse(X4)),
inference(substitution,[status(thm)],[c459]) ).
cnf(c461,plain,
join(converse(composition(X,converse(X3))),converse(X4)) = converse(join(composition(X,converse(X3)),X4)),
inference(symmetry,[status(thm)],[c460]) ).
cnf(c462,plain,
join(composition(X,converse(X3)),X4) = join(X4,composition(X,converse(X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c463,plain,
converse(join(composition(X,converse(X3)),X4)) = converse(join(X4,composition(X,converse(X3)))),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
join(converse(composition(X,converse(X3))),converse(X4)) = converse(join(X4,composition(X,converse(X3)))),
inference(transitivity,[status(thm)],[c461,c463]) ).
cnf(c465,plain,
join(composition(X3,converse(X)),converse(X4)) = converse(join(X4,composition(X,converse(X3)))),
inference(transitivity,[status(thm)],[c458,c464]) ).
cnf(c466,plain,
join(converse(X4),composition(X3,converse(X))) = converse(join(X4,composition(X,converse(X3)))),
inference(transitivity,[status(thm)],[c451,c465]) ).
cnf(c467,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = converse(join(composition(X4,X3),composition(X4,converse(X)))),
inference(substitution,[status(thm)],[c466]) ).
cnf(c468,plain,
converse(join(composition(X4,X3),composition(X4,converse(X)))) = join(converse(composition(X4,X3)),composition(X,converse(X4))),
inference(symmetry,[status(thm)],[c467]) ).
cnf(c469,plain,
converse(composition(X3,X)) = composition(converse(X),converse(X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c470,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = join(composition(converse(X3),converse(X4)),composition(X,converse(X4))),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c472,plain,
composition(join(converse(X3),X),converse(X4)) = join(composition(converse(X3),converse(X4)),composition(X,converse(X4))),
inference(substitution,[status(thm)],[c471]) ).
cnf(c473,plain,
join(composition(converse(X3),converse(X4)),composition(X,converse(X4))) = composition(join(converse(X3),X),converse(X4)),
inference(symmetry,[status(thm)],[c472]) ).
cnf(c474,plain,
join(X,converse(X3)) = join(converse(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c475,plain,
join(converse(X3),X) = join(X,converse(X3)),
inference(symmetry,[status(thm)],[c474]) ).
cnf(c476,plain,
composition(join(converse(X4),X3),converse(X)) = composition(join(X3,converse(X4)),converse(X)),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c478,plain,
join(X3,converse(X)) = join(converse(X),X3),
inference(symmetry,[status(thm)],[c477]) ).
cnf(c479,plain,
converse(join(X3,converse(X))) = converse(join(converse(X),X3)),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,plain,
converse(join(converse(X),X3)) = join(converse(converse(X)),converse(X3)),
inference(substitution,[status(thm)],[c459]) ).
cnf(c481,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c482,plain,
join(converse(converse(X)),converse(X3)) = join(X,converse(X3)),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
converse(join(converse(X),X3)) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c480,c482]) ).
cnf(c484,plain,
converse(join(X3,converse(X))) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c479,c483]) ).
cnf(c485,plain,
converse(join(X,converse(X3))) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c484]) ).
cnf(c486,plain,
join(X3,converse(X)) = converse(join(X,converse(X3))),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
composition(join(X4,converse(X3)),converse(X)) = composition(converse(join(X3,converse(X4))),converse(X)),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
converse(composition(X,join(X3,converse(X4)))) = composition(converse(join(X3,converse(X4))),converse(X)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c489,plain,
composition(converse(join(X3,converse(X4))),converse(X)) = converse(composition(X,join(X3,converse(X4)))),
inference(symmetry,[status(thm)],[c488]) ).
cnf(c490,plain,
composition(join(X4,converse(X3)),converse(X)) = converse(composition(X,join(X3,converse(X4)))),
inference(transitivity,[status(thm)],[c487,c489]) ).
cnf(c491,plain,
composition(join(X3,converse(X4)),converse(X)) = converse(composition(X,join(X4,converse(X3)))),
inference(substitution,[status(thm)],[c490]) ).
cnf(c492,plain,
composition(join(converse(X4),X3),converse(X)) = converse(composition(X,join(X4,converse(X3)))),
inference(transitivity,[status(thm)],[c476,c491]) ).
cnf(c493,plain,
composition(join(converse(X3),X),converse(X4)) = converse(composition(X4,join(X3,converse(X)))),
inference(substitution,[status(thm)],[c492]) ).
cnf(c494,plain,
join(composition(converse(X3),converse(X4)),composition(X,converse(X4))) = converse(composition(X4,join(X3,converse(X)))),
inference(transitivity,[status(thm)],[c473,c493]) ).
cnf(c495,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = converse(composition(X4,join(X3,converse(X)))),
inference(transitivity,[status(thm)],[c470,c494]) ).
cnf(c496,plain,
converse(join(composition(X4,X3),composition(X4,converse(X)))) = converse(composition(X4,join(X3,converse(X)))),
inference(transitivity,[status(thm)],[c468,c495]) ).
cnf(c497,plain,
converse(converse(join(composition(X4,X3),composition(X4,converse(X))))) = converse(converse(composition(X4,join(X3,converse(X))))),
inference(congruence,[status(thm)],[c496]) ).
cnf(c498,plain,
converse(converse(composition(X4,join(X3,converse(X))))) = composition(X4,join(X3,converse(X))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c499,plain,
converse(converse(join(composition(X4,X3),composition(X4,converse(X))))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c497,c498]) ).
cnf(c500,plain,
join(composition(X4,X3),composition(X4,converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c449,c499]) ).
cnf(c501,plain,
join(composition(X4,X),composition(X4,converse(converse(X3)))) = composition(X4,join(X,converse(converse(X3)))),
inference(substitution,[status(thm)],[c500]) ).
cnf(c502,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c503,plain,
join(X,converse(converse(X3))) = join(X,X3),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
composition(X4,join(X,converse(converse(X3)))) = composition(X4,join(X,X3)),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c506,plain,
composition(X4,join(X,X3)) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
composition(X4,join(X,converse(converse(X3)))) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c504,c506]) ).
cnf(c508,plain,
join(composition(X4,X),composition(X4,converse(converse(X3)))) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c501,c507]) ).
cnf(c509,plain,
join(composition(X4,X),composition(X4,X3)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c447,c508]) ).
cnf(c510,plain,
join(composition(X3,X),composition(X3,complement(X))) = composition(X3,join(complement(X),X)),
inference(substitution,[status(thm)],[c509]) ).
cnf(c511,plain,
composition(X3,join(complement(X),X)) = composition(X3,top),
inference(congruence,[status(thm)],[c227]) ).
cnf(c512,plain,
join(composition(X3,X),composition(X3,complement(X))) = composition(X3,top),
inference(transitivity,[status(thm)],[c510,c511]) ).
cnf(c513,plain,
join(composition(x0,X),composition(x0,complement(X))) = composition(x0,top),
inference(substitution,[status(thm)],[c512]) ).
cnf(c514,plain,
composition(x0,top) = join(composition(x0,X),composition(x0,complement(X))),
inference(symmetry,[status(thm)],[c513]) ).
cnf(c515,plain,
join(complement(X),composition(x0,top)) = join(complement(X),join(composition(x0,X),composition(x0,complement(X)))),
inference(congruence,[status(thm)],[c514]) ).
cnf(c516,plain,
join(composition(x0,X3),X) = join(X,composition(x0,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c517,plain,
join(X,composition(x0,X3)) = join(composition(x0,X3),X),
inference(symmetry,[status(thm)],[c516]) ).
cnf(c518,plain,
join(X3,join(X,composition(x0,X3))) = join(X3,join(composition(x0,X3),X)),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
join(X3,join(composition(x0,X3),X)) = join(join(X3,composition(x0,X3)),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c520,plain,
join(X,join(x0,one)) = join(join(x0,one),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c521,plain,
join(join(x0,one),X) = join(X,join(x0,one)),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c522,plain,
composition(join(join(x0,one),X),X3) = composition(join(X,join(x0,one)),X3),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
join(join(x0,one),X) = join(X,join(x0,one)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c524,plain,
join(X,join(x0,one)) = join(join(x0,one),X),
inference(symmetry,[status(thm)],[c523]) ).
cnf(c525,plain,
composition(join(X3,join(x0,one)),X) = composition(join(join(x0,one),X3),X),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
composition(join(join(x0,one),X3),X) = join(composition(join(x0,one),X),composition(X3,X)),
inference(substitution,[status(thm)],[c471]) ).
cnf(c527,plain,
join(composition(join(x0,one),X),composition(X3,X)) = join(X,composition(X3,X)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c528,plain,
composition(join(join(x0,one),X3),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c526,c527]) ).
cnf(c529,plain,
composition(join(X3,join(x0,one)),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c525,c528]) ).
cnf(c530,plain,
composition(join(X,join(x0,one)),X3) = join(X3,composition(X,X3)),
inference(substitution,[status(thm)],[c529]) ).
cnf(c531,plain,
composition(join(join(x0,one),X),X3) = join(X3,composition(X,X3)),
inference(transitivity,[status(thm)],[c522,c530]) ).
cnf(c532,plain,
composition(join(join(x0,one),x0),X) = join(X,composition(x0,X)),
inference(substitution,[status(thm)],[c531]) ).
cnf(c533,plain,
join(X,composition(x0,X)) = composition(join(join(x0,one),x0),X),
inference(symmetry,[status(thm)],[c532]) ).
cnf(c534,plain,
join(X,join(x0,one)) = join(join(x0,one),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c535,plain,
join(join(x0,one),X) = join(X,join(x0,one)),
inference(symmetry,[status(thm)],[c534]) ).
cnf(c536,plain,
join(X,join(x0,one)) = join(X,one),
inference(congruence,[status(thm)],[c50]) ).
cnf(c537,plain,
join(join(x0,one),X) = join(X,one),
inference(transitivity,[status(thm)],[c535,c536]) ).
cnf(c538,plain,
join(join(x0,one),x0) = join(x0,one),
inference(substitution,[status(thm)],[c537]) ).
cnf(c539,plain,
composition(join(join(x0,one),x0),X) = composition(join(x0,one),X),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
composition(join(join(x0,one),x0),X) = X,
inference(transitivity,[status(thm)],[c539,c71]) ).
cnf(c541,plain,
join(X,composition(x0,X)) = X,
inference(transitivity,[status(thm)],[c533,c540]) ).
cnf(c542,plain,
join(join(X3,composition(x0,X3)),X) = join(X3,X),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
join(X3,join(composition(x0,X3),X)) = join(X3,X),
inference(transitivity,[status(thm)],[c519,c542]) ).
cnf(c544,plain,
join(X3,join(X,composition(x0,X3))) = join(X3,X),
inference(transitivity,[status(thm)],[c518,c543]) ).
cnf(c545,plain,
join(complement(X),join(composition(x0,X),composition(x0,complement(X)))) = join(complement(X),composition(x0,X)),
inference(substitution,[status(thm)],[c544]) ).
cnf(c546,plain,
join(complement(X),composition(x0,top)) = join(complement(X),composition(x0,X)),
inference(transitivity,[status(thm)],[c515,c545]) ).
cnf(c547,plain,
join(complement(X),composition(x0,X)) = join(complement(X),composition(x0,top)),
inference(symmetry,[status(thm)],[c546]) ).
cnf(c548,plain,
meet(composition(x0,X3),join(complement(X),composition(x0,X))) = meet(composition(x0,X3),join(complement(X),composition(x0,top))),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
composition(X3,top) = join(composition(X3,X),composition(X3,complement(X))),
inference(symmetry,[status(thm)],[c512]) ).
cnf(c550,plain,
join(X,composition(X4,top)) = join(X,join(composition(X4,X3),composition(X4,complement(X3)))),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
meet(composition(X4,X3),join(X,composition(X4,top))) = meet(composition(X4,X3),join(X,join(composition(X4,X3),composition(X4,complement(X3))))),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
join(join(X4,X),X3) = join(X3,join(X4,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c553,plain,
join(X3,join(X4,X)) = join(join(X4,X),X3),
inference(symmetry,[status(thm)],[c552]) ).
cnf(c554,plain,
join(X4,join(X,X3)) = join(join(X4,X),X3),
inference(substitution,[status(thm)],[c148]) ).
cnf(c555,plain,
join(join(X4,X),X3) = join(X4,join(X,X3)),
inference(symmetry,[status(thm)],[c554]) ).
cnf(c556,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c557,plain,
join(X4,join(X,X3)) = join(X4,join(X3,X)),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
join(join(X4,X),X3) = join(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c555,c557]) ).
cnf(c559,plain,
join(X3,join(X4,X)) = join(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c553,c558]) ).
cnf(c560,plain,
meet(X4,join(X3,join(X4,X))) = meet(X4,join(X4,join(X3,X))),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
join(X4,join(X3,X)) = join(X3,join(X4,X)),
inference(substitution,[status(thm)],[c559]) ).
cnf(c562,plain,
meet(X4,join(X4,join(X3,X))) = meet(X4,join(X3,join(X4,X))),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
join(meet(X4,join(X3,join(X4,X))),zero) = meet(X4,join(X3,join(X4,X))),
inference(substitution,[status(thm)],[c246]) ).
cnf(c564,plain,
meet(X4,join(X3,join(X4,X))) = join(meet(X4,join(X3,join(X4,X))),zero),
inference(symmetry,[status(thm)],[c563]) ).
cnf(c565,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c566,plain,
join(meet(X4,join(X3,join(X4,X))),zero) = join(meet(X4,join(X3,join(X4,X))),complement(top)),
inference(congruence,[status(thm)],[c565]) ).
cnf(c567,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c568,plain,
join(X3,X) = join(complement(complement(X3)),X),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
join(X3,join(X4,X)) = join(X3,join(complement(complement(X4)),X)),
inference(congruence,[status(thm)],[c568]) ).
cnf(c570,plain,
meet(X4,join(X3,join(X4,X))) = meet(X4,join(X3,join(complement(complement(X4)),X))),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
join(meet(X4,join(X3,join(X4,X))),complement(top)) = join(meet(X4,join(X3,join(complement(complement(X4)),X))),complement(top)),
inference(congruence,[status(thm)],[c570]) ).
cnf(c572,plain,
join(X3,join(complement(X4),X)) = join(complement(X4),join(X3,X)),
inference(substitution,[status(thm)],[c559]) ).
cnf(c573,plain,
join(X4,join(X3,join(complement(X4),X))) = join(X4,join(complement(X4),join(X3,X))),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c575,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c574]) ).
cnf(c576,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c578,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c577,c229]) ).
cnf(c579,plain,
join(X3,join(X,complement(X3))) = top,
inference(transitivity,[status(thm)],[c156,c578]) ).
cnf(c580,plain,
join(X3,join(complement(X3),X)) = top,
inference(transitivity,[status(thm)],[c576,c579]) ).
cnf(c581,plain,
join(X4,join(complement(X4),join(X3,X))) = top,
inference(substitution,[status(thm)],[c580]) ).
cnf(c582,plain,
join(X4,join(X3,join(complement(X4),X))) = top,
inference(transitivity,[status(thm)],[c573,c581]) ).
cnf(c583,plain,
join(complement(X4),join(X3,join(complement(complement(X4)),X))) = top,
inference(substitution,[status(thm)],[c582]) ).
cnf(c584,plain,
top = join(complement(X4),join(X3,join(complement(complement(X4)),X))),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c585,plain,
complement(top) = complement(join(complement(X4),join(X3,join(complement(complement(X4)),X)))),
inference(congruence,[status(thm)],[c584]) ).
cnf(c586,plain,
join(meet(X4,join(X3,join(complement(complement(X4)),X))),complement(top)) = join(meet(X4,join(X3,join(complement(complement(X4)),X))),complement(join(complement(X4),join(X3,join(complement(complement(X4)),X))))),
inference(congruence,[status(thm)],[c585]) ).
cnf(c587,plain,
join(meet(X4,join(X3,join(complement(complement(X4)),X))),complement(join(complement(X4),join(X3,join(complement(complement(X4)),X))))) = X4,
inference(substitution,[status(thm)],[c92]) ).
cnf(c588,plain,
join(meet(X4,join(X3,join(complement(complement(X4)),X))),complement(top)) = X4,
inference(transitivity,[status(thm)],[c586,c587]) ).
cnf(c589,plain,
join(meet(X4,join(X3,join(X4,X))),complement(top)) = X4,
inference(transitivity,[status(thm)],[c571,c588]) ).
cnf(c590,plain,
join(meet(X4,join(X3,join(X4,X))),zero) = X4,
inference(transitivity,[status(thm)],[c566,c589]) ).
cnf(c591,plain,
meet(X4,join(X3,join(X4,X))) = X4,
inference(transitivity,[status(thm)],[c564,c590]) ).
cnf(c592,plain,
meet(X4,join(X4,join(X3,X))) = X4,
inference(transitivity,[status(thm)],[c562,c591]) ).
cnf(c593,plain,
meet(X4,join(X3,join(X4,X))) = X4,
inference(transitivity,[status(thm)],[c560,c592]) ).
cnf(c594,plain,
meet(composition(X4,X3),join(X,join(composition(X4,X3),composition(X4,complement(X3))))) = composition(X4,X3),
inference(substitution,[status(thm)],[c593]) ).
cnf(c595,plain,
meet(composition(X4,X3),join(X,composition(X4,top))) = composition(X4,X3),
inference(transitivity,[status(thm)],[c551,c594]) ).
cnf(c596,plain,
meet(composition(x0,X3),join(complement(X),composition(x0,top))) = composition(x0,X3),
inference(substitution,[status(thm)],[c595]) ).
cnf(c597,plain,
meet(composition(x0,X3),join(complement(X),composition(x0,X))) = composition(x0,X3),
inference(transitivity,[status(thm)],[c548,c596]) ).
cnf(c598,plain,
meet(composition(x0,X),join(complement(X3),composition(x0,X3))) = composition(x0,X),
inference(substitution,[status(thm)],[c597]) ).
cnf(c599,plain,
join(complement(meet(composition(x0,X),complement(composition(x0,X3)))),meet(composition(x0,X),join(complement(X3),composition(x0,X3)))) = join(complement(meet(composition(x0,X),complement(composition(x0,X3)))),composition(x0,X)),
inference(congruence,[status(thm)],[c598]) ).
cnf(c600,plain,
join(complement(meet(composition(x0,X),complement(composition(x0,X3)))),composition(x0,X)) = join(composition(x0,X),complement(meet(composition(x0,X),complement(composition(x0,X3))))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c601,plain,
join(complement(meet(X3,complement(X))),X3) = join(X3,complement(meet(X3,complement(X)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c602,plain,
join(X3,complement(meet(X3,complement(X)))) = join(complement(meet(X3,complement(X))),X3),
inference(symmetry,[status(thm)],[c601]) ).
cnf(c603,plain,
join(meet(X4,X3),X) = join(X,meet(X4,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c604,plain,
join(X,meet(X4,X3)) = join(meet(X4,X3),X),
inference(symmetry,[status(thm)],[c603]) ).
cnf(c605,plain,
join(meet(X4,complement(X3)),join(X,meet(X4,X3))) = join(meet(X4,complement(X3)),join(meet(X4,X3),X)),
inference(congruence,[status(thm)],[c604]) ).
cnf(c606,plain,
join(meet(X4,complement(X3)),join(meet(X4,X3),X)) = join(join(meet(X4,complement(X3)),meet(X4,X3)),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c607,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(substitution,[status(thm)],[c274]) ).
cnf(c608,plain,
meet(X3,X) = complement(join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c607]) ).
cnf(c609,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X),complement(X3)))),
inference(congruence,[status(thm)],[c608]) ).
cnf(c610,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c611,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c610]) ).
cnf(c612,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c611]) ).
cnf(c613,plain,
join(meet(X3,complement(X)),complement(join(complement(X),complement(X3)))) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c92]) ).
cnf(c615,plain,
join(meet(X3,complement(X)),complement(join(complement(X),complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c613,c614]) ).
cnf(c616,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c609,c615]) ).
cnf(c617,plain,
join(join(meet(X4,complement(X3)),meet(X4,X3)),X) = join(X4,X),
inference(congruence,[status(thm)],[c616]) ).
cnf(c618,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c619,plain,
join(join(meet(X4,complement(X3)),meet(X4,X3)),X) = join(X,X4),
inference(transitivity,[status(thm)],[c617,c618]) ).
cnf(c620,plain,
join(meet(X4,complement(X3)),join(meet(X4,X3),X)) = join(X,X4),
inference(transitivity,[status(thm)],[c606,c619]) ).
cnf(c621,plain,
join(meet(X4,complement(X3)),join(X,meet(X4,X3))) = join(X,X4),
inference(transitivity,[status(thm)],[c605,c620]) ).
cnf(c622,plain,
join(meet(X3,complement(X)),join(complement(meet(X3,complement(X))),meet(X3,X))) = join(complement(meet(X3,complement(X))),X3),
inference(substitution,[status(thm)],[c621]) ).
cnf(c623,plain,
join(complement(meet(X3,complement(X))),X3) = join(meet(X3,complement(X)),join(complement(meet(X3,complement(X))),meet(X3,X))),
inference(symmetry,[status(thm)],[c622]) ).
cnf(c624,plain,
join(meet(X3,complement(X)),join(complement(meet(X3,complement(X))),meet(X3,X))) = top,
inference(substitution,[status(thm)],[c580]) ).
cnf(c625,plain,
join(complement(meet(X3,complement(X))),X3) = top,
inference(transitivity,[status(thm)],[c623,c624]) ).
cnf(c626,plain,
join(X3,complement(meet(X3,complement(X)))) = top,
inference(transitivity,[status(thm)],[c602,c625]) ).
cnf(c627,plain,
join(composition(x0,X),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = top,
inference(substitution,[status(thm)],[c626]) ).
cnf(c628,plain,
join(complement(meet(composition(x0,X),complement(composition(x0,X3)))),composition(x0,X)) = top,
inference(transitivity,[status(thm)],[c600,c627]) ).
cnf(c629,plain,
join(complement(meet(composition(x0,X),complement(composition(x0,X3)))),meet(composition(x0,X),join(complement(X3),composition(x0,X3)))) = top,
inference(transitivity,[status(thm)],[c599,c628]) ).
cnf(c630,plain,
join(join(complement(X3),composition(x0,X3)),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = top,
inference(transitivity,[status(thm)],[c443,c629]) ).
cnf(c631,plain,
join(complement(X3),join(composition(x0,X3),complement(meet(composition(x0,X),complement(composition(x0,X3)))))) = top,
inference(transitivity,[status(thm)],[c318,c630]) ).
cnf(c632,plain,
join(complement(X3),complement(meet(composition(x0,X),complement(composition(x0,X3))))) = top,
inference(transitivity,[status(thm)],[c317,c631]) ).
cnf(c633,plain,
join(complement(X),complement(meet(composition(x0,X3),complement(composition(x0,X))))) = top,
inference(substitution,[status(thm)],[c632]) ).
cnf(c634,plain,
meet(join(complement(X),complement(meet(composition(x0,X3),complement(composition(x0,X))))),join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X)))))) = meet(top,join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X)))))),
inference(congruence,[status(thm)],[c633]) ).
cnf(c635,plain,
meet(top,join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X)))))) = join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X))))),
inference(substitution,[status(thm)],[c255]) ).
cnf(c636,plain,
join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X))))) = join(X,complement(meet(composition(x0,X3),complement(composition(x0,X))))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c637,plain,
complement(meet(X,complement(composition(x0,X3)))) = join(composition(x0,X3),complement(X)),
inference(substitution,[status(thm)],[c281]) ).
cnf(c638,plain,
join(X3,complement(meet(X,complement(composition(x0,X3))))) = join(X3,join(composition(x0,X3),complement(X))),
inference(congruence,[status(thm)],[c637]) ).
cnf(c639,plain,
join(composition(x0,X3),complement(meet(X,complement(X3)))) = join(X3,join(composition(x0,X3),complement(X))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c640,plain,
join(X3,join(composition(x0,X3),complement(X))) = join(composition(x0,X3),complement(meet(X,complement(X3)))),
inference(symmetry,[status(thm)],[c639]) ).
cnf(c641,plain,
join(composition(x0,X3),complement(meet(X,complement(X3)))) = join(composition(x0,X3),join(X3,complement(X))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c642,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c643,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c642]) ).
cnf(c644,plain,
join(composition(x0,X3),join(X3,X)) = join(composition(x0,X3),join(X,X3)),
inference(congruence,[status(thm)],[c643]) ).
cnf(c645,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c646,plain,
join(X,X3) = join(X3,X),
inference(symmetry,[status(thm)],[c645]) ).
cnf(c647,plain,
join(composition(x0,X3),join(X,X3)) = join(composition(x0,X3),join(X3,X)),
inference(congruence,[status(thm)],[c646]) ).
cnf(c648,plain,
join(composition(x0,X3),join(X3,X)) = join(join(composition(x0,X3),X3),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c649,plain,
X = composition(join(x0,one),X),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c650,plain,
join(composition(x0,X),X) = join(composition(x0,X),composition(join(x0,one),X)),
inference(congruence,[status(thm)],[c649]) ).
cnf(c651,plain,
composition(join(x0,one),X) = composition(one,X),
inference(congruence,[status(thm)],[c50]) ).
cnf(c652,plain,
join(composition(x0,X),composition(join(x0,one),X)) = join(composition(x0,X),composition(one,X)),
inference(congruence,[status(thm)],[c651]) ).
cnf(c653,plain,
composition(join(X3,X4),X) = join(composition(X3,X),composition(X4,X)),
inference(substitution,[status(thm)],[c471]) ).
cnf(c654,plain,
join(composition(X3,X),composition(X4,X)) = composition(join(X3,X4),X),
inference(symmetry,[status(thm)],[c653]) ).
cnf(c655,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c656,plain,
composition(join(X3,X4),X) = composition(join(X4,X3),X),
inference(congruence,[status(thm)],[c655]) ).
cnf(c657,plain,
join(composition(X3,X),composition(X4,X)) = composition(join(X4,X3),X),
inference(transitivity,[status(thm)],[c654,c656]) ).
cnf(c658,plain,
join(composition(x0,X),composition(one,X)) = composition(join(one,x0),X),
inference(substitution,[status(thm)],[c657]) ).
cnf(c659,plain,
join(x0,one) = join(one,x0),
inference(substitution,[status(thm)],[c7]) ).
cnf(c660,plain,
join(one,x0) = join(x0,one),
inference(symmetry,[status(thm)],[c659]) ).
cnf(c661,plain,
composition(join(one,x0),X) = composition(join(x0,one),X),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
composition(join(one,x0),X) = X,
inference(transitivity,[status(thm)],[c661,c71]) ).
cnf(c663,plain,
join(composition(x0,X),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c658,c662]) ).
cnf(c664,plain,
join(composition(x0,X),composition(join(x0,one),X)) = X,
inference(transitivity,[status(thm)],[c652,c663]) ).
cnf(c665,plain,
join(composition(x0,X),X) = X,
inference(transitivity,[status(thm)],[c650,c664]) ).
cnf(c666,plain,
join(join(composition(x0,X3),X3),X) = join(X3,X),
inference(congruence,[status(thm)],[c665]) ).
cnf(c667,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c668,plain,
join(join(composition(x0,X3),X3),X) = join(X,X3),
inference(transitivity,[status(thm)],[c666,c667]) ).
cnf(c669,plain,
join(composition(x0,X3),join(X3,X)) = join(X,X3),
inference(transitivity,[status(thm)],[c648,c668]) ).
cnf(c670,plain,
join(composition(x0,X3),join(X,X3)) = join(X,X3),
inference(transitivity,[status(thm)],[c647,c669]) ).
cnf(c671,plain,
join(composition(x0,X3),join(X3,X)) = join(X,X3),
inference(transitivity,[status(thm)],[c644,c670]) ).
cnf(c672,plain,
join(composition(x0,X3),join(X3,complement(X))) = join(complement(X),X3),
inference(substitution,[status(thm)],[c671]) ).
cnf(c673,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c674,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c675,plain,
join(complement(X),X3) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c673,c674]) ).
cnf(c676,plain,
join(composition(x0,X3),join(X3,complement(X))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c672,c675]) ).
cnf(c677,plain,
join(composition(x0,X3),complement(meet(X,complement(X3)))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c641,c676]) ).
cnf(c678,plain,
join(X3,join(composition(x0,X3),complement(X))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c640,c677]) ).
cnf(c679,plain,
join(X3,complement(meet(X,complement(composition(x0,X3))))) = complement(meet(X,complement(X3))),
inference(transitivity,[status(thm)],[c638,c678]) ).
cnf(c680,plain,
join(X,complement(meet(composition(x0,X3),complement(composition(x0,X))))) = complement(meet(composition(x0,X3),complement(X))),
inference(substitution,[status(thm)],[c679]) ).
cnf(c681,plain,
join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X))))) = complement(meet(composition(x0,X3),complement(X))),
inference(transitivity,[status(thm)],[c636,c680]) ).
cnf(c682,plain,
meet(top,join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X)))))) = complement(meet(composition(x0,X3),complement(X))),
inference(transitivity,[status(thm)],[c635,c681]) ).
cnf(c683,plain,
meet(join(complement(X),complement(meet(composition(x0,X3),complement(composition(x0,X))))),join(complement(complement(X)),complement(meet(composition(x0,X3),complement(composition(x0,X)))))) = complement(meet(composition(x0,X3),complement(X))),
inference(transitivity,[status(thm)],[c634,c682]) ).
cnf(c684,plain,
complement(meet(composition(x0,X3),complement(composition(x0,X)))) = complement(meet(composition(x0,X3),complement(X))),
inference(transitivity,[status(thm)],[c206,c683]) ).
cnf(c685,plain,
complement(complement(meet(composition(x0,X3),complement(composition(x0,X))))) = complement(complement(meet(composition(x0,X3),complement(X)))),
inference(congruence,[status(thm)],[c684]) ).
cnf(c686,plain,
complement(complement(meet(composition(x0,X3),complement(X)))) = meet(composition(x0,X3),complement(X)),
inference(substitution,[status(thm)],[c180]) ).
cnf(c687,plain,
complement(complement(meet(composition(x0,X3),complement(composition(x0,X))))) = meet(composition(x0,X3),complement(X)),
inference(transitivity,[status(thm)],[c685,c686]) ).
cnf(c688,plain,
meet(composition(x0,X3),complement(composition(x0,X))) = meet(composition(x0,X3),complement(X)),
inference(transitivity,[status(thm)],[c182,c687]) ).
cnf(c689,plain,
meet(composition(x0,x1),complement(composition(x0,x2))) = meet(composition(x0,x1),complement(x2)),
inference(substitution,[status(thm)],[c688]) ).
cnf(c690,plain,
meet(composition(x0,x1),complement(x2)) = meet(composition(x0,x1),complement(composition(x0,x2))),
inference(symmetry,[status(thm)],[c689]) ).
cnf(c691,plain,
$false,
inference(resolution,[status(thm)],[c4,c690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL030+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.43 % Computer : n006.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Sun Sep 27 22:53:55 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.21/4.77 Command-line arguments: --flatten --complete-subsets
% 33.21/4.77
% 33.21/4.77 % SZS status Theorem
% 33.21/4.77
% 34.05/4.83 % SZS output start CNFRefutation
% See solution above
% 35.64/5.16
% 35.64/5.16 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------