%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL023+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 12:33:13 PM UTC 2026
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 87
% Number of leaves : 13
% Syntax : Number of formulae : 378 ( 378 unt; 0 def)
% Number of atoms : 378 ( 377 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 : 550 ( 45 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] : join(composition(meet(X0_2,converse(X1_2)),meet(X1_2,X2_2)),composition(X0_2,meet(X1_2,X2_2))) = composition(X0_2,meet(X1_2,X2_2)),
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
join(composition(meet(x0,converse(x1)),meet(x1,x2)),composition(x0,meet(x1,x2))) != composition(x0,meet(x1,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(meet(x0,converse(x1)),meet(x1,x2)),composition(x0,meet(x1,x2))) = join(composition(x0,meet(x1,x2)),composition(meet(x0,converse(x1)),meet(x1,x2))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,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(c7,plain,
composition(join(x0,meet(x0,converse(x1))),meet(x1,x2)) = join(composition(x0,meet(x1,x2)),composition(meet(x0,converse(x1)),meet(x1,x2))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
join(composition(x0,meet(x1,x2)),composition(meet(x0,converse(x1)),meet(x1,x2))) = composition(join(x0,meet(x0,converse(x1))),meet(x1,x2)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,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(c10,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c12,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c15,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
meet(X,X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c10,c16]) ).
cnf(c18,plain,
meet(x2,x1) = meet(x1,x2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
meet(x1,x2) = meet(x2,x1),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
composition(join(x0,meet(x0,converse(x1))),meet(x1,x2)) = composition(join(x0,meet(x0,converse(x1))),meet(x2,x1)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c22,plain,
join(X3,meet(X3,X)) = join(X3,complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
meet(complement(X3),X) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c24,plain,
complement(meet(complement(X3),X)) = complement(meet(X,complement(X3))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c26,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c4]) ).
cnf(c28,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
join(complement(complement(X)),X3) = join(X3,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c30,plain,
join(X3,complement(complement(X))) = join(complement(complement(X)),X3),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
join(zero,join(X3,complement(complement(X)))) = join(zero,join(complement(complement(X)),X3)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c33,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c34,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c38,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c41,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c46,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c44,c45]) ).
cnf(c47,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c36,c46]) ).
cnf(c48,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
composition(converse(one),one) = converse(one),
inference(substitution,[status(thm)],[c40]) ).
cnf(c52,plain,
converse(one) = composition(converse(one),one),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
composition(converse(one),one) = one,
inference(substitution,[status(thm)],[c47]) ).
cnf(c54,plain,
converse(one) = one,
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
composition(one,X) = composition(converse(one),X),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c56,c47]) ).
cnf(c58,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,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(c63,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)],[c62]) ).
cnf(c64,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(c65,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c61,c67]) ).
cnf(c69,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c50,c68]) ).
cnf(c70,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
meet(X,X) = complement(complement(X)),
inference(transitivity,[status(thm)],[c32,c70]) ).
cnf(c72,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
join(complement(complement(X)),X3) = join(meet(X,X),X3),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
join(zero,join(complement(complement(X)),X3)) = join(zero,join(meet(X,X),X3)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,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(c76,plain,
join(zero,join(meet(X,X),X3)) = join(join(zero,meet(X,X)),X3),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c78,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c80,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
join(zero,complement(join(complement(X),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)],[c9]) ).
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(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c81,c88]) ).
cnf(c90,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c78,c89]) ).
cnf(c91,plain,
join(join(zero,meet(X,X)),X3) = join(X,X3),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c93,plain,
join(join(zero,meet(X,X)),X3) = join(X3,X),
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
join(zero,join(meet(X,X),X3)) = join(X3,X),
inference(transitivity,[status(thm)],[c76,c93]) ).
cnf(c95,plain,
join(zero,join(complement(complement(X)),X3)) = join(X3,X),
inference(transitivity,[status(thm)],[c74,c94]) ).
cnf(c96,plain,
join(zero,join(X3,complement(complement(X)))) = join(X3,X),
inference(transitivity,[status(thm)],[c31,c95]) ).
cnf(c97,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,X),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
join(zero,X) = join(zero,join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c17]) ).
cnf(c100,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c101,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c104,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c106,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c102,c107]) ).
cnf(c109,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c113,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c17]) ).
cnf(c115,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c113,c115]) ).
cnf(c117,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c111,c116]) ).
cnf(c118,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c121,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c123,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c87]) ).
cnf(c126,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c121,c126]) ).
cnf(c128,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c119,c128]) ).
cnf(c130,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c99,c129]) ).
cnf(c131,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c17]) ).
cnf(c134,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c136,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c138,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c140,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c143,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c146,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c144,c147]) ).
cnf(c149,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c141,c149]) ).
cnf(c151,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
converse(top) = join(complement(X),converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(complement(converse(complement(X)))))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c155,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c158,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c75]) ).
cnf(c161,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c162,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c4]) ).
cnf(c165,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c163,c164]) ).
cnf(c166,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c160,c165]) ).
cnf(c167,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c159,c166]) ).
cnf(c168,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c169,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c167]) ).
cnf(c171,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c173,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c174,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c172,c174]) ).
cnf(c176,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c171,c175]) ).
cnf(c177,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c169,c176]) ).
cnf(c178,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c167]) ).
cnf(c181,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c167]) ).
cnf(c182,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c177]) ).
cnf(c184,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c182,c183]) ).
cnf(c185,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c180,c184]) ).
cnf(c186,plain,
join(X3,top) = join(X,top),
inference(transitivity,[status(thm)],[c179,c185]) ).
cnf(c187,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
join(X4,join(X3,complement(X4))) = join(X,top),
inference(transitivity,[status(thm)],[c167,c187]) ).
cnf(c189,plain,
join(X4,join(complement(X4),X3)) = join(X,top),
inference(transitivity,[status(thm)],[c156,c188]) ).
cnf(c190,plain,
join(X3,join(complement(X3),converse(complement(converse(complement(X3)))))) = join(X,top),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = join(X4,top),
inference(substitution,[status(thm)],[c189]) ).
cnf(c192,plain,
join(X4,top) = join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = join(X3,complement(X3)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c194,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c195,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
join(X3,join(complement(X3),composition(converse(X),complement(composition(X,X3))))) = top,
inference(transitivity,[status(thm)],[c193,c195]) ).
cnf(c197,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c192,c196]) ).
cnf(c198,plain,
join(X,join(complement(X),converse(complement(converse(complement(X)))))) = top,
inference(transitivity,[status(thm)],[c190,c197]) ).
cnf(c199,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c153,c198]) ).
cnf(c200,plain,
top = join(X,converse(top)),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
converse(top) = converse(join(X,converse(top))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
converse(join(X,converse(top))) = join(converse(X),converse(converse(top))),
inference(substitution,[status(thm)],[c142]) ).
cnf(c203,plain,
converse(converse(top)) = top,
inference(substitution,[status(thm)],[c33]) ).
cnf(c204,plain,
join(converse(X),converse(converse(top))) = join(converse(X),top),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
join(converse(X),top) = top,
inference(substitution,[status(thm)],[c197]) ).
cnf(c206,plain,
join(converse(X),converse(converse(top))) = top,
inference(transitivity,[status(thm)],[c204,c205]) ).
cnf(c207,plain,
converse(join(X,converse(top))) = top,
inference(transitivity,[status(thm)],[c202,c206]) ).
cnf(c208,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c201,c207]) ).
cnf(c209,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
meet(X,top) = meet(X,converse(top)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
join(meet(X,top),complement(top)) = join(meet(X,converse(top)),complement(top)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
join(complement(X),converse(top)) = top,
inference(substitution,[status(thm)],[c199]) ).
cnf(c213,plain,
top = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
complement(top) = complement(join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
join(meet(X,converse(top)),complement(top)) = join(meet(X,converse(top)),complement(join(complement(X),converse(top)))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
join(meet(X,converse(top)),complement(join(complement(X),converse(top)))) = X,
inference(substitution,[status(thm)],[c87]) ).
cnf(c217,plain,
join(meet(X,converse(top)),complement(top)) = X,
inference(transitivity,[status(thm)],[c215,c216]) ).
cnf(c218,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c211,c217]) ).
cnf(c219,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c138,c218]) ).
cnf(c220,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c136,c219]) ).
cnf(c221,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c134,c220]) ).
cnf(c222,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c132,c222]) ).
cnf(c224,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c223]) ).
cnf(c225,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
join(zero,join(zero,complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c225,c127]) ).
cnf(c227,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c98,c226]) ).
cnf(c228,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c28,c227]) ).
cnf(c229,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c26,c228]) ).
cnf(c230,plain,
join(zero,meet(X3,complement(X))) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
meet(X3,complement(X)) = join(zero,meet(X3,complement(X))),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
complement(meet(X3,complement(X))) = complement(join(zero,meet(X3,complement(X)))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c234,plain,
join(X3,complement(X)) = join(complement(X),X3),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
complement(join(X3,complement(X))) = complement(join(complement(X),X3)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c17]) ).
cnf(c237,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c238,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c223]) ).
cnf(c239,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c241,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c240,c220]) ).
cnf(c242,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c239,c241]) ).
cnf(c243,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c237,c242]) ).
cnf(c244,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c236,c243]) ).
cnf(c245,plain,
X = meet(top,X),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
join(complement(X),X3) = join(complement(X),meet(top,X3)),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
complement(join(complement(X),X3)) = complement(join(complement(X),meet(top,X3))),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c249,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
meet(X4,join(complement(X3),complement(X))) = meet(X4,join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
meet(X4,join(complement(X),complement(X3))) = meet(join(complement(X),complement(X3)),X4),
inference(substitution,[status(thm)],[c17]) ).
cnf(c252,plain,
meet(join(complement(X),complement(X3)),X4) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c253,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c254,plain,
complement(join(complement(X),complement(X3))) = meet(X,X3),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
join(complement(join(complement(X),complement(X3))),complement(X4)) = join(meet(X,X3),complement(X4)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = complement(join(meet(X,X3),complement(X4))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
join(meet(X,X3),complement(X4)) = join(complement(X4),meet(X,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c258,plain,
complement(join(meet(X,X3),complement(X4))) = complement(join(complement(X4),meet(X,X3))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c260,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
join(complement(X4),meet(X,X3)) = join(complement(X4),meet(X3,X)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
complement(join(complement(X4),meet(X,X3))) = complement(join(complement(X4),meet(X3,X))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
complement(join(meet(X,X3),complement(X4))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c258,c262]) ).
cnf(c264,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c256,c263]) ).
cnf(c265,plain,
meet(join(complement(X),complement(X3)),X4) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c252,c264]) ).
cnf(c266,plain,
meet(X4,join(complement(X),complement(X3))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c251,c265]) ).
cnf(c267,plain,
meet(X4,join(complement(X3),complement(X))) = complement(join(complement(X4),meet(X3,X))),
inference(transitivity,[status(thm)],[c250,c266]) ).
cnf(c268,plain,
meet(X,join(complement(top),complement(X3))) = complement(join(complement(X),meet(top,X3))),
inference(substitution,[status(thm)],[c267]) ).
cnf(c269,plain,
complement(join(complement(X),meet(top,X3))) = meet(X,join(complement(top),complement(X3))),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
join(complement(top),complement(X)) = join(zero,complement(X)),
inference(congruence,[status(thm)],[c108]) ).
cnf(c271,plain,
meet(X,join(complement(top),complement(X3))) = meet(X,join(zero,complement(X3))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
meet(X,join(zero,complement(X3))) = meet(X,complement(X3)),
inference(congruence,[status(thm)],[c223]) ).
cnf(c273,plain,
meet(X,join(complement(top),complement(X3))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c271,c272]) ).
cnf(c274,plain,
complement(join(complement(X),meet(top,X3))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c269,c273]) ).
cnf(c275,plain,
complement(join(complement(X),X3)) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c247,c274]) ).
cnf(c276,plain,
complement(join(X3,complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c235,c275]) ).
cnf(c277,plain,
complement(join(X,complement(X3))) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c276]) ).
cnf(c278,plain,
meet(X3,complement(X)) = complement(join(X,complement(X3))),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
join(zero,meet(X3,complement(X))) = join(zero,complement(join(X,complement(X3)))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
complement(join(zero,meet(X3,complement(X)))) = complement(join(zero,complement(join(X,complement(X3))))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
complement(join(zero,complement(join(X,complement(X3))))) = meet(join(X,complement(X3)),top),
inference(substitution,[status(thm)],[c117]) ).
cnf(c282,plain,
meet(join(X,complement(X3)),top) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c243]) ).
cnf(c283,plain,
complement(join(zero,complement(join(X,complement(X3))))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c281,c282]) ).
cnf(c284,plain,
complement(join(zero,meet(X3,complement(X)))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c280,c283]) ).
cnf(c285,plain,
complement(meet(X3,complement(X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c232,c284]) ).
cnf(c286,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
complement(meet(complement(X3),X)) = join(X3,complement(X)),
inference(transitivity,[status(thm)],[c24,c286]) ).
cnf(c288,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = join(X3,complement(join(complement(X3),complement(X)))),
inference(substitution,[status(thm)],[c287]) ).
cnf(c289,plain,
join(X3,complement(join(complement(X3),complement(X)))) = complement(meet(complement(X3),join(complement(X3),complement(X)))),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c285]) ).
cnf(c291,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
meet(X3,join(X3,complement(X))) = meet(X3,complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c294,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
complement(join(complement(X3),X)) = complement(join(X,complement(X3))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
complement(join(X,complement(X3))) = meet(X3,complement(X)),
inference(substitution,[status(thm)],[c276]) ).
cnf(c297,plain,
complement(join(complement(X3),X)) = meet(X3,complement(X)),
inference(transitivity,[status(thm)],[c295,c296]) ).
cnf(c298,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = meet(X3,complement(meet(X,complement(X3)))),
inference(substitution,[status(thm)],[c297]) ).
cnf(c299,plain,
meet(X3,complement(meet(X,complement(X3)))) = complement(join(complement(X3),meet(X,complement(X3)))),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = complement(join(complement(X3),meet(X,complement(X3)))),
inference(substitution,[status(thm)],[c223]) ).
cnf(c301,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = join(zero,complement(join(complement(X3),meet(X,complement(X3))))),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
meet(X,complement(X3)) = meet(complement(X3),X),
inference(substitution,[status(thm)],[c17]) ).
cnf(c303,plain,
meet(X3,meet(X,complement(X3))) = meet(X3,meet(complement(X3),X)),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
meet(X3,meet(complement(X3),X)) = complement(join(complement(X3),complement(meet(complement(X3),X)))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c305,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c306,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
join(X3,complement(meet(X3,X))) = join(X3,complement(meet(X,X3))),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c309,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
join(zero,meet(join(complement(X),complement(X3)),join(complement(X),complement(X3)))) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c311,plain,
join(complement(X),complement(X3)) = join(zero,meet(join(complement(X),complement(X3)),join(complement(X),complement(X3)))),
inference(symmetry,[status(thm)],[c310]) ).
cnf(c312,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)],[c267]) ).
cnf(c313,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)],[c312]) ).
cnf(c314,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)],[c223]) ).
cnf(c315,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c316,plain,
complement(join(complement(X),complement(X3))) = meet(X,X3),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
join(complement(join(complement(X),complement(X3))),meet(X,X3)) = join(meet(X,X3),meet(X,X3)),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
complement(join(complement(join(complement(X),complement(X3))),meet(X,X3))) = complement(join(meet(X,X3),meet(X,X3))),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c223]) ).
cnf(c320,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c321,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c320,c127]) ).
cnf(c322,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c323,plain,
join(X,X) = join(X,complement(complement(X))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
join(complement(complement(X)),X) = join(X,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c325,plain,
join(X,complement(complement(X))) = join(complement(complement(X)),X),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(complement(complement(X)),X),
inference(substitution,[status(thm)],[c96]) ).
cnf(c327,plain,
join(complement(complement(X)),X) = join(zero,join(complement(complement(X)),complement(complement(X)))),
inference(symmetry,[status(thm)],[c326]) ).
cnf(c328,plain,
join(complement(complement(X)),complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c329,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c329,c127]) ).
cnf(c331,plain,
join(complement(complement(X)),X) = X,
inference(transitivity,[status(thm)],[c327,c330]) ).
cnf(c332,plain,
join(X,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c325,c331]) ).
cnf(c333,plain,
join(X,X) = X,
inference(transitivity,[status(thm)],[c323,c332]) ).
cnf(c334,plain,
join(meet(X,X3),meet(X,X3)) = meet(X,X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
complement(join(meet(X,X3),meet(X,X3))) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c337,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
complement(meet(X,X3)) = complement(meet(X3,X)),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
complement(join(meet(X,X3),meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c335,c338]) ).
cnf(c340,plain,
complement(join(complement(join(complement(X),complement(X3))),meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c318,c339]) ).
cnf(c341,plain,
join(zero,complement(join(complement(join(complement(X),complement(X3))),meet(X,X3)))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c314,c340]) ).
cnf(c342,plain,
join(zero,meet(join(complement(X),complement(X3)),join(complement(X),complement(X3)))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c313,c341]) ).
cnf(c343,plain,
join(complement(X),complement(X3)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c311,c342]) ).
cnf(c344,plain,
join(complement(X3),complement(X)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c309,c343]) ).
cnf(c345,plain,
join(complement(X),complement(X3)) = complement(meet(X,X3)),
inference(substitution,[status(thm)],[c344]) ).
cnf(c346,plain,
complement(meet(X,X3)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c345]) ).
cnf(c347,plain,
join(X3,complement(meet(X,X3))) = join(X3,join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
join(X3,join(complement(X),complement(X3))) = join(complement(X),top),
inference(substitution,[status(thm)],[c167]) ).
cnf(c349,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c197]) ).
cnf(c350,plain,
join(X3,join(complement(X),complement(X3))) = top,
inference(transitivity,[status(thm)],[c348,c349]) ).
cnf(c351,plain,
join(X3,complement(meet(X,X3))) = top,
inference(transitivity,[status(thm)],[c347,c350]) ).
cnf(c352,plain,
join(X3,complement(meet(X3,X))) = top,
inference(transitivity,[status(thm)],[c307,c351]) ).
cnf(c353,plain,
join(complement(X3),complement(meet(complement(X3),X))) = top,
inference(substitution,[status(thm)],[c352]) ).
cnf(c354,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = complement(top),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = zero,
inference(transitivity,[status(thm)],[c354,c108]) ).
cnf(c356,plain,
meet(X3,meet(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c304,c355]) ).
cnf(c357,plain,
meet(X3,meet(X,complement(X3))) = zero,
inference(transitivity,[status(thm)],[c303,c356]) ).
cnf(c358,plain,
zero = meet(X3,meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,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)],[c358]) ).
cnf(c360,plain,
join(meet(X3,meet(X,complement(X3))),complement(join(complement(X3),meet(X,complement(X3))))) = X3,
inference(substitution,[status(thm)],[c87]) ).
cnf(c361,plain,
join(zero,complement(join(complement(X3),meet(X,complement(X3))))) = X3,
inference(transitivity,[status(thm)],[c359,c360]) ).
cnf(c362,plain,
complement(join(complement(X3),meet(X,complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c301,c361]) ).
cnf(c363,plain,
meet(X3,complement(meet(X,complement(X3)))) = X3,
inference(transitivity,[status(thm)],[c299,c362]) ).
cnf(c364,plain,
meet(X3,join(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c292,c363]) ).
cnf(c365,plain,
meet(complement(X3),join(complement(X3),complement(X))) = complement(X3),
inference(substitution,[status(thm)],[c364]) ).
cnf(c366,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = complement(complement(X3)),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
complement(meet(complement(X3),join(complement(X3),complement(X)))) = X3,
inference(transitivity,[status(thm)],[c366,c321]) ).
cnf(c368,plain,
join(X3,complement(join(complement(X3),complement(X)))) = X3,
inference(transitivity,[status(thm)],[c289,c367]) ).
cnf(c369,plain,
join(X3,meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c22,c368]) ).
cnf(c370,plain,
join(x0,meet(x0,converse(x1))) = x0,
inference(substitution,[status(thm)],[c369]) ).
cnf(c371,plain,
composition(join(x0,meet(x0,converse(x1))),meet(x2,x1)) = composition(x0,meet(x2,x1)),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
meet(x2,x1) = meet(x1,x2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c373,plain,
composition(x0,meet(x2,x1)) = composition(x0,meet(x1,x2)),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
composition(join(x0,meet(x0,converse(x1))),meet(x2,x1)) = composition(x0,meet(x1,x2)),
inference(transitivity,[status(thm)],[c371,c373]) ).
cnf(c375,plain,
composition(join(x0,meet(x0,converse(x1))),meet(x1,x2)) = composition(x0,meet(x1,x2)),
inference(transitivity,[status(thm)],[c20,c374]) ).
cnf(c376,plain,
join(composition(x0,meet(x1,x2)),composition(meet(x0,converse(x1)),meet(x1,x2))) = composition(x0,meet(x1,x2)),
inference(transitivity,[status(thm)],[c8,c375]) ).
cnf(c377,plain,
join(composition(meet(x0,converse(x1)),meet(x1,x2)),composition(x0,meet(x1,x2))) = composition(x0,meet(x1,x2)),
inference(transitivity,[status(thm)],[c5,c376]) ).
cnf(c378,plain,
$false,
inference(resolution,[status(thm)],[c3,c377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:52:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 Command-line arguments: --no-flatten-goal
% 0.19/0.52
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52
% 0.19/0.54 % SZS output start CNFRefutation
% See solution above
% 1.29/0.67
% 1.29/0.67 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------