%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL037+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:33:26 PM UTC 2026
% Result : Theorem 18.27s 2.85s
% Output : CNFRefutation 22.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 15
% Syntax : Number of formulae : 579 ( 573 unt; 0 def)
% Number of atoms : 585 ( 584 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 : 7 ( 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 : 992 ( 35 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0,X1,X2] :
( composition(X0,top) = X0
=> composition(meet(X1,converse(X0)),meet(X0,X2)) = composition(meet(X1,converse(X0)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( composition(X0_2,top) = X0_2
=> composition(meet(X1_2,converse(X0_2)),meet(X0_2,X2_2)) = composition(meet(X1_2,converse(X0_2)),X2_2) ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( composition(meet(x1,converse(x0)),meet(x0,x2)) != composition(meet(x1,converse(x0)),x2)
& composition(x0,top) = x0 ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
composition(meet(x1,converse(x0)),meet(x0,x2)) != composition(meet(x1,converse(x0)),x2),
inference(clausify,[status(thm)],[c3]) ).
cnf(c5,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c6,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
meet(X0_2,X1_2) = complement(join(complement(X0_2),complement(X1_2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
cnf(c9,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c11,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c14,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c12,c14]) ).
cnf(c16,plain,
meet(X,X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c9,c15]) ).
cnf(c17,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c20,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c22,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c25,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c27,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c23,c29]) ).
cnf(c31,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c34,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c36,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
join(X0_2,join(X1_2,X2_2)) = join(join(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c39,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c41,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c5]) ).
cnf(c44,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c42,c43]) ).
cnf(c45,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c39,c44]) ).
cnf(c46,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c37,c45]) ).
cnf(c47,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c50,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c54,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c57,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c55,c58]) ).
cnf(c60,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c62,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c52,c62]) ).
cnf(c64,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c63]) ).
cnf(c68,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,axiom,
composition(X0_2,composition(X1_2,X2_2)) = composition(composition(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c70,plain,
composition(X3,composition(one,X)) = composition(composition(X3,one),X),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c56]) ).
cnf(c72,plain,
composition(composition(X3,one),X) = composition(X3,X),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
composition(X3,composition(one,X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c74,c63]) ).
cnf(c76,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c68,c75]) ).
cnf(c77,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,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)],[c5]) ).
cnf(c82,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)],[c81]) ).
cnf(c83,axiom,
join(composition(converse(X0_2),complement(composition(X0_2,X1_2))),complement(X1_2)) = complement(X1_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
cnf(c84,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c82,c84]) ).
cnf(c86,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c80,c86]) ).
cnf(c88,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c66,c87]) ).
cnf(c89,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c91,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c89,c91]) ).
cnf(c93,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c48,c92]) ).
cnf(c94,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c34,c93]) ).
cnf(c95,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c46]) ).
cnf(c98,plain,
join(complement(zero),top) = join(top,complement(zero)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c99,plain,
join(top,complement(zero)) = join(complement(zero),top),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c101,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
join(top,join(zero,X)) = join(top,join(X,zero)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c5]) ).
cnf(c104,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
join(top,join(X,zero)) = join(top,join(zero,X)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
join(top,join(zero,X)) = join(join(top,zero),X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c107,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c108,plain,
join(top,zero) = join(top,complement(top)),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
top = join(top,complement(top)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c110,plain,
join(top,complement(top)) = top,
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
join(top,zero) = top,
inference(transitivity,[status(thm)],[c108,c110]) ).
cnf(c112,plain,
join(join(top,zero),X) = join(top,X),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c5]) ).
cnf(c114,plain,
join(join(top,zero),X) = join(X,top),
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
join(top,join(zero,X)) = join(X,top),
inference(transitivity,[status(thm)],[c106,c114]) ).
cnf(c116,plain,
join(top,join(X,zero)) = join(X,top),
inference(transitivity,[status(thm)],[c105,c115]) ).
cnf(c117,plain,
join(top,join(zero,X)) = join(X,top),
inference(transitivity,[status(thm)],[c102,c116]) ).
cnf(c118,plain,
join(top,join(zero,complement(zero))) = join(complement(zero),top),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
join(complement(zero),top) = join(top,join(zero,complement(zero))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c121,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
join(top,join(zero,complement(zero))) = join(top,top),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
join(complement(zero),top) = join(top,top),
inference(transitivity,[status(thm)],[c119,c122]) ).
cnf(c124,plain,
join(top,complement(zero)) = join(top,top),
inference(transitivity,[status(thm)],[c99,c123]) ).
cnf(c125,plain,
join(top,top) = join(top,complement(zero)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
join(top,complement(zero)) = top,
inference(substitution,[status(thm)],[c94]) ).
cnf(c127,plain,
join(top,top) = top,
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
join(X,join(top,complement(X))) = top,
inference(transitivity,[status(thm)],[c97,c127]) ).
cnf(c129,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c96,c128]) ).
cnf(c130,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
top = join(complement(X),top),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
complement(top) = complement(join(complement(X),top)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
join(meet(X,top),complement(top)) = join(meet(X,top),complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c135,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)],[c134]) ).
cnf(c136,axiom,
X0_2 = join(complement(join(complement(X0_2),complement(X1_2))),complement(join(complement(X0_2),X1_2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
cnf(c137,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c135,c138]) ).
cnf(c140,plain,
join(meet(X,top),complement(join(complement(X),top))) = X,
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c133,c140]) ).
cnf(c142,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c32,c141]) ).
cnf(c143,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c20,c142]) ).
cnf(c144,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c18,c143]) ).
cnf(c145,plain,
join(zero,meet(top,meet(X,X))) = meet(X,X),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
meet(X,X) = join(zero,meet(top,meet(X,X))),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c148,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c150,plain,
complement(join(complement(X),complement(X))) = meet(X,X),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
complement(complement(X)) = meet(X,X),
inference(transitivity,[status(thm)],[c148,c150]) ).
cnf(c152,plain,
meet(X,X) = complement(complement(X)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
meet(top,meet(X,X)) = meet(top,complement(complement(X))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c16]) ).
cnf(c155,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c156,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c159,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c161,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c159,c161]) ).
cnf(c163,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c157,c162]) ).
cnf(c164,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
join(zero,complement(complement(X))) = join(zero,meet(X,X)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c167,plain,
complement(join(zero,complement(complement(X)))) = complement(join(zero,meet(X,X))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c169,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c171,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c139]) ).
cnf(c173,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c171,c172]) ).
cnf(c174,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c169,c173]) ).
cnf(c175,plain,
complement(join(zero,meet(X,X))) = complement(X),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(transitivity,[status(thm)],[c167,c175]) ).
cnf(c177,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c165,c176]) ).
cnf(c178,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c154,c177]) ).
cnf(c179,plain,
meet(top,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
meet(top,meet(X,X)) = complement(complement(X)),
inference(transitivity,[status(thm)],[c153,c179]) ).
cnf(c181,plain,
join(zero,meet(top,meet(X,X))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
join(zero,complement(complement(X))) = join(zero,meet(X,X)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c183,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c182,c174]) ).
cnf(c184,plain,
join(zero,meet(top,meet(X,X))) = X,
inference(transitivity,[status(thm)],[c181,c183]) ).
cnf(c185,plain,
meet(X,X) = X,
inference(transitivity,[status(thm)],[c146,c184]) ).
cnf(c186,plain,
X = meet(X,X),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
join(zero,X) = join(zero,meet(X,X)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c187,c174]) ).
cnf(c189,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c7,c188]) ).
cnf(c190,plain,
join(composition(meet(X3,converse(x0)),meet(x0,X)),zero) = composition(meet(X3,converse(x0)),meet(x0,X)),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
composition(meet(X3,converse(x0)),meet(x0,X)) = join(composition(meet(X3,converse(x0)),meet(x0,X)),zero),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
join(converse(x0),X) = join(X,converse(x0)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c193,plain,
join(X,converse(x0)) = join(converse(x0),X),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
composition(join(X,converse(x0)),complement(x0)) = composition(join(converse(x0),X),complement(x0)),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c196,plain,
composition(join(converse(x0),X),complement(x0)) = join(composition(converse(x0),complement(x0)),composition(X,complement(x0))),
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c198,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c198,c189]) ).
cnf(c200,plain,
join(zero,composition(converse(x0),complement(x0))) = composition(converse(x0),complement(x0)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
composition(converse(x0),complement(x0)) = join(zero,composition(converse(x0),complement(x0))),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c203,plain,
join(zero,composition(converse(x0),complement(x0))) = join(complement(top),composition(converse(x0),complement(x0))),
inference(congruence,[status(thm)],[c202]) ).
fof(c204,conjecture,
! [X0_2,X1_2,X2_2] :
( composition(X0_2,top) = X0_2
=> composition(meet(X1_2,converse(X0_2)),meet(X0_2,X2_2)) = composition(meet(X1_2,converse(X0_2)),X2_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c205,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( composition(X0_2,top) = X0_2
=> composition(meet(X1_2,converse(X0_2)),meet(X0_2,X2_2)) = composition(meet(X1_2,converse(X0_2)),X2_2) ),
inference(negate_conjecture,[status(cth)],[c204]) ).
fof(c206,plain,
( composition(meet(x1,converse(x0)),meet(x0,x2)) != composition(meet(x1,converse(x0)),x2)
& composition(x0,top) = x0 ),
inference(clausify,[status(esa)],[c205]) ).
cnf(c207,plain,
composition(x0,top) = x0,
inference(clausify,[status(thm)],[c206]) ).
cnf(c208,plain,
x0 = composition(x0,top),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
complement(x0) = complement(composition(x0,top)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
composition(converse(x0),complement(x0)) = composition(converse(x0),complement(composition(x0,top))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
join(complement(top),composition(converse(x0),complement(x0))) = join(complement(top),composition(converse(x0),complement(composition(x0,top)))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
join(complement(top),composition(converse(x0),complement(composition(x0,top)))) = complement(top),
inference(substitution,[status(thm)],[c85]) ).
cnf(c213,plain,
join(complement(top),composition(converse(x0),complement(composition(x0,top)))) = zero,
inference(transitivity,[status(thm)],[c212,c30]) ).
cnf(c214,plain,
join(complement(top),composition(converse(x0),complement(x0))) = zero,
inference(transitivity,[status(thm)],[c211,c213]) ).
cnf(c215,plain,
join(zero,composition(converse(x0),complement(x0))) = zero,
inference(transitivity,[status(thm)],[c203,c214]) ).
cnf(c216,plain,
composition(converse(x0),complement(x0)) = zero,
inference(transitivity,[status(thm)],[c201,c215]) ).
cnf(c217,plain,
join(composition(converse(x0),complement(x0)),composition(X,complement(x0))) = join(zero,composition(X,complement(x0))),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
join(zero,composition(X,complement(x0))) = composition(X,complement(x0)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c219,plain,
join(composition(converse(x0),complement(x0)),composition(X,complement(x0))) = composition(X,complement(x0)),
inference(transitivity,[status(thm)],[c217,c218]) ).
cnf(c220,plain,
composition(join(converse(x0),X),complement(x0)) = composition(X,complement(x0)),
inference(transitivity,[status(thm)],[c196,c219]) ).
cnf(c221,plain,
composition(join(X,converse(x0)),complement(x0)) = composition(X,complement(x0)),
inference(transitivity,[status(thm)],[c194,c220]) ).
cnf(c222,plain,
composition(join(meet(X,converse(x0)),converse(x0)),complement(x0)) = composition(meet(X,converse(x0)),complement(x0)),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
composition(meet(X,converse(x0)),complement(x0)) = composition(join(meet(X,converse(x0)),converse(x0)),complement(x0)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
join(X,meet(X3,X)) = join(meet(X3,X),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c225,plain,
join(meet(X3,X),X) = join(X,meet(X3,X)),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
join(X3,meet(X,X3)) = join(X3,meet(X3,X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c227,plain,
join(meet(X3,X),X3) = join(X3,meet(X3,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c228,plain,
join(X3,meet(X3,X)) = join(meet(X3,X),X3),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
X3 = join(meet(X3,X),complement(join(complement(X3),X))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c230,plain,
join(meet(X3,X),X3) = join(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c232,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
join(X3,join(X3,X)) = join(X3,join(X,X3)),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c151,c185]) ).
cnf(c235,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
join(X,X3) = join(X,complement(complement(X3))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
join(X3,join(X,X3)) = join(X3,join(X,complement(complement(X3)))),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
X = meet(X,X),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c239,plain,
join(X3,join(X,complement(complement(X3)))) = join(meet(X3,X3),join(X,complement(complement(X3)))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
meet(X,X) = complement(complement(X)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c241,plain,
join(meet(X3,X3),join(X,complement(complement(X3)))) = join(complement(complement(X3)),join(X,complement(complement(X3)))),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c243,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
join(complement(X3),join(X,complement(X3))) = join(complement(X3),join(complement(X3),X)),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
join(complement(X3),join(complement(X3),X)) = join(join(complement(X3),complement(X3)),X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c246,plain,
join(join(complement(X3),complement(X3)),X) = join(complement(X3),X),
inference(congruence,[status(thm)],[c88]) ).
cnf(c247,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c248,plain,
join(join(complement(X3),complement(X3)),X) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c246,c247]) ).
cnf(c249,plain,
join(complement(X3),join(complement(X3),X)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c245,c248]) ).
cnf(c250,plain,
join(complement(X3),join(X,complement(X3))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c244,c249]) ).
cnf(c251,plain,
join(complement(complement(X3)),join(X,complement(complement(X3)))) = join(X,complement(complement(X3))),
inference(substitution,[status(thm)],[c250]) ).
cnf(c252,plain,
join(X,complement(complement(X3))) = join(X,X3),
inference(congruence,[status(thm)],[c234]) ).
cnf(c253,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c254,plain,
join(X,complement(complement(X3))) = join(X3,X),
inference(transitivity,[status(thm)],[c252,c253]) ).
cnf(c255,plain,
join(complement(complement(X3)),join(X,complement(complement(X3)))) = join(X3,X),
inference(transitivity,[status(thm)],[c251,c254]) ).
cnf(c256,plain,
join(meet(X3,X3),join(X,complement(complement(X3)))) = join(X3,X),
inference(transitivity,[status(thm)],[c241,c255]) ).
cnf(c257,plain,
join(X3,join(X,complement(complement(X3)))) = join(X3,X),
inference(transitivity,[status(thm)],[c239,c256]) ).
cnf(c258,plain,
join(X3,join(X,X3)) = join(X3,X),
inference(transitivity,[status(thm)],[c237,c257]) ).
cnf(c259,plain,
join(X3,join(X3,X)) = join(X3,X),
inference(transitivity,[status(thm)],[c233,c258]) ).
cnf(c260,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)],[c259]) ).
cnf(c261,plain,
join(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))) = X3,
inference(transitivity,[status(thm)],[c260,c139]) ).
cnf(c262,plain,
join(meet(X3,X),X3) = X3,
inference(transitivity,[status(thm)],[c230,c261]) ).
cnf(c263,plain,
join(X3,meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c228,c262]) ).
cnf(c264,plain,
join(X3,meet(X,X3)) = X3,
inference(transitivity,[status(thm)],[c226,c263]) ).
cnf(c265,plain,
join(X,meet(X3,X)) = X,
inference(substitution,[status(thm)],[c264]) ).
cnf(c266,plain,
join(meet(X3,X),X) = X,
inference(transitivity,[status(thm)],[c225,c265]) ).
cnf(c267,plain,
join(meet(X,converse(x0)),converse(x0)) = converse(x0),
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
composition(join(meet(X,converse(x0)),converse(x0)),complement(x0)) = composition(converse(x0),complement(x0)),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
composition(join(meet(X,converse(x0)),converse(x0)),complement(x0)) = zero,
inference(transitivity,[status(thm)],[c268,c216]) ).
cnf(c270,plain,
composition(meet(X,converse(x0)),complement(x0)) = zero,
inference(transitivity,[status(thm)],[c223,c269]) ).
cnf(c271,plain,
zero = composition(meet(X,converse(x0)),complement(x0)),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
join(composition(meet(X3,converse(x0)),meet(x0,X)),zero) = join(composition(meet(X3,converse(x0)),meet(x0,X)),composition(meet(X3,converse(x0)),complement(x0))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c274,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
composition(X3,X) = composition(X3,converse(converse(X))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
join(composition(X4,X3),composition(X4,X)) = join(composition(X4,X3),composition(X4,converse(converse(X)))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c278,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
composition(X3,converse(X)) = composition(converse(converse(X3)),converse(X)),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
join(composition(X4,X3),composition(X4,converse(X))) = join(composition(X4,X3),composition(converse(converse(X4)),converse(X))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
converse(composition(X,converse(X3))) = composition(converse(converse(X3)),converse(X)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c282,plain,
composition(converse(converse(X3)),converse(X)) = converse(composition(X,converse(X3))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = join(composition(X4,X3),converse(composition(X,converse(X4)))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
converse(converse(composition(X3,X))) = composition(X3,X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c285,plain,
composition(X3,X) = converse(converse(composition(X3,X))),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
join(composition(X4,X3),converse(composition(X,converse(X4)))) = join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c288,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))),
inference(substitution,[status(thm)],[c287]) ).
cnf(c289,plain,
join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))) = converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
converse(composition(X3,X)) = composition(converse(X),converse(X3)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c291,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = join(composition(converse(X3),converse(X4)),composition(X,converse(X4))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
composition(join(converse(X3),X),converse(X4)) = join(composition(converse(X3),converse(X4)),composition(X,converse(X4))),
inference(substitution,[status(thm)],[c195]) ).
cnf(c293,plain,
join(composition(converse(X3),converse(X4)),composition(X,converse(X4))) = composition(join(converse(X3),X),converse(X4)),
inference(symmetry,[status(thm)],[c292]) ).
cnf(c294,plain,
join(converse(X3),X) = join(X,converse(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c295,plain,
composition(join(converse(X3),X),converse(X4)) = composition(join(X,converse(X3)),converse(X4)),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
join(composition(converse(X3),converse(X4)),composition(X,converse(X4))) = composition(join(X,converse(X3)),converse(X4)),
inference(transitivity,[status(thm)],[c293,c295]) ).
cnf(c297,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = composition(join(X,converse(X3)),converse(X4)),
inference(transitivity,[status(thm)],[c291,c296]) ).
cnf(c298,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = converse(composition(join(X,converse(X3)),converse(X4))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(converse(converse(X4)),converse(join(X,converse(X3)))),
inference(substitution,[status(thm)],[c53]) ).
cnf(c300,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c301,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,converse(join(X,converse(X3)))),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
converse(join(X,converse(X3))) = join(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c287]) ).
cnf(c303,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(converse(X),converse(converse(X3)))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c305,plain,
join(converse(X),converse(converse(X3))) = join(converse(X),X3),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(converse(X),X3)),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c308,plain,
composition(X4,join(converse(X),X3)) = composition(X4,join(X3,converse(X))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c306,c308]) ).
cnf(c310,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c303,c309]) ).
cnf(c311,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c301,c310]) ).
cnf(c312,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c299,c311]) ).
cnf(c313,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c298,c312]) ).
cnf(c314,plain,
join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c289,c313]) ).
cnf(c315,plain,
join(composition(X4,X3),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c286,c314]) ).
cnf(c316,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c283,c315]) ).
cnf(c317,plain,
join(composition(X4,X3),composition(X4,converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c280,c316]) ).
cnf(c318,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X3,converse(converse(X)))),
inference(substitution,[status(thm)],[c317]) ).
cnf(c319,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c320,plain,
join(X3,converse(converse(X))) = join(X3,X),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
composition(X4,join(X3,converse(converse(X)))) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c323,plain,
composition(X4,join(X3,X)) = composition(X4,join(X,X3)),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
composition(X4,join(X3,converse(converse(X)))) = composition(X4,join(X,X3)),
inference(transitivity,[status(thm)],[c321,c323]) ).
cnf(c325,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X,X3)),
inference(transitivity,[status(thm)],[c318,c324]) ).
cnf(c326,plain,
join(composition(X4,X3),composition(X4,X)) = composition(X4,join(X,X3)),
inference(transitivity,[status(thm)],[c276,c325]) ).
cnf(c327,plain,
join(composition(meet(X3,converse(x0)),meet(x0,X)),composition(meet(X3,converse(x0)),complement(x0))) = composition(meet(X3,converse(x0)),join(complement(x0),meet(x0,X))),
inference(substitution,[status(thm)],[c326]) ).
cnf(c328,plain,
join(complement(x0),meet(x0,X)) = join(meet(x0,X),complement(x0)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c329,plain,
composition(meet(X3,converse(x0)),join(complement(x0),meet(x0,X))) = composition(meet(X3,converse(x0)),join(meet(x0,X),complement(x0))),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
meet(X3,complement(X)) = meet(complement(X),X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c331,plain,
complement(meet(X3,complement(X))) = complement(meet(complement(X),X3)),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c199]) ).
cnf(c333,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
meet(complement(X),X3) = meet(join(zero,complement(X)),X3),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
complement(meet(complement(X),X3)) = complement(meet(join(zero,complement(X)),X3)),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c337,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c16]) ).
cnf(c339,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c340,plain,
X = meet(X,X),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c341,plain,
meet(top,X) = meet(top,meet(X,X)),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c343,plain,
meet(top,meet(X3,X)) = meet(top,meet(X,X3)),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c345,plain,
meet(top,meet(X,X3)) = meet(top,complement(join(complement(X),complement(X3)))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
meet(top,complement(join(complement(X),complement(X3)))) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c178]) ).
cnf(c347,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c348,plain,
complement(join(complement(X),complement(X3))) = meet(X,X3),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c350,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c348,c350]) ).
cnf(c352,plain,
meet(top,complement(join(complement(X),complement(X3)))) = meet(X3,X),
inference(transitivity,[status(thm)],[c346,c351]) ).
cnf(c353,plain,
meet(top,meet(X,X3)) = meet(X3,X),
inference(transitivity,[status(thm)],[c345,c352]) ).
cnf(c354,plain,
meet(top,meet(X3,X)) = meet(X3,X),
inference(transitivity,[status(thm)],[c343,c353]) ).
cnf(c355,plain,
meet(top,meet(X,X)) = meet(X,X),
inference(substitution,[status(thm)],[c354]) ).
cnf(c356,plain,
meet(top,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c355,c185]) ).
cnf(c357,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c341,c356]) ).
cnf(c358,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c339,c357]) ).
cnf(c359,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c338,c358]) ).
cnf(c360,plain,
meet(top,join(complement(X),complement(X3))) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c359]) ).
cnf(c361,plain,
join(complement(X),complement(X3)) = meet(top,join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c363,plain,
join(complement(X4),meet(X3,X)) = join(complement(X4),meet(X,X3)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
complement(join(complement(X4),meet(X3,X))) = complement(join(complement(X4),meet(X,X3))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
join(meet(X,X3),complement(X4)) = join(complement(X4),meet(X,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c366,plain,
join(complement(X4),meet(X,X3)) = join(meet(X,X3),complement(X4)),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
complement(join(complement(X4),meet(X,X3))) = complement(join(meet(X,X3),complement(X4))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c369,plain,
join(meet(X,X3),complement(X4)) = join(complement(join(complement(X),complement(X3))),complement(X4)),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
complement(join(meet(X,X3),complement(X4))) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
meet(join(complement(X),complement(X3)),X4) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c372,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = meet(join(complement(X),complement(X3)),X4),
inference(symmetry,[status(thm)],[c371]) ).
cnf(c373,plain,
meet(X4,join(complement(X),complement(X3))) = meet(join(complement(X),complement(X3)),X4),
inference(substitution,[status(thm)],[c16]) ).
cnf(c374,plain,
meet(join(complement(X),complement(X3)),X4) = meet(X4,join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c376,plain,
meet(X4,join(complement(X),complement(X3))) = meet(X4,join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
meet(join(complement(X),complement(X3)),X4) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c374,c376]) ).
cnf(c378,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c372,c377]) ).
cnf(c379,plain,
complement(join(meet(X,X3),complement(X4))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c370,c378]) ).
cnf(c380,plain,
complement(join(complement(X4),meet(X,X3))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c367,c379]) ).
cnf(c381,plain,
complement(join(complement(X4),meet(X3,X))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c364,c380]) ).
cnf(c382,plain,
complement(join(complement(top),meet(X,X3))) = meet(top,join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c381]) ).
cnf(c383,plain,
meet(top,join(complement(X),complement(X3))) = complement(join(complement(top),meet(X,X3))),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
join(complement(top),meet(X,X3)) = join(zero,meet(X,X3)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c385,plain,
complement(join(complement(top),meet(X,X3))) = complement(join(zero,meet(X,X3))),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
join(zero,meet(X,X3)) = meet(X,X3),
inference(substitution,[status(thm)],[c199]) ).
cnf(c387,plain,
complement(join(zero,meet(X,X3))) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c389,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
complement(meet(X,X3)) = complement(meet(X3,X)),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
complement(join(zero,meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c387,c390]) ).
cnf(c392,plain,
complement(join(complement(top),meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c385,c391]) ).
cnf(c393,plain,
meet(top,join(complement(X),complement(X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c383,c392]) ).
cnf(c394,plain,
join(complement(X),complement(X3)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c361,c393]) ).
cnf(c395,plain,
join(complement(X3),complement(X)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c337,c394]) ).
cnf(c396,plain,
join(complement(join(zero,complement(X))),complement(X3)) = complement(meet(join(zero,complement(X)),X3)),
inference(substitution,[status(thm)],[c395]) ).
cnf(c397,plain,
complement(meet(join(zero,complement(X)),X3)) = join(complement(join(zero,complement(X))),complement(X3)),
inference(symmetry,[status(thm)],[c396]) ).
cnf(c398,plain,
join(complement(join(zero,complement(X))),complement(X3)) = join(meet(X,top),complement(X3)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c399,plain,
join(meet(X,top),complement(X3)) = join(X,complement(X3)),
inference(congruence,[status(thm)],[c358]) ).
cnf(c400,plain,
join(complement(join(zero,complement(X))),complement(X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c398,c399]) ).
cnf(c401,plain,
complement(meet(join(zero,complement(X)),X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c397,c400]) ).
cnf(c402,plain,
complement(meet(complement(X),X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c335,c401]) ).
cnf(c403,plain,
complement(meet(X3,complement(X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c331,c402]) ).
cnf(c404,plain,
complement(meet(X3,complement(meet(X3,X)))) = join(meet(X3,X),complement(X3)),
inference(substitution,[status(thm)],[c403]) ).
cnf(c405,plain,
join(meet(X3,X),complement(X3)) = complement(meet(X3,complement(meet(X3,X)))),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c406,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c407,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
meet(X3,complement(meet(X3,X))) = meet(X3,complement(meet(X,X3))),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c410,plain,
join(meet(X3,X),meet(X,complement(X3))) = join(meet(X,X3),meet(X,complement(X3))),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,X),meet(X3,complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c412,plain,
join(meet(X3,X),meet(X3,complement(X))) = join(meet(X3,complement(X)),meet(X3,X)),
inference(symmetry,[status(thm)],[c411]) ).
cnf(c413,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c414,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c139]) ).
cnf(c416,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c414,c415]) ).
cnf(c417,plain,
join(meet(X3,X),meet(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c412,c416]) ).
cnf(c418,plain,
join(meet(X,X3),meet(X,complement(X3))) = X,
inference(substitution,[status(thm)],[c417]) ).
cnf(c419,plain,
join(meet(X3,X),meet(X,complement(X3))) = X,
inference(transitivity,[status(thm)],[c410,c418]) ).
cnf(c420,plain,
join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(X3,complement(meet(X,X3))),
inference(substitution,[status(thm)],[c419]) ).
cnf(c421,plain,
meet(X3,complement(meet(X,X3))) = join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))),
inference(symmetry,[status(thm)],[c420]) ).
cnf(c422,plain,
meet(X,complement(meet(X3,X))) = meet(complement(meet(X3,X)),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c423,plain,
meet(X3,meet(X,complement(meet(X3,X)))) = meet(X3,meet(complement(meet(X3,X)),X)),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c425,plain,
meet(X3,meet(X4,X)) = meet(X3,meet(X,X4)),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
meet(meet(X3,meet(X,X4)),top) = meet(X3,meet(X,X4)),
inference(substitution,[status(thm)],[c358]) ).
cnf(c427,plain,
meet(X3,meet(X,X4)) = meet(meet(X3,meet(X,X4)),top),
inference(symmetry,[status(thm)],[c426]) ).
cnf(c428,plain,
complement(join(zero,complement(meet(X3,meet(X,X4))))) = meet(meet(X3,meet(X,X4)),top),
inference(substitution,[status(thm)],[c163]) ).
cnf(c429,plain,
meet(meet(X3,meet(X,X4)),top) = complement(join(zero,complement(meet(X3,meet(X,X4))))),
inference(symmetry,[status(thm)],[c428]) ).
cnf(c430,plain,
meet(X3,meet(X,X4)) = meet(X3,meet(X4,X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c431,plain,
complement(meet(X3,meet(X,X4))) = complement(meet(X3,meet(X4,X))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c433,plain,
meet(X3,meet(X4,X)) = meet(X3,complement(join(complement(X4),complement(X)))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
complement(meet(X3,meet(X4,X))) = complement(meet(X3,complement(join(complement(X4),complement(X))))),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
complement(meet(X3,complement(join(complement(X4),complement(X))))) = join(join(complement(X4),complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c403]) ).
cnf(c436,plain,
join(complement(X4),join(complement(X),complement(X3))) = join(join(complement(X4),complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c437,plain,
join(join(complement(X4),complement(X)),complement(X3)) = join(complement(X4),join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c436]) ).
cnf(c438,plain,
join(complement(X),complement(X3)) = complement(meet(X,X3)),
inference(substitution,[status(thm)],[c395]) ).
cnf(c439,plain,
join(complement(X4),join(complement(X),complement(X3))) = join(complement(X4),complement(meet(X,X3))),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
join(complement(X4),complement(meet(X,X3))) = complement(meet(X4,meet(X,X3))),
inference(substitution,[status(thm)],[c395]) ).
cnf(c441,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c442,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
meet(X4,meet(X,X3)) = meet(X4,meet(X3,X)),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
complement(meet(X4,meet(X,X3))) = complement(meet(X4,meet(X3,X))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
join(complement(X4),complement(meet(X,X3))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c440,c444]) ).
cnf(c446,plain,
join(complement(X4),join(complement(X),complement(X3))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c439,c445]) ).
cnf(c447,plain,
join(join(complement(X4),complement(X)),complement(X3)) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c437,c446]) ).
cnf(c448,plain,
complement(meet(X3,complement(join(complement(X4),complement(X))))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c435,c447]) ).
cnf(c449,plain,
complement(meet(X3,meet(X4,X))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c434,c448]) ).
cnf(c450,plain,
complement(meet(X3,meet(X,X4))) = complement(meet(X4,meet(X3,X))),
inference(transitivity,[status(thm)],[c431,c449]) ).
cnf(c451,plain,
join(zero,complement(meet(X3,meet(X,X4)))) = join(zero,complement(meet(X4,meet(X3,X)))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
complement(join(zero,complement(meet(X3,meet(X,X4))))) = complement(join(zero,complement(meet(X4,meet(X3,X))))),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
complement(join(zero,complement(meet(X4,meet(X3,X))))) = meet(meet(X4,meet(X3,X)),top),
inference(substitution,[status(thm)],[c163]) ).
cnf(c454,plain,
meet(meet(X4,meet(X3,X)),top) = meet(X4,meet(X3,X)),
inference(substitution,[status(thm)],[c358]) ).
cnf(c455,plain,
complement(join(zero,complement(meet(X4,meet(X3,X))))) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c453,c454]) ).
cnf(c456,plain,
complement(join(zero,complement(meet(X3,meet(X,X4))))) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c452,c455]) ).
cnf(c457,plain,
meet(meet(X3,meet(X,X4)),top) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c429,c456]) ).
cnf(c458,plain,
meet(X3,meet(X,X4)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c427,c457]) ).
cnf(c459,plain,
meet(X3,meet(X4,X)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c425,c458]) ).
cnf(c460,plain,
meet(X3,meet(complement(meet(X3,X)),X)) = meet(complement(meet(X3,X)),meet(X3,X)),
inference(substitution,[status(thm)],[c459]) ).
cnf(c461,plain,
meet(X3,meet(X3,X)) = meet(meet(X3,X),X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c462,plain,
X3 = join(meet(X3,X),complement(join(complement(X3),X))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c463,plain,
meet(meet(X3,X),X3) = meet(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
join(meet(X3,join(X3,complement(X))),zero) = meet(X3,join(X3,complement(X))),
inference(substitution,[status(thm)],[c189]) ).
cnf(c465,plain,
meet(X3,join(X3,complement(X))) = join(meet(X3,join(X3,complement(X))),zero),
inference(symmetry,[status(thm)],[c464]) ).
cnf(c466,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c467,plain,
join(meet(X3,join(X3,complement(X))),zero) = join(meet(X3,join(X3,complement(X))),complement(top)),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
meet(complement(X3),X) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c469,plain,
complement(meet(complement(X3),X)) = complement(meet(X,complement(X3))),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c403]) ).
cnf(c471,plain,
complement(meet(complement(X3),X)) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c469,c470]) ).
cnf(c472,plain,
join(X3,complement(X)) = complement(meet(complement(X3),X)),
inference(symmetry,[status(thm)],[c471]) ).
cnf(c473,plain,
meet(X3,join(X3,complement(X))) = meet(X3,complement(meet(complement(X3),X))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
join(meet(X3,join(X3,complement(X))),complement(top)) = join(meet(X3,complement(meet(complement(X3),X))),complement(top)),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c476,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
join(X3,complement(meet(X3,X))) = join(X3,complement(meet(X,X3))),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
join(complement(X),complement(X3)) = complement(meet(X,X3)),
inference(substitution,[status(thm)],[c395]) ).
cnf(c479,plain,
complement(meet(X,X3)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c478]) ).
cnf(c480,plain,
join(X3,complement(meet(X,X3))) = join(X3,join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
join(X3,join(complement(X),complement(X3))) = join(complement(X),top),
inference(substitution,[status(thm)],[c46]) ).
cnf(c482,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c129]) ).
cnf(c483,plain,
join(X3,join(complement(X),complement(X3))) = top,
inference(transitivity,[status(thm)],[c481,c482]) ).
cnf(c484,plain,
join(X3,complement(meet(X,X3))) = top,
inference(transitivity,[status(thm)],[c480,c483]) ).
cnf(c485,plain,
join(X3,complement(meet(X3,X))) = top,
inference(transitivity,[status(thm)],[c477,c484]) ).
cnf(c486,plain,
join(complement(X3),complement(meet(complement(X3),X))) = top,
inference(substitution,[status(thm)],[c485]) ).
cnf(c487,plain,
top = join(complement(X3),complement(meet(complement(X3),X))),
inference(symmetry,[status(thm)],[c486]) ).
cnf(c488,plain,
complement(top) = complement(join(complement(X3),complement(meet(complement(X3),X)))),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
join(meet(X3,complement(meet(complement(X3),X))),complement(top)) = join(meet(X3,complement(meet(complement(X3),X))),complement(join(complement(X3),complement(meet(complement(X3),X))))),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
join(meet(X3,complement(meet(complement(X3),X))),complement(join(complement(X3),complement(meet(complement(X3),X))))) = X3,
inference(substitution,[status(thm)],[c139]) ).
cnf(c491,plain,
join(meet(X3,complement(meet(complement(X3),X))),complement(top)) = X3,
inference(transitivity,[status(thm)],[c489,c490]) ).
cnf(c492,plain,
join(meet(X3,join(X3,complement(X))),complement(top)) = X3,
inference(transitivity,[status(thm)],[c474,c491]) ).
cnf(c493,plain,
join(meet(X3,join(X3,complement(X))),zero) = X3,
inference(transitivity,[status(thm)],[c467,c492]) ).
cnf(c494,plain,
meet(X3,join(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c465,c493]) ).
cnf(c495,plain,
meet(meet(X3,X),join(meet(X3,X),complement(join(complement(X3),X)))) = meet(X3,X),
inference(substitution,[status(thm)],[c494]) ).
cnf(c496,plain,
meet(meet(X3,X),X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c463,c495]) ).
cnf(c497,plain,
meet(X3,meet(X3,X)) = meet(X3,X),
inference(transitivity,[status(thm)],[c461,c496]) ).
cnf(c498,plain,
meet(X3,X) = meet(X3,meet(X3,X)),
inference(symmetry,[status(thm)],[c497]) ).
cnf(c499,plain,
meet(complement(meet(X3,X)),meet(X3,X)) = meet(complement(meet(X3,X)),meet(X3,meet(X3,X))),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
meet(complement(X3),meet(X,X3)) = meet(complement(X3),meet(X3,X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c501,plain,
meet(complement(X3),meet(X3,X)) = meet(meet(X3,X),complement(X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c502,plain,
join(zero,join(X3,complement(X))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c503,plain,
join(X3,complement(X)) = join(zero,join(X3,complement(X))),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
complement(join(X3,complement(X))) = complement(join(zero,join(X3,complement(X)))),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c403]) ).
cnf(c506,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c505]) ).
cnf(c507,plain,
join(zero,join(X3,complement(X))) = join(zero,complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c506]) ).
cnf(c508,plain,
complement(join(zero,join(X3,complement(X)))) = complement(join(zero,complement(meet(X,complement(X3))))),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
complement(join(zero,complement(meet(X,complement(X3))))) = meet(meet(X,complement(X3)),top),
inference(substitution,[status(thm)],[c163]) ).
cnf(c510,plain,
meet(meet(X,complement(X3)),top) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c358]) ).
cnf(c511,plain,
complement(join(zero,complement(meet(X,complement(X3))))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c509,c510]) ).
cnf(c512,plain,
complement(join(zero,join(X3,complement(X)))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c508,c511]) ).
cnf(c513,plain,
complement(join(X3,complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c504,c512]) ).
cnf(c514,plain,
complement(join(X3,complement(meet(X3,X)))) = meet(meet(X3,X),complement(X3)),
inference(substitution,[status(thm)],[c513]) ).
cnf(c515,plain,
meet(meet(X3,X),complement(X3)) = complement(join(X3,complement(meet(X3,X)))),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
complement(join(X3,complement(meet(X3,X)))) = complement(top),
inference(congruence,[status(thm)],[c485]) ).
cnf(c517,plain,
complement(join(X3,complement(meet(X3,X)))) = zero,
inference(transitivity,[status(thm)],[c516,c30]) ).
cnf(c518,plain,
meet(meet(X3,X),complement(X3)) = zero,
inference(transitivity,[status(thm)],[c515,c517]) ).
cnf(c519,plain,
meet(complement(X3),meet(X3,X)) = zero,
inference(transitivity,[status(thm)],[c501,c518]) ).
cnf(c520,plain,
meet(complement(X3),meet(X,X3)) = zero,
inference(transitivity,[status(thm)],[c500,c519]) ).
cnf(c521,plain,
meet(complement(meet(X3,X)),meet(X3,meet(X3,X))) = zero,
inference(substitution,[status(thm)],[c520]) ).
cnf(c522,plain,
meet(complement(meet(X3,X)),meet(X3,X)) = zero,
inference(transitivity,[status(thm)],[c499,c521]) ).
cnf(c523,plain,
meet(X3,meet(complement(meet(X3,X)),X)) = zero,
inference(transitivity,[status(thm)],[c460,c522]) ).
cnf(c524,plain,
meet(X3,meet(X,complement(meet(X3,X)))) = zero,
inference(transitivity,[status(thm)],[c423,c523]) ).
cnf(c525,plain,
meet(X,meet(X3,complement(meet(X,X3)))) = zero,
inference(substitution,[status(thm)],[c524]) ).
cnf(c526,plain,
join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))) = join(zero,meet(meet(X3,complement(meet(X,X3))),complement(X))),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
join(zero,meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(meet(X3,complement(meet(X,X3))),complement(X)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c528,plain,
meet(meet(X4,X3),X) = meet(X,meet(X4,X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c529,plain,
meet(X4,meet(X,X3)) = meet(X,meet(X4,X3)),
inference(substitution,[status(thm)],[c459]) ).
cnf(c530,plain,
meet(X,meet(X4,X3)) = meet(X4,meet(X,X3)),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
meet(meet(X4,X3),X) = meet(X4,meet(X,X3)),
inference(transitivity,[status(thm)],[c528,c530]) ).
cnf(c532,plain,
meet(meet(X3,complement(meet(X,X3))),complement(X)) = meet(X3,meet(complement(X),complement(meet(X,X3)))),
inference(substitution,[status(thm)],[c531]) ).
cnf(c533,plain,
meet(complement(X3),complement(X)) = meet(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c534,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c199]) ).
cnf(c535,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c534]) ).
cnf(c536,plain,
meet(complement(X),complement(X3)) = meet(join(zero,complement(X)),complement(X3)),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
complement(join(X3,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c513]) ).
cnf(c538,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c537]) ).
cnf(c539,plain,
join(X3,complement(join(zero,complement(X)))) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c540,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
join(X3,meet(X,top)) = join(X3,X),
inference(congruence,[status(thm)],[c358]) ).
cnf(c542,plain,
complement(join(X3,meet(X,top))) = complement(join(X3,X)),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c540,c542]) ).
cnf(c544,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c538,c543]) ).
cnf(c545,plain,
meet(complement(X),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c536,c544]) ).
cnf(c546,plain,
meet(complement(X3),complement(X)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c533,c545]) ).
cnf(c547,plain,
meet(complement(X),complement(meet(X,X3))) = complement(join(X,meet(X,X3))),
inference(substitution,[status(thm)],[c546]) ).
cnf(c548,plain,
meet(X3,meet(complement(X),complement(meet(X,X3)))) = meet(X3,complement(join(X,meet(X,X3)))),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
join(X,meet(X,X3)) = X,
inference(substitution,[status(thm)],[c263]) ).
cnf(c550,plain,
complement(join(X,meet(X,X3))) = complement(X),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
meet(X3,complement(join(X,meet(X,X3)))) = meet(X3,complement(X)),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
meet(X3,meet(complement(X),complement(meet(X,X3)))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c548,c551]) ).
cnf(c553,plain,
meet(meet(X3,complement(meet(X,X3))),complement(X)) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c532,c552]) ).
cnf(c554,plain,
join(zero,meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c527,c553]) ).
cnf(c555,plain,
join(meet(X,meet(X3,complement(meet(X,X3)))),meet(meet(X3,complement(meet(X,X3))),complement(X))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c526,c554]) ).
cnf(c556,plain,
meet(X3,complement(meet(X,X3))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c421,c555]) ).
cnf(c557,plain,
meet(X3,complement(meet(X3,X))) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c408,c556]) ).
cnf(c558,plain,
complement(meet(X3,complement(meet(X3,X)))) = complement(meet(X3,complement(X))),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
complement(meet(X3,complement(meet(X3,X)))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c558,c403]) ).
cnf(c560,plain,
join(meet(X3,X),complement(X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c405,c559]) ).
cnf(c561,plain,
join(meet(x0,X),complement(x0)) = join(X,complement(x0)),
inference(substitution,[status(thm)],[c560]) ).
cnf(c562,plain,
composition(meet(X3,converse(x0)),join(meet(x0,X),complement(x0))) = composition(meet(X3,converse(x0)),join(X,complement(x0))),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
join(complement(x0),X) = join(X,complement(x0)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c564,plain,
join(X,complement(x0)) = join(complement(x0),X),
inference(symmetry,[status(thm)],[c563]) ).
cnf(c565,plain,
composition(meet(X3,converse(x0)),join(X,complement(x0))) = composition(meet(X3,converse(x0)),join(complement(x0),X)),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
join(composition(meet(X3,converse(x0)),X),composition(meet(X3,converse(x0)),complement(x0))) = composition(meet(X3,converse(x0)),join(complement(x0),X)),
inference(substitution,[status(thm)],[c326]) ).
cnf(c567,plain,
composition(meet(X3,converse(x0)),join(complement(x0),X)) = join(composition(meet(X3,converse(x0)),X),composition(meet(X3,converse(x0)),complement(x0))),
inference(symmetry,[status(thm)],[c566]) ).
cnf(c568,plain,
join(composition(meet(X3,converse(x0)),X),composition(meet(X3,converse(x0)),complement(x0))) = join(composition(meet(X3,converse(x0)),X),zero),
inference(congruence,[status(thm)],[c270]) ).
cnf(c569,plain,
join(composition(meet(X3,converse(x0)),X),zero) = composition(meet(X3,converse(x0)),X),
inference(substitution,[status(thm)],[c189]) ).
cnf(c570,plain,
join(composition(meet(X3,converse(x0)),X),composition(meet(X3,converse(x0)),complement(x0))) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c568,c569]) ).
cnf(c571,plain,
composition(meet(X3,converse(x0)),join(complement(x0),X)) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c567,c570]) ).
cnf(c572,plain,
composition(meet(X3,converse(x0)),join(X,complement(x0))) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c565,c571]) ).
cnf(c573,plain,
composition(meet(X3,converse(x0)),join(meet(x0,X),complement(x0))) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c562,c572]) ).
cnf(c574,plain,
composition(meet(X3,converse(x0)),join(complement(x0),meet(x0,X))) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c329,c573]) ).
cnf(c575,plain,
join(composition(meet(X3,converse(x0)),meet(x0,X)),composition(meet(X3,converse(x0)),complement(x0))) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c327,c574]) ).
cnf(c576,plain,
join(composition(meet(X3,converse(x0)),meet(x0,X)),zero) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c272,c575]) ).
cnf(c577,plain,
composition(meet(X3,converse(x0)),meet(x0,X)) = composition(meet(X3,converse(x0)),X),
inference(transitivity,[status(thm)],[c191,c576]) ).
cnf(c578,plain,
composition(meet(x1,converse(x0)),meet(x0,x2)) = composition(meet(x1,converse(x0)),x2),
inference(substitution,[status(thm)],[c577]) ).
cnf(c579,plain,
$false,
inference(resolution,[status(thm)],[c4,c578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL037+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n011.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 22:56:00 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.27/2.85 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 18.27/2.85
% 18.27/2.85 % SZS status Theorem
% 18.27/2.85
% 19.07/2.90 % SZS output start CNFRefutation
% See solution above
% 22.24/3.38
% 22.24/3.38 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------