%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL032+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:33:22 PM UTC 2026
% Result : Theorem 5.95s 1.25s
% Output : CNFRefutation 10.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 13
% Syntax : Number of formulae : 589 ( 589 unt; 0 def)
% Number of atoms : 589 ( 588 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 1084 ( 84 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
join(composition(X0,meet(X1,X2)),meet(composition(X0,X1),composition(X0,X2))) = meet(composition(X0,X1),composition(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] : join(composition(X0_2,meet(X1_2,X2_2)),meet(composition(X0_2,X1_2),composition(X0_2,X2_2))) = meet(composition(X0_2,X1_2),composition(X0_2,X2_2)),
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
join(composition(x0,meet(x1,x2)),meet(composition(x0,x1),composition(x0,x2))) != meet(composition(x0,x1),composition(x0,x2)),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c5,plain,
join(composition(X4,meet(X3,X)),meet(composition(X4,X3),composition(X4,X))) = join(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,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(c7,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c4]) ).
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)],[c6]) ).
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)],[c7,c13]) ).
cnf(c15,plain,
meet(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X))) = meet(composition(X4,meet(X3,X)),meet(composition(X4,X3),composition(X4,X))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
meet(X3,meet(X,X4)) = meet(X3,meet(X4,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c17,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c18,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c21,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c23,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c21,c24]) ).
cnf(c26,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c19,c25]) ).
cnf(c27,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c31,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c33,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c29,c34]) ).
cnf(c36,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c38,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c35]) ).
cnf(c39,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c41,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c43,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c47,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c50,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c48,c51]) ).
cnf(c53,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c55,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c45,c55]) ).
cnf(c57,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
composition(converse(one),one) = converse(one),
inference(substitution,[status(thm)],[c49]) ).
cnf(c61,plain,
converse(one) = composition(converse(one),one),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
composition(converse(one),one) = one,
inference(substitution,[status(thm)],[c56]) ).
cnf(c63,plain,
converse(one) = one,
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
composition(one,X) = composition(converse(one),X),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c65,c56]) ).
cnf(c67,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,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)],[c4]) ).
cnf(c72,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)],[c71]) ).
cnf(c73,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(c74,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c72,c74]) ).
cnf(c76,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c70,c76]) ).
cnf(c78,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c59,c77]) ).
cnf(c79,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c83,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)],[c82]) ).
cnf(c84,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(c85,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c83,c86]) ).
cnf(c88,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c81,c88]) ).
cnf(c90,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c41,c89]) ).
cnf(c91,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c39,c91]) ).
cnf(c93,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c37,c92]) ).
cnf(c94,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c97,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c99,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c101,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c103,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c106,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c109,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c107,c110]) ).
cnf(c112,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c104,c112]) ).
cnf(c114,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
converse(top) = join(complement(X),converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(complement(converse(complement(X)))))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c118,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c121,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,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(c124,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c126,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c4]) ).
cnf(c129,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c124,c129]) ).
cnf(c131,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c122,c130]) ).
cnf(c132,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c133,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c131]) ).
cnf(c135,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c137,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c138,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c136,c138]) ).
cnf(c140,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c135,c139]) ).
cnf(c141,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c133,c140]) ).
cnf(c142,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c131]) ).
cnf(c145,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c131]) ).
cnf(c146,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c141]) ).
cnf(c148,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c146,c147]) ).
cnf(c149,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c144,c148]) ).
cnf(c150,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c143,c149]) ).
cnf(c151,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
join(X4,join(X3,complement(X4))) = join(X,top),
inference(transitivity,[status(thm)],[c131,c151]) ).
cnf(c153,plain,
join(X4,join(complement(X4),X3)) = join(X,top),
inference(transitivity,[status(thm)],[c119,c152]) ).
cnf(c154,plain,
join(X3,join(complement(X3),converse(complement(converse(complement(X3)))))) = join(X,top),
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = join(X4,top),
inference(substitution,[status(thm)],[c153]) ).
cnf(c156,plain,
join(X4,top) = join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = join(X3,complement(X3)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c158,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c159,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = top,
inference(transitivity,[status(thm)],[c157,c159]) ).
cnf(c161,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c156,c160]) ).
cnf(c162,plain,
join(X,join(complement(X),converse(complement(converse(complement(X)))))) = top,
inference(transitivity,[status(thm)],[c154,c161]) ).
cnf(c163,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c116,c162]) ).
cnf(c164,plain,
top = join(X,converse(top)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
converse(top) = converse(join(X,converse(top))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
converse(join(X,converse(top))) = join(converse(X),converse(converse(top))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c167,plain,
converse(converse(top)) = top,
inference(substitution,[status(thm)],[c42]) ).
cnf(c168,plain,
join(converse(X),converse(converse(top))) = join(converse(X),top),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
join(converse(X),top) = top,
inference(substitution,[status(thm)],[c161]) ).
cnf(c170,plain,
join(converse(X),converse(converse(top))) = top,
inference(transitivity,[status(thm)],[c168,c169]) ).
cnf(c171,plain,
converse(join(X,converse(top))) = top,
inference(transitivity,[status(thm)],[c166,c170]) ).
cnf(c172,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c165,c171]) ).
cnf(c173,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
meet(X,top) = meet(X,converse(top)),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
join(meet(X,top),complement(top)) = join(meet(X,converse(top)),complement(top)),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
join(complement(X),converse(top)) = top,
inference(substitution,[status(thm)],[c163]) ).
cnf(c177,plain,
top = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
complement(top) = complement(join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
join(meet(X,converse(top)),complement(top)) = join(meet(X,converse(top)),complement(join(complement(X),converse(top)))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
join(meet(X,converse(top)),complement(join(complement(X),converse(top)))) = X,
inference(substitution,[status(thm)],[c87]) ).
cnf(c181,plain,
join(meet(X,converse(top)),complement(top)) = X,
inference(transitivity,[status(thm)],[c179,c180]) ).
cnf(c182,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c175,c181]) ).
cnf(c183,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c101,c182]) ).
cnf(c184,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c99,c183]) ).
cnf(c185,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c97,c184]) ).
cnf(c186,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c95,c186]) ).
cnf(c188,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c191,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c190,c184]) ).
cnf(c192,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c189,c191]) ).
cnf(c193,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c36,c192]) ).
cnf(c194,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
meet(X3,meet(X4,X)) = meet(meet(X3,top),meet(X4,X)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c197,plain,
meet(meet(X3,top),meet(X4,X)) = meet(complement(join(zero,complement(X3))),meet(X4,X)),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
meet(complement(X),meet(X4,X3)) = meet(meet(X4,X3),complement(X)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c199,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c200,plain,
meet(meet(X4,X3),complement(X)) = meet(complement(join(complement(X4),complement(X3))),complement(X)),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
meet(complement(X3),complement(X)) = meet(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c202,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c203,plain,
meet(complement(X),complement(X3)) = meet(join(zero,complement(X)),complement(X3)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c205,plain,
join(X3,complement(X)) = join(complement(X),X3),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
complement(join(X3,complement(X))) = complement(join(complement(X),X3)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c14]) ).
cnf(c208,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c207,c193]) ).
cnf(c209,plain,
X = meet(top,X),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
join(complement(X),X3) = join(complement(X),meet(top,X3)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
complement(join(complement(X),X3)) = complement(join(complement(X),meet(top,X3))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c213,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
meet(X4,join(complement(X3),complement(X))) = meet(X4,join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
meet(X4,join(complement(X),complement(X3))) = meet(join(complement(X),complement(X3)),X4),
inference(substitution,[status(thm)],[c14]) ).
cnf(c216,plain,
meet(join(complement(X),complement(X3)),X4) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c217,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c218,plain,
complement(join(complement(X),complement(X3))) = meet(X,X3),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
join(complement(join(complement(X),complement(X3))),complement(X4)) = join(meet(X,X3),complement(X4)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = complement(join(meet(X,X3),complement(X4))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
join(meet(X,X3),complement(X4)) = join(complement(X4),meet(X,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c222,plain,
complement(join(meet(X,X3),complement(X4))) = complement(join(complement(X4),meet(X,X3))),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c224,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
join(complement(X4),meet(X,X3)) = join(complement(X4),meet(X3,X)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
complement(join(complement(X4),meet(X,X3))) = complement(join(complement(X4),meet(X3,X))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
complement(join(meet(X,X3),complement(X4))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c222,c226]) ).
cnf(c228,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c220,c227]) ).
cnf(c229,plain,
meet(join(complement(X),complement(X3)),X4) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c216,c228]) ).
cnf(c230,plain,
meet(X4,join(complement(X),complement(X3))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c215,c229]) ).
cnf(c231,plain,
meet(X4,join(complement(X3),complement(X))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c214,c230]) ).
cnf(c232,plain,
meet(X,join(complement(top),complement(X3))) = complement(join(complement(X),meet(top,X3))),
inference(substitution,[status(thm)],[c231]) ).
cnf(c233,plain,
complement(join(complement(X),meet(top,X3))) = meet(X,join(complement(top),complement(X3))),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
join(complement(top),complement(X)) = join(zero,complement(X)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c235,plain,
meet(X,join(complement(top),complement(X3))) = meet(X,join(zero,complement(X3))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
meet(X,join(zero,complement(X3))) = meet(X,complement(X3)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c237,plain,
meet(X,join(complement(top),complement(X3))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
complement(join(complement(X),meet(top,X3))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c233,c237]) ).
cnf(c239,plain,
complement(join(complement(X),X3)) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c211,c238]) ).
cnf(c240,plain,
complement(join(X3,complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c206,c239]) ).
cnf(c241,plain,
complement(join(X3,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c240]) ).
cnf(c242,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
join(X3,complement(join(zero,complement(X)))) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c244,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
join(X3,meet(X,top)) = join(X3,X),
inference(congruence,[status(thm)],[c193]) ).
cnf(c246,plain,
complement(join(X3,meet(X,top))) = complement(join(X3,X)),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c244,c246]) ).
cnf(c248,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c242,c247]) ).
cnf(c249,plain,
meet(complement(X),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c203,c248]) ).
cnf(c250,plain,
meet(complement(X3),complement(X)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c201,c249]) ).
cnf(c251,plain,
meet(complement(join(complement(X4),complement(X3))),complement(X)) = complement(join(join(complement(X4),complement(X3)),X)),
inference(substitution,[status(thm)],[c250]) ).
cnf(c252,plain,
join(complement(X4),join(complement(X3),X)) = join(join(complement(X4),complement(X3)),X),
inference(substitution,[status(thm)],[c123]) ).
cnf(c253,plain,
join(join(complement(X4),complement(X3)),X) = join(complement(X4),join(complement(X3),X)),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
complement(join(join(complement(X4),complement(X3)),X)) = complement(join(complement(X4),join(complement(X3),X))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c256,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
complement(join(complement(X3),X)) = complement(join(X,complement(X3))),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
complement(join(X,complement(X3))) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c240]) ).
cnf(c259,plain,
complement(join(complement(X3),X)) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c257,c258]) ).
cnf(c260,plain,
complement(join(complement(X4),join(complement(X3),X))) = meet(X4,complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c259]) ).
cnf(c261,plain,
meet(X4,complement(join(complement(X3),X))) = meet(X4,meet(X3,complement(X))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c262,plain,
complement(join(complement(X4),join(complement(X3),X))) = meet(X4,meet(X3,complement(X))),
inference(transitivity,[status(thm)],[c260,c261]) ).
cnf(c263,plain,
complement(join(join(complement(X4),complement(X3)),X)) = meet(X4,meet(X3,complement(X))),
inference(transitivity,[status(thm)],[c254,c262]) ).
cnf(c264,plain,
meet(complement(join(complement(X4),complement(X3))),complement(X)) = meet(X4,meet(X3,complement(X))),
inference(transitivity,[status(thm)],[c251,c263]) ).
cnf(c265,plain,
meet(meet(X4,X3),complement(X)) = meet(X4,meet(X3,complement(X))),
inference(transitivity,[status(thm)],[c200,c264]) ).
cnf(c266,plain,
meet(complement(X),meet(X4,X3)) = meet(X4,meet(X3,complement(X))),
inference(transitivity,[status(thm)],[c198,c265]) ).
cnf(c267,plain,
meet(complement(join(zero,complement(X3))),meet(X4,X)) = meet(X4,meet(X,complement(join(zero,complement(X3))))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
meet(X,complement(join(zero,complement(X3)))) = meet(X,meet(X3,top)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c269,plain,
meet(X4,meet(X,complement(join(zero,complement(X3))))) = meet(X4,meet(X,meet(X3,top))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(X,meet(X3,top)) = meet(X,X3),
inference(congruence,[status(thm)],[c193]) ).
cnf(c271,plain,
meet(X4,meet(X,meet(X3,top))) = meet(X4,meet(X,X3)),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c273,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
meet(X4,meet(X,X3)) = meet(X4,meet(X3,X)),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
meet(X4,meet(X,meet(X3,top))) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c271,c274]) ).
cnf(c276,plain,
meet(X4,meet(X,complement(join(zero,complement(X3))))) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c269,c275]) ).
cnf(c277,plain,
meet(complement(join(zero,complement(X3))),meet(X4,X)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c267,c276]) ).
cnf(c278,plain,
meet(meet(X3,top),meet(X4,X)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c197,c277]) ).
cnf(c279,plain,
meet(X3,meet(X4,X)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c195,c278]) ).
cnf(c280,plain,
meet(X3,meet(X,X4)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c16,c279]) ).
cnf(c281,plain,
meet(X4,meet(X,X3)) = meet(X3,meet(X4,X)),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
meet(X3,meet(X4,X)) = meet(X4,meet(X,X3)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c284,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
meet(X4,meet(X,X3)) = meet(X4,meet(X3,X)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
meet(X3,meet(X4,X)) = meet(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c282,c285]) ).
cnf(c287,plain,
meet(composition(X4,meet(X3,X)),meet(composition(X4,X3),composition(X4,X))) = meet(composition(X4,X3),meet(composition(X4,meet(X3,X)),composition(X4,X))),
inference(substitution,[status(thm)],[c286]) ).
cnf(c288,plain,
join(composition(X4,X),composition(X4,meet(X3,X))) = join(composition(X4,meet(X3,X)),composition(X4,X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c289,plain,
join(composition(X4,meet(X3,X)),composition(X4,X)) = join(composition(X4,X),composition(X4,meet(X3,X))),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c291,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
composition(X3,X) = composition(X3,converse(converse(X))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
join(composition(X4,X3),composition(X4,X)) = join(composition(X4,X3),composition(X4,converse(converse(X)))),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c295,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
composition(X3,converse(X)) = composition(converse(converse(X3)),converse(X)),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
join(composition(X4,X3),composition(X4,converse(X))) = join(composition(X4,X3),composition(converse(converse(X4)),converse(X))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
converse(composition(X,converse(X3))) = composition(converse(converse(X3)),converse(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c299,plain,
composition(converse(converse(X3)),converse(X)) = converse(composition(X,converse(X3))),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = join(composition(X4,X3),converse(composition(X,converse(X4)))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
converse(converse(composition(X3,X))) = composition(X3,X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c302,plain,
composition(X3,X) = converse(converse(composition(X3,X))),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c303,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)],[c302]) ).
cnf(c304,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)],[c105]) ).
cnf(c305,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)],[c304]) ).
cnf(c306,plain,
converse(composition(X,X3)) = composition(converse(X3),converse(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c307,plain,
join(converse(composition(X,X3)),composition(X4,converse(X))) = join(composition(converse(X3),converse(X)),composition(X4,converse(X))),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,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(c309,plain,
composition(join(converse(X3),X4),converse(X)) = join(composition(converse(X3),converse(X)),composition(X4,converse(X))),
inference(substitution,[status(thm)],[c308]) ).
cnf(c310,plain,
join(composition(converse(X3),converse(X)),composition(X4,converse(X))) = composition(join(converse(X3),X4),converse(X)),
inference(symmetry,[status(thm)],[c309]) ).
cnf(c311,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c312,plain,
composition(join(converse(X3),X4),converse(X)) = composition(join(X4,converse(X3)),converse(X)),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
join(composition(converse(X3),converse(X)),composition(X4,converse(X))) = composition(join(X4,converse(X3)),converse(X)),
inference(transitivity,[status(thm)],[c310,c312]) ).
cnf(c314,plain,
join(converse(composition(X,X3)),composition(X4,converse(X))) = composition(join(X4,converse(X3)),converse(X)),
inference(transitivity,[status(thm)],[c307,c313]) ).
cnf(c315,plain,
join(converse(composition(X4,X3)),composition(X,converse(X4))) = composition(join(X,converse(X3)),converse(X4)),
inference(substitution,[status(thm)],[c314]) ).
cnf(c316,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = converse(composition(join(X,converse(X3)),converse(X4))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(converse(converse(X4)),converse(join(X,converse(X3)))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c318,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c319,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,converse(join(X,converse(X3)))),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
converse(join(X,converse(X3))) = join(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c321,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(converse(X),converse(converse(X3)))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c323,plain,
join(converse(X),converse(converse(X3))) = join(converse(X),X3),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(converse(X),X3)),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c326,plain,
composition(X4,join(converse(X),X3)) = composition(X4,join(X3,converse(X))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
composition(X4,join(converse(X),converse(converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c324,c326]) ).
cnf(c328,plain,
composition(X4,converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c321,c327]) ).
cnf(c329,plain,
composition(converse(converse(X4)),converse(join(X,converse(X3)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c319,c328]) ).
cnf(c330,plain,
converse(composition(join(X,converse(X3)),converse(X4))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c317,c329]) ).
cnf(c331,plain,
converse(join(converse(composition(X4,X3)),composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c316,c330]) ).
cnf(c332,plain,
join(converse(converse(composition(X4,X3))),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c305,c331]) ).
cnf(c333,plain,
join(composition(X4,X3),converse(composition(X,converse(X4)))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c303,c332]) ).
cnf(c334,plain,
join(composition(X4,X3),composition(converse(converse(X4)),converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c300,c333]) ).
cnf(c335,plain,
join(composition(X4,X3),composition(X4,converse(X))) = composition(X4,join(X3,converse(X))),
inference(transitivity,[status(thm)],[c297,c334]) ).
cnf(c336,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X3,converse(converse(X)))),
inference(substitution,[status(thm)],[c335]) ).
cnf(c337,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c338,plain,
join(X3,converse(converse(X))) = join(X3,X),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
composition(X4,join(X3,converse(converse(X)))) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
join(composition(X4,X3),composition(X4,converse(converse(X)))) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c336,c339]) ).
cnf(c341,plain,
join(composition(X4,X3),composition(X4,X)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c293,c340]) ).
cnf(c342,plain,
join(composition(X4,X),composition(X4,X3)) = composition(X4,join(X,X3)),
inference(substitution,[status(thm)],[c341]) ).
cnf(c343,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c344,plain,
composition(X4,join(X,X3)) = composition(X4,join(X3,X)),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
join(composition(X4,X),composition(X4,X3)) = composition(X4,join(X3,X)),
inference(transitivity,[status(thm)],[c342,c344]) ).
cnf(c346,plain,
join(composition(X4,X),composition(X4,meet(X3,X))) = composition(X4,join(meet(X3,X),X)),
inference(substitution,[status(thm)],[c345]) ).
cnf(c347,plain,
meet(join(meet(X3,X),X),top) = join(meet(X3,X),X),
inference(substitution,[status(thm)],[c193]) ).
cnf(c348,plain,
join(meet(X3,X),X) = meet(join(meet(X3,X),X),top),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
complement(join(zero,complement(join(meet(X3,X),X)))) = meet(join(meet(X3,X),X),top),
inference(substitution,[status(thm)],[c35]) ).
cnf(c350,plain,
meet(join(meet(X3,X),X),top) = complement(join(zero,complement(join(meet(X3,X),X)))),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
join(X,meet(X3,X)) = join(meet(X3,X),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c352,plain,
join(meet(X3,X),X) = join(X,meet(X3,X)),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
complement(join(meet(X3,X),X)) = complement(join(X,meet(X3,X))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
meet(complement(X),complement(meet(X3,X))) = complement(join(X,meet(X3,X))),
inference(substitution,[status(thm)],[c250]) ).
cnf(c355,plain,
complement(join(X,meet(X3,X))) = meet(complement(X),complement(meet(X3,X))),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c357,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c356]) ).
cnf(c358,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c4]) ).
cnf(c359,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
join(complement(complement(X)),X3) = join(X3,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c361,plain,
join(X3,complement(complement(X))) = join(complement(complement(X)),X3),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
join(zero,join(X3,complement(complement(X)))) = join(zero,join(complement(complement(X)),X3)),
inference(congruence,[status(thm)],[c361]) ).
cnf(c363,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c364,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c365,plain,
meet(X,X) = complement(complement(X)),
inference(transitivity,[status(thm)],[c363,c364]) ).
cnf(c366,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
join(complement(complement(X)),X3) = join(meet(X,X),X3),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
join(zero,join(complement(complement(X)),X3)) = join(zero,join(meet(X,X),X3)),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
join(zero,join(meet(X,X),X3)) = join(join(zero,meet(X,X)),X3),
inference(substitution,[status(thm)],[c123]) ).
cnf(c370,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c371,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c373,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c87]) ).
cnf(c375,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c373,c374]) ).
cnf(c376,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c371,c375]) ).
cnf(c377,plain,
join(join(zero,meet(X,X)),X3) = join(X,X3),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c379,plain,
join(join(zero,meet(X,X)),X3) = join(X3,X),
inference(transitivity,[status(thm)],[c377,c378]) ).
cnf(c380,plain,
join(zero,join(meet(X,X),X3)) = join(X3,X),
inference(transitivity,[status(thm)],[c369,c379]) ).
cnf(c381,plain,
join(zero,join(complement(complement(X)),X3)) = join(X3,X),
inference(transitivity,[status(thm)],[c368,c380]) ).
cnf(c382,plain,
join(zero,join(X3,complement(complement(X)))) = join(X3,X),
inference(transitivity,[status(thm)],[c362,c381]) ).
cnf(c383,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,X),
inference(substitution,[status(thm)],[c382]) ).
cnf(c384,plain,
join(zero,X) = join(zero,join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c386,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
join(zero,join(zero,complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c386,c90]) ).
cnf(c388,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c384,c387]) ).
cnf(c389,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c359,c388]) ).
cnf(c390,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c357,c389]) ).
cnf(c391,plain,
join(zero,meet(complement(X),complement(meet(X3,X)))) = meet(complement(X),complement(meet(X3,X))),
inference(substitution,[status(thm)],[c390]) ).
cnf(c392,plain,
meet(complement(X),complement(meet(X3,X))) = join(zero,meet(complement(X),complement(meet(X3,X)))),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
complement(join(X,complement(meet(X3,X)))) = meet(meet(X3,X),complement(X)),
inference(substitution,[status(thm)],[c240]) ).
cnf(c394,plain,
meet(meet(X3,X),complement(X)) = complement(join(X,complement(meet(X3,X)))),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
complement(meet(X,X3)) = complement(meet(X3,X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c396,plain,
join(X3,complement(meet(X,X3))) = join(X3,complement(meet(X3,X))),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c398,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
join(X3,complement(meet(X3,X))) = join(X3,complement(meet(X,X3))),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c401,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c400]) ).
cnf(c402,plain,
join(zero,meet(join(complement(X),complement(X3)),join(complement(X),complement(X3)))) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c376]) ).
cnf(c403,plain,
join(complement(X),complement(X3)) = join(zero,meet(join(complement(X),complement(X3)),join(complement(X),complement(X3)))),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
meet(join(complement(X),complement(X3)),join(complement(X),complement(X3))) = complement(join(complement(join(complement(X),complement(X3))),meet(X,X3))),
inference(substitution,[status(thm)],[c231]) ).
cnf(c405,plain,
join(zero,meet(join(complement(X),complement(X3)),join(complement(X),complement(X3)))) = join(zero,complement(join(complement(join(complement(X),complement(X3))),meet(X,X3)))),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
join(zero,complement(join(complement(join(complement(X),complement(X3))),meet(X,X3)))) = complement(join(complement(join(complement(X),complement(X3))),meet(X,X3))),
inference(substitution,[status(thm)],[c187]) ).
cnf(c407,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c408,plain,
complement(join(complement(X),complement(X3))) = meet(X,X3),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c409,plain,
join(complement(join(complement(X),complement(X3))),meet(X,X3)) = join(meet(X,X3),meet(X,X3)),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
complement(join(complement(join(complement(X),complement(X3))),meet(X,X3))) = complement(join(meet(X,X3),meet(X,X3))),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c187]) ).
cnf(c412,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c411]) ).
cnf(c413,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c412,c90]) ).
cnf(c414,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c413]) ).
cnf(c415,plain,
join(X,X) = join(X,complement(complement(X))),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
join(complement(complement(X)),X) = join(X,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c417,plain,
join(X,complement(complement(X))) = join(complement(complement(X)),X),
inference(symmetry,[status(thm)],[c416]) ).
cnf(c418,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(complement(complement(X)),X),
inference(substitution,[status(thm)],[c382]) ).
cnf(c419,plain,
join(complement(complement(X)),X) = join(zero,join(complement(complement(X)),complement(complement(X)))),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
join(complement(complement(X)),complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c421,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c421,c90]) ).
cnf(c423,plain,
join(complement(complement(X)),X) = X,
inference(transitivity,[status(thm)],[c419,c422]) ).
cnf(c424,plain,
join(X,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c417,c423]) ).
cnf(c425,plain,
join(X,X) = X,
inference(transitivity,[status(thm)],[c415,c424]) ).
cnf(c426,plain,
join(meet(X,X3),meet(X,X3)) = meet(X,X3),
inference(substitution,[status(thm)],[c425]) ).
cnf(c427,plain,
complement(join(meet(X,X3),meet(X,X3))) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c429,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c428]) ).
cnf(c430,plain,
complement(meet(X,X3)) = complement(meet(X3,X)),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
complement(join(meet(X,X3),meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c427,c430]) ).
cnf(c432,plain,
complement(join(complement(join(complement(X),complement(X3))),meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c410,c431]) ).
cnf(c433,plain,
join(zero,complement(join(complement(join(complement(X),complement(X3))),meet(X,X3)))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c406,c432]) ).
cnf(c434,plain,
join(zero,meet(join(complement(X),complement(X3)),join(complement(X),complement(X3)))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c405,c433]) ).
cnf(c435,plain,
join(complement(X),complement(X3)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c403,c434]) ).
cnf(c436,plain,
join(complement(X3),complement(X)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c401,c435]) ).
cnf(c437,plain,
join(complement(X),complement(X3)) = complement(meet(X,X3)),
inference(substitution,[status(thm)],[c436]) ).
cnf(c438,plain,
complement(meet(X,X3)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
join(X3,complement(meet(X,X3))) = join(X3,join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
join(X3,join(complement(X),complement(X3))) = join(complement(X),top),
inference(substitution,[status(thm)],[c131]) ).
cnf(c441,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c161]) ).
cnf(c442,plain,
join(X3,join(complement(X),complement(X3))) = top,
inference(transitivity,[status(thm)],[c440,c441]) ).
cnf(c443,plain,
join(X3,complement(meet(X,X3))) = top,
inference(transitivity,[status(thm)],[c439,c442]) ).
cnf(c444,plain,
join(X3,complement(meet(X3,X))) = top,
inference(transitivity,[status(thm)],[c399,c443]) ).
cnf(c445,plain,
join(X3,complement(meet(X,X3))) = top,
inference(transitivity,[status(thm)],[c396,c444]) ).
cnf(c446,plain,
join(X,complement(meet(X3,X))) = top,
inference(substitution,[status(thm)],[c445]) ).
cnf(c447,plain,
complement(join(X,complement(meet(X3,X)))) = complement(top),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
complement(join(X,complement(meet(X3,X)))) = zero,
inference(transitivity,[status(thm)],[c447,c26]) ).
cnf(c449,plain,
meet(meet(X3,X),complement(X)) = zero,
inference(transitivity,[status(thm)],[c394,c448]) ).
cnf(c450,plain,
zero = meet(meet(X3,X),complement(X)),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c451,plain,
join(zero,meet(complement(X),complement(meet(X3,X)))) = join(meet(meet(X3,X),complement(X)),meet(complement(X),complement(meet(X3,X)))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c453,plain,
join(meet(X3,X),meet(X,complement(X3))) = join(meet(X,X3),meet(X,complement(X3))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,X),meet(X3,complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c455,plain,
join(meet(X3,X),meet(X3,complement(X))) = join(meet(X3,complement(X)),meet(X3,X)),
inference(symmetry,[status(thm)],[c454]) ).
cnf(c456,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c457,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c87]) ).
cnf(c459,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c457,c458]) ).
cnf(c460,plain,
join(meet(X3,X),meet(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c455,c459]) ).
cnf(c461,plain,
join(meet(X,X3),meet(X,complement(X3))) = X,
inference(substitution,[status(thm)],[c460]) ).
cnf(c462,plain,
join(meet(X3,X),meet(X,complement(X3))) = X,
inference(transitivity,[status(thm)],[c453,c461]) ).
cnf(c463,plain,
join(meet(meet(X3,X),complement(X)),meet(complement(X),complement(meet(X3,X)))) = complement(X),
inference(substitution,[status(thm)],[c462]) ).
cnf(c464,plain,
join(zero,meet(complement(X),complement(meet(X3,X)))) = complement(X),
inference(transitivity,[status(thm)],[c451,c463]) ).
cnf(c465,plain,
meet(complement(X),complement(meet(X3,X))) = complement(X),
inference(transitivity,[status(thm)],[c392,c464]) ).
cnf(c466,plain,
complement(join(X,meet(X3,X))) = complement(X),
inference(transitivity,[status(thm)],[c355,c465]) ).
cnf(c467,plain,
complement(join(meet(X3,X),X)) = complement(X),
inference(transitivity,[status(thm)],[c353,c466]) ).
cnf(c468,plain,
join(zero,complement(join(meet(X3,X),X))) = join(zero,complement(X)),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
complement(join(zero,complement(join(meet(X3,X),X)))) = complement(join(zero,complement(X))),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c35,c193]) ).
cnf(c471,plain,
complement(join(zero,complement(join(meet(X3,X),X)))) = X,
inference(transitivity,[status(thm)],[c469,c470]) ).
cnf(c472,plain,
meet(join(meet(X3,X),X),top) = X,
inference(transitivity,[status(thm)],[c350,c471]) ).
cnf(c473,plain,
join(meet(X3,X),X) = X,
inference(transitivity,[status(thm)],[c348,c472]) ).
cnf(c474,plain,
composition(X4,join(meet(X3,X),X)) = composition(X4,X),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
join(composition(X4,X),composition(X4,meet(X3,X))) = composition(X4,X),
inference(transitivity,[status(thm)],[c346,c474]) ).
cnf(c476,plain,
join(composition(X4,meet(X3,X)),composition(X4,X)) = composition(X4,X),
inference(transitivity,[status(thm)],[c289,c475]) ).
cnf(c477,plain,
composition(X4,X) = join(composition(X4,meet(X3,X)),composition(X4,X)),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c478,plain,
meet(composition(X4,meet(X3,X)),composition(X4,X)) = meet(composition(X4,meet(X3,X)),join(composition(X4,meet(X3,X)),composition(X4,X))),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c480,plain,
join(X3,X) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
meet(X3,join(X3,X)) = meet(X3,join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c483,plain,
join(X3,meet(X,top)) = join(X3,complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
meet(X3,join(X3,meet(X,top))) = meet(X3,join(X3,complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
join(zero,meet(X3,complement(X))) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c390]) ).
cnf(c486,plain,
meet(X3,complement(X)) = join(zero,meet(X3,complement(X))),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
complement(meet(X3,complement(X))) = complement(join(zero,meet(X3,complement(X)))),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
complement(join(X,complement(X3))) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c240]) ).
cnf(c489,plain,
meet(X3,complement(X)) = complement(join(X,complement(X3))),
inference(symmetry,[status(thm)],[c488]) ).
cnf(c490,plain,
join(zero,meet(X3,complement(X))) = join(zero,complement(join(X,complement(X3)))),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
complement(join(zero,meet(X3,complement(X)))) = complement(join(zero,complement(join(X,complement(X3))))),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
complement(join(zero,complement(join(X,complement(X3))))) = meet(join(X,complement(X3)),top),
inference(substitution,[status(thm)],[c35]) ).
cnf(c493,plain,
meet(join(X,complement(X3)),top) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c494,plain,
complement(join(zero,complement(join(X,complement(X3))))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c492,c493]) ).
cnf(c495,plain,
complement(join(zero,meet(X3,complement(X)))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c491,c494]) ).
cnf(c496,plain,
complement(meet(X3,complement(X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c487,c495]) ).
cnf(c497,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c496]) ).
cnf(c498,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c497]) ).
cnf(c499,plain,
meet(X3,join(X3,complement(X))) = meet(X3,complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = meet(X3,complement(meet(X,complement(X3)))),
inference(substitution,[status(thm)],[c259]) ).
cnf(c501,plain,
meet(X3,complement(meet(X,complement(X3)))) = complement(join(complement(X3),meet(X,complement(X3)))),
inference(symmetry,[status(thm)],[c500]) ).
cnf(c502,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = complement(join(complement(X3),meet(X,complement(X3)))),
inference(substitution,[status(thm)],[c187]) ).
cnf(c503,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = join(zero,complement(join(complement(X3),meet(X,complement(X3))))),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
meet(X,complement(X3)) = meet(complement(X3),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c505,plain,
meet(X3,meet(X,complement(X3))) = meet(X3,meet(complement(X3),X)),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
meet(X3,meet(complement(X3),X)) = complement(join(complement(X3),complement(meet(complement(X3),X)))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c507,plain,
join(complement(X3),complement(meet(complement(X3),X))) = top,
inference(substitution,[status(thm)],[c444]) ).
cnf(c508,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = complement(top),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = zero,
inference(transitivity,[status(thm)],[c508,c26]) ).
cnf(c510,plain,
meet(X3,meet(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c506,c509]) ).
cnf(c511,plain,
meet(X3,meet(X,complement(X3))) = zero,
inference(transitivity,[status(thm)],[c505,c510]) ).
cnf(c512,plain,
zero = meet(X3,meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c511]) ).
cnf(c513,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = join(meet(X3,meet(X,complement(X3))),complement(join(complement(X3),meet(X,complement(X3))))),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
join(meet(X3,meet(X,complement(X3))),complement(join(complement(X3),meet(X,complement(X3))))) = X3,
inference(substitution,[status(thm)],[c87]) ).
cnf(c515,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = X3,
inference(transitivity,[status(thm)],[c513,c514]) ).
cnf(c516,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c503,c515]) ).
cnf(c517,plain,
meet(X3,complement(meet(X,complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c501,c516]) ).
cnf(c518,plain,
meet(X3,join(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c499,c517]) ).
cnf(c519,plain,
meet(X3,join(X3,complement(join(zero,complement(X))))) = X3,
inference(substitution,[status(thm)],[c518]) ).
cnf(c520,plain,
meet(X3,join(X3,meet(X,top))) = X3,
inference(transitivity,[status(thm)],[c484,c519]) ).
cnf(c521,plain,
meet(X3,join(X3,X)) = X3,
inference(transitivity,[status(thm)],[c481,c520]) ).
cnf(c522,plain,
meet(composition(X4,meet(X3,X)),join(composition(X4,meet(X3,X)),composition(X4,X))) = composition(X4,meet(X3,X)),
inference(substitution,[status(thm)],[c521]) ).
cnf(c523,plain,
meet(composition(X4,meet(X3,X)),composition(X4,X)) = composition(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c478,c522]) ).
cnf(c524,plain,
meet(composition(X4,X3),meet(composition(X4,meet(X3,X)),composition(X4,X))) = meet(composition(X4,X3),composition(X4,meet(X3,X))),
inference(congruence,[status(thm)],[c523]) ).
cnf(c525,plain,
meet(composition(X4,meet(X3,X)),composition(X4,X3)) = meet(composition(X4,X3),composition(X4,meet(X3,X))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c526,plain,
meet(composition(X4,X3),composition(X4,meet(X3,X))) = meet(composition(X4,meet(X3,X)),composition(X4,X3)),
inference(symmetry,[status(thm)],[c525]) ).
cnf(c527,plain,
join(composition(X4,X3),composition(X4,meet(X3,X))) = join(composition(X4,meet(X3,X)),composition(X4,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c528,plain,
join(composition(X4,meet(X3,X)),composition(X4,X3)) = join(composition(X4,X3),composition(X4,meet(X3,X))),
inference(symmetry,[status(thm)],[c527]) ).
cnf(c529,plain,
join(composition(X4,X3),composition(X4,meet(X3,X))) = composition(X4,join(meet(X3,X),X3)),
inference(substitution,[status(thm)],[c345]) ).
cnf(c530,plain,
meet(join(meet(X3,X),X3),top) = join(meet(X3,X),X3),
inference(substitution,[status(thm)],[c193]) ).
cnf(c531,plain,
join(meet(X3,X),X3) = meet(join(meet(X3,X),X3),top),
inference(symmetry,[status(thm)],[c530]) ).
cnf(c532,plain,
complement(join(zero,complement(join(meet(X3,X),X3)))) = meet(join(meet(X3,X),X3),top),
inference(substitution,[status(thm)],[c35]) ).
cnf(c533,plain,
meet(join(meet(X3,X),X3),top) = complement(join(zero,complement(join(meet(X3,X),X3)))),
inference(symmetry,[status(thm)],[c532]) ).
cnf(c534,plain,
join(X3,meet(X3,X)) = join(meet(X3,X),X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c535,plain,
join(meet(X3,X),X3) = join(X3,meet(X3,X)),
inference(symmetry,[status(thm)],[c534]) ).
cnf(c536,plain,
complement(join(meet(X3,X),X3)) = complement(join(X3,meet(X3,X))),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
meet(complement(X3),complement(meet(X3,X))) = complement(join(X3,meet(X3,X))),
inference(substitution,[status(thm)],[c250]) ).
cnf(c538,plain,
complement(join(X3,meet(X3,X))) = meet(complement(X3),complement(meet(X3,X))),
inference(symmetry,[status(thm)],[c537]) ).
cnf(c539,plain,
join(zero,meet(complement(X3),complement(meet(X3,X)))) = meet(complement(X3),complement(meet(X3,X))),
inference(substitution,[status(thm)],[c390]) ).
cnf(c540,plain,
meet(complement(X3),complement(meet(X3,X))) = join(zero,meet(complement(X3),complement(meet(X3,X)))),
inference(symmetry,[status(thm)],[c539]) ).
cnf(c541,plain,
complement(join(X3,complement(meet(X3,X)))) = meet(meet(X3,X),complement(X3)),
inference(substitution,[status(thm)],[c240]) ).
cnf(c542,plain,
meet(meet(X3,X),complement(X3)) = complement(join(X3,complement(meet(X3,X)))),
inference(symmetry,[status(thm)],[c541]) ).
cnf(c543,plain,
complement(join(X3,complement(meet(X3,X)))) = complement(top),
inference(congruence,[status(thm)],[c444]) ).
cnf(c544,plain,
complement(join(X3,complement(meet(X3,X)))) = zero,
inference(transitivity,[status(thm)],[c543,c26]) ).
cnf(c545,plain,
meet(meet(X3,X),complement(X3)) = zero,
inference(transitivity,[status(thm)],[c542,c544]) ).
cnf(c546,plain,
zero = meet(meet(X3,X),complement(X3)),
inference(symmetry,[status(thm)],[c545]) ).
cnf(c547,plain,
join(zero,meet(complement(X3),complement(meet(X3,X)))) = join(meet(meet(X3,X),complement(X3)),meet(complement(X3),complement(meet(X3,X)))),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
join(meet(meet(X3,X),complement(X3)),meet(complement(X3),complement(meet(X3,X)))) = complement(X3),
inference(substitution,[status(thm)],[c462]) ).
cnf(c549,plain,
join(zero,meet(complement(X3),complement(meet(X3,X)))) = complement(X3),
inference(transitivity,[status(thm)],[c547,c548]) ).
cnf(c550,plain,
meet(complement(X3),complement(meet(X3,X))) = complement(X3),
inference(transitivity,[status(thm)],[c540,c549]) ).
cnf(c551,plain,
complement(join(X3,meet(X3,X))) = complement(X3),
inference(transitivity,[status(thm)],[c538,c550]) ).
cnf(c552,plain,
complement(join(meet(X3,X),X3)) = complement(X3),
inference(transitivity,[status(thm)],[c536,c551]) ).
cnf(c553,plain,
join(zero,complement(join(meet(X3,X),X3))) = join(zero,complement(X3)),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
complement(join(zero,complement(join(meet(X3,X),X3)))) = complement(join(zero,complement(X3))),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c35,c193]) ).
cnf(c556,plain,
complement(join(zero,complement(join(meet(X3,X),X3)))) = X3,
inference(transitivity,[status(thm)],[c554,c555]) ).
cnf(c557,plain,
meet(join(meet(X3,X),X3),top) = X3,
inference(transitivity,[status(thm)],[c533,c556]) ).
cnf(c558,plain,
join(meet(X3,X),X3) = X3,
inference(transitivity,[status(thm)],[c531,c557]) ).
cnf(c559,plain,
composition(X4,join(meet(X3,X),X3)) = composition(X4,X3),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
join(composition(X4,X3),composition(X4,meet(X3,X))) = composition(X4,X3),
inference(transitivity,[status(thm)],[c529,c559]) ).
cnf(c561,plain,
join(composition(X4,meet(X3,X)),composition(X4,X3)) = composition(X4,X3),
inference(transitivity,[status(thm)],[c528,c560]) ).
cnf(c562,plain,
composition(X4,X3) = join(composition(X4,meet(X3,X)),composition(X4,X3)),
inference(symmetry,[status(thm)],[c561]) ).
cnf(c563,plain,
meet(composition(X4,meet(X3,X)),composition(X4,X3)) = meet(composition(X4,meet(X3,X)),join(composition(X4,meet(X3,X)),composition(X4,X3))),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
meet(composition(X4,meet(X3,X)),join(composition(X4,meet(X3,X)),composition(X4,X3))) = composition(X4,meet(X3,X)),
inference(substitution,[status(thm)],[c521]) ).
cnf(c565,plain,
meet(composition(X4,meet(X3,X)),composition(X4,X3)) = composition(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c563,c564]) ).
cnf(c566,plain,
meet(composition(X4,X3),composition(X4,meet(X3,X))) = composition(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c526,c565]) ).
cnf(c567,plain,
meet(composition(X4,X3),meet(composition(X4,meet(X3,X)),composition(X4,X))) = composition(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c524,c566]) ).
cnf(c568,plain,
meet(composition(X4,meet(X3,X)),meet(composition(X4,X3),composition(X4,X))) = composition(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c287,c567]) ).
cnf(c569,plain,
meet(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X))) = composition(X4,meet(X3,X)),
inference(transitivity,[status(thm)],[c15,c568]) ).
cnf(c570,plain,
composition(X4,meet(X3,X)) = meet(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X))),
inference(symmetry,[status(thm)],[c569]) ).
cnf(c571,plain,
join(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X))) = join(meet(composition(X4,X3),composition(X4,X)),meet(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X)))),
inference(congruence,[status(thm)],[c570]) ).
cnf(c572,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c573,plain,
join(X3,meet(X3,X)) = join(X3,complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
meet(complement(X3),X) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c575,plain,
complement(meet(complement(X3),X)) = complement(meet(X,complement(X3))),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c496]) ).
cnf(c577,plain,
complement(meet(complement(X3),X)) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c575,c576]) ).
cnf(c578,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = join(X3,complement(join(complement(X3),complement(X)))),
inference(substitution,[status(thm)],[c577]) ).
cnf(c579,plain,
join(X3,complement(join(complement(X3),complement(X)))) = complement(meet(complement(X3),join(complement(X3),complement(X)))),
inference(symmetry,[status(thm)],[c578]) ).
cnf(c580,plain,
meet(complement(X3),join(complement(X3),complement(X))) = complement(X3),
inference(substitution,[status(thm)],[c518]) ).
cnf(c581,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = complement(complement(X3)),
inference(congruence,[status(thm)],[c580]) ).
cnf(c582,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = X3,
inference(transitivity,[status(thm)],[c581,c413]) ).
cnf(c583,plain,
join(X3,complement(join(complement(X3),complement(X)))) = X3,
inference(transitivity,[status(thm)],[c579,c582]) ).
cnf(c584,plain,
join(X3,meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c573,c583]) ).
cnf(c585,plain,
join(meet(composition(X4,X3),composition(X4,X)),meet(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X)))) = meet(composition(X4,X3),composition(X4,X)),
inference(substitution,[status(thm)],[c584]) ).
cnf(c586,plain,
join(meet(composition(X4,X3),composition(X4,X)),composition(X4,meet(X3,X))) = meet(composition(X4,X3),composition(X4,X)),
inference(transitivity,[status(thm)],[c571,c585]) ).
cnf(c587,plain,
join(composition(X4,meet(X3,X)),meet(composition(X4,X3),composition(X4,X))) = meet(composition(X4,X3),composition(X4,X)),
inference(transitivity,[status(thm)],[c5,c586]) ).
cnf(c588,plain,
join(composition(x0,meet(x1,x2)),meet(composition(x0,x1),composition(x0,x2))) = meet(composition(x0,x1),composition(x0,x2)),
inference(substitution,[status(thm)],[c587]) ).
cnf(c589,plain,
$false,
inference(resolution,[status(thm)],[c3,c588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL032+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 22:54:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.95/1.25 Command-line arguments: --flatten --complete-subsets
% 5.95/1.25
% 5.95/1.25 % SZS status Theorem
% 5.95/1.25
% 6.71/1.31 % SZS output start CNFRefutation
% See solution above
% 10.22/1.81
% 10.22/1.81 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------