Twee---2.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : REL045-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n005.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 12:33:32 PM UTC 2026

% Result   : Unsatisfiable 21.13s 3.23s
% Output   : CNFRefutation 28.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  127
%            Number of leaves      :   14
% Syntax   : Number of clauses     :  926 ( 926 unt;   0 nHn;  57 RR)
%            Number of literals    :  926 ( 925 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   : 1495 ( 106 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
    join(sk1,composition(composition(sk1,converse(sk1)),sk1)) != composition(composition(sk1,converse(sk1)),sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).

cnf(c2,axiom,
    top = join(A,complement(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).

cnf(c3,plain,
    top = join(complement(X),complement(complement(X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c4,plain,
    complement(top) = complement(join(complement(X),complement(complement(X)))),
    inference(congruence,[status(thm)],[c3]) ).

cnf(c5,axiom,
    meet(A2,B) = complement(join(complement(A2),complement(B))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).

cnf(c6,plain,
    meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c7,plain,
    complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
    inference(symmetry,[status(thm)],[c6]) ).

cnf(c8,axiom,
    zero = meet(A2,complement(A2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).

cnf(c9,plain,
    zero = meet(X,complement(X)),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c10,plain,
    meet(X,complement(X)) = zero,
    inference(symmetry,[status(thm)],[c9]) ).

cnf(c11,plain,
    complement(join(complement(X),complement(complement(X)))) = zero,
    inference(transitivity,[status(thm)],[c7,c10]) ).

cnf(c12,plain,
    complement(top) = zero,
    inference(transitivity,[status(thm)],[c4,c11]) ).

cnf(c13,plain,
    zero = complement(top),
    inference(symmetry,[status(thm)],[c12]) ).

cnf(c14,plain,
    join(zero,complement(X)) = join(complement(top),complement(X)),
    inference(congruence,[status(thm)],[c13]) ).

cnf(c15,plain,
    complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
    inference(congruence,[status(thm)],[c14]) ).

cnf(c16,plain,
    meet(top,X) = complement(join(complement(top),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c17,plain,
    complement(join(complement(top),complement(X))) = meet(top,X),
    inference(symmetry,[status(thm)],[c16]) ).

cnf(c18,plain,
    meet(X2,X) = complement(join(complement(X2),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c19,axiom,
    join(A2,B2) = join(B2,A2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).

cnf(c20,plain,
    join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c21,plain,
    join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
    inference(symmetry,[status(thm)],[c20]) ).

cnf(c22,plain,
    complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
    inference(congruence,[status(thm)],[c21]) ).

cnf(c23,plain,
    meet(X2,X) = complement(join(complement(X2),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c24,plain,
    complement(join(complement(X2),complement(X))) = meet(X2,X),
    inference(symmetry,[status(thm)],[c23]) ).

cnf(c25,plain,
    complement(join(complement(X),complement(X2))) = meet(X2,X),
    inference(transitivity,[status(thm)],[c22,c24]) ).

cnf(c26,plain,
    meet(X,X2) = meet(X2,X),
    inference(transitivity,[status(thm)],[c18,c25]) ).

cnf(c27,plain,
    meet(X,top) = meet(top,X),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c28,plain,
    meet(top,X) = meet(X,top),
    inference(symmetry,[status(thm)],[c27]) ).

cnf(c29,plain,
    complement(join(complement(top),complement(X))) = meet(X,top),
    inference(transitivity,[status(thm)],[c17,c28]) ).

cnf(c30,plain,
    complement(join(zero,complement(X))) = meet(X,top),
    inference(transitivity,[status(thm)],[c15,c29]) ).

cnf(c31,plain,
    meet(X,top) = complement(join(zero,complement(X))),
    inference(symmetry,[status(thm)],[c30]) ).

cnf(c32,plain,
    meet(top,complement(X)) = meet(complement(X),top),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c33,plain,
    complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c34,plain,
    meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
    inference(symmetry,[status(thm)],[c33]) ).

cnf(c35,axiom,
    converse(converse(A2)) = A2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).

cnf(c36,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c37,plain,
    X = converse(converse(X)),
    inference(symmetry,[status(thm)],[c36]) ).

cnf(c38,plain,
    composition(converse(one),X) = composition(converse(one),converse(converse(X))),
    inference(congruence,[status(thm)],[c37]) ).

cnf(c39,axiom,
    converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).

cnf(c40,plain,
    converse(composition(X,one)) = composition(converse(one),converse(X)),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c41,plain,
    composition(converse(one),converse(X)) = converse(composition(X,one)),
    inference(symmetry,[status(thm)],[c40]) ).

cnf(c42,axiom,
    composition(A2,one) = A2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).

cnf(c43,plain,
    composition(X,one) = X,
    inference(substitution,[status(thm)],[c42]) ).

cnf(c44,plain,
    converse(composition(X,one)) = converse(X),
    inference(congruence,[status(thm)],[c43]) ).

cnf(c45,plain,
    composition(converse(one),converse(X)) = converse(X),
    inference(transitivity,[status(thm)],[c41,c44]) ).

cnf(c46,plain,
    composition(converse(one),converse(converse(X))) = converse(converse(X)),
    inference(substitution,[status(thm)],[c45]) ).

cnf(c47,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c48,plain,
    composition(converse(one),converse(converse(X))) = X,
    inference(transitivity,[status(thm)],[c46,c47]) ).

cnf(c49,plain,
    composition(converse(one),X) = X,
    inference(transitivity,[status(thm)],[c38,c48]) ).

cnf(c50,plain,
    composition(converse(one),complement(X)) = complement(X),
    inference(substitution,[status(thm)],[c49]) ).

cnf(c51,plain,
    complement(X) = composition(converse(one),complement(X)),
    inference(symmetry,[status(thm)],[c50]) ).

cnf(c52,plain,
    join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
    inference(congruence,[status(thm)],[c51]) ).

cnf(c53,plain,
    composition(converse(one),one) = converse(one),
    inference(substitution,[status(thm)],[c42]) ).

cnf(c54,plain,
    converse(one) = composition(converse(one),one),
    inference(symmetry,[status(thm)],[c53]) ).

cnf(c55,plain,
    composition(converse(one),one) = one,
    inference(substitution,[status(thm)],[c49]) ).

cnf(c56,plain,
    converse(one) = one,
    inference(transitivity,[status(thm)],[c54,c55]) ).

cnf(c57,plain,
    one = converse(one),
    inference(symmetry,[status(thm)],[c56]) ).

cnf(c58,plain,
    composition(one,X) = composition(converse(one),X),
    inference(congruence,[status(thm)],[c57]) ).

cnf(c59,plain,
    composition(one,X) = X,
    inference(transitivity,[status(thm)],[c58,c49]) ).

cnf(c60,plain,
    X = composition(one,X),
    inference(symmetry,[status(thm)],[c59]) ).

cnf(c61,plain,
    complement(X) = complement(composition(one,X)),
    inference(congruence,[status(thm)],[c60]) ).

cnf(c62,plain,
    composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
    inference(congruence,[status(thm)],[c61]) ).

cnf(c63,plain,
    join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
    inference(congruence,[status(thm)],[c62]) ).

cnf(c64,plain,
    join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = join(complement(X2),composition(converse(X),complement(composition(X,X2)))),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c65,plain,
    join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = join(composition(converse(X),complement(composition(X,X2))),complement(X2)),
    inference(symmetry,[status(thm)],[c64]) ).

cnf(c66,axiom,
    join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).

cnf(c67,plain,
    join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
    inference(substitution,[status(thm)],[c66]) ).

cnf(c68,plain,
    join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
    inference(transitivity,[status(thm)],[c65,c67]) ).

cnf(c69,plain,
    join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
    inference(substitution,[status(thm)],[c68]) ).

cnf(c70,plain,
    join(complement(X),composition(converse(one),complement(X))) = complement(X),
    inference(transitivity,[status(thm)],[c63,c69]) ).

cnf(c71,plain,
    join(complement(X),complement(X)) = complement(X),
    inference(transitivity,[status(thm)],[c52,c70]) ).

cnf(c72,plain,
    complement(X) = join(complement(X),complement(X)),
    inference(symmetry,[status(thm)],[c71]) ).

cnf(c73,plain,
    complement(complement(X)) = complement(join(complement(X),complement(X))),
    inference(congruence,[status(thm)],[c72]) ).

cnf(c74,plain,
    meet(X,X) = complement(join(complement(X),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c75,plain,
    complement(join(complement(X),complement(X))) = meet(X,X),
    inference(symmetry,[status(thm)],[c74]) ).

cnf(c76,plain,
    complement(complement(X)) = meet(X,X),
    inference(transitivity,[status(thm)],[c73,c75]) ).

cnf(c77,plain,
    join(zero,complement(complement(X))) = join(zero,meet(X,X)),
    inference(congruence,[status(thm)],[c76]) ).

cnf(c78,plain,
    complement(join(zero,complement(complement(X)))) = complement(join(zero,meet(X,X))),
    inference(congruence,[status(thm)],[c77]) ).

cnf(c79,plain,
    meet(X,X) = complement(join(complement(X),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c80,plain,
    join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
    inference(congruence,[status(thm)],[c79]) ).

cnf(c81,plain,
    zero = meet(X,complement(X)),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c82,plain,
    join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
    inference(congruence,[status(thm)],[c81]) ).

cnf(c83,plain,
    meet(X2,X) = complement(join(complement(X2),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c84,plain,
    join(meet(X2,X),complement(join(complement(X2),X))) = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
    inference(congruence,[status(thm)],[c83]) ).

cnf(c85,axiom,
    A2 = join(complement(join(complement(A2),complement(B2))),complement(join(complement(A2),B2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).

cnf(c86,plain,
    X2 = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
    inference(substitution,[status(thm)],[c85]) ).

cnf(c87,plain,
    join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))) = X2,
    inference(symmetry,[status(thm)],[c86]) ).

cnf(c88,plain,
    join(meet(X2,X),complement(join(complement(X2),X))) = X2,
    inference(transitivity,[status(thm)],[c84,c87]) ).

cnf(c89,plain,
    join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
    inference(substitution,[status(thm)],[c88]) ).

cnf(c90,plain,
    join(zero,complement(join(complement(X),complement(X)))) = X,
    inference(transitivity,[status(thm)],[c82,c89]) ).

cnf(c91,plain,
    join(zero,meet(X,X)) = X,
    inference(transitivity,[status(thm)],[c80,c90]) ).

cnf(c92,plain,
    complement(join(zero,meet(X,X))) = complement(X),
    inference(congruence,[status(thm)],[c91]) ).

cnf(c93,plain,
    complement(join(zero,complement(complement(X)))) = complement(X),
    inference(transitivity,[status(thm)],[c78,c92]) ).

cnf(c94,plain,
    meet(complement(X),top) = complement(X),
    inference(transitivity,[status(thm)],[c34,c93]) ).

cnf(c95,plain,
    meet(top,complement(X)) = complement(X),
    inference(transitivity,[status(thm)],[c32,c94]) ).

cnf(c96,plain,
    complement(X) = meet(top,complement(X)),
    inference(symmetry,[status(thm)],[c95]) ).

cnf(c97,plain,
    join(zero,complement(X)) = join(zero,meet(top,complement(X))),
    inference(congruence,[status(thm)],[c96]) ).

cnf(c98,plain,
    meet(top,X) = meet(X,top),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c99,plain,
    join(zero,meet(top,X)) = join(zero,meet(X,top)),
    inference(congruence,[status(thm)],[c98]) ).

cnf(c100,plain,
    join(meet(X,top),zero) = join(zero,meet(X,top)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c101,plain,
    join(zero,meet(X,top)) = join(meet(X,top),zero),
    inference(symmetry,[status(thm)],[c100]) ).

cnf(c102,plain,
    zero = complement(top),
    inference(symmetry,[status(thm)],[c12]) ).

cnf(c103,plain,
    join(meet(X,top),zero) = join(meet(X,top),complement(top)),
    inference(congruence,[status(thm)],[c102]) ).

cnf(c104,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c105,plain,
    X = converse(converse(X)),
    inference(symmetry,[status(thm)],[c104]) ).

cnf(c106,plain,
    join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
    inference(congruence,[status(thm)],[c105]) ).

cnf(c107,axiom,
    converse(join(A2,B2)) = join(converse(A2),converse(B2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).

cnf(c108,plain,
    converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c109,plain,
    join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
    inference(symmetry,[status(thm)],[c108]) ).

cnf(c110,plain,
    top = join(X,complement(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c111,plain,
    join(X,complement(X)) = top,
    inference(symmetry,[status(thm)],[c110]) ).

cnf(c112,plain,
    converse(join(X,complement(X))) = converse(top),
    inference(congruence,[status(thm)],[c111]) ).

cnf(c113,plain,
    join(converse(X),converse(complement(X))) = converse(top),
    inference(transitivity,[status(thm)],[c109,c112]) ).

cnf(c114,plain,
    join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
    inference(substitution,[status(thm)],[c113]) ).

cnf(c115,plain,
    join(X,converse(complement(converse(X)))) = converse(top),
    inference(transitivity,[status(thm)],[c106,c114]) ).

cnf(c116,plain,
    join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
    inference(substitution,[status(thm)],[c115]) ).

cnf(c117,plain,
    converse(top) = join(complement(X),converse(complement(converse(complement(X))))),
    inference(symmetry,[status(thm)],[c116]) ).

cnf(c118,plain,
    join(X,converse(top)) = join(X,join(complement(X),converse(complement(converse(complement(X)))))),
    inference(congruence,[status(thm)],[c117]) ).

cnf(c119,plain,
    join(X,complement(X2)) = join(complement(X2),X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c120,plain,
    join(complement(X2),X) = join(X,complement(X2)),
    inference(symmetry,[status(thm)],[c119]) ).

cnf(c121,plain,
    join(X2,join(complement(X2),X)) = join(X2,join(X,complement(X2))),
    inference(congruence,[status(thm)],[c120]) ).

cnf(c122,plain,
    join(complement(X2),X) = join(X,complement(X2)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c123,plain,
    join(X,complement(X2)) = join(complement(X2),X),
    inference(symmetry,[status(thm)],[c122]) ).

cnf(c124,plain,
    join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
    inference(congruence,[status(thm)],[c123]) ).

cnf(c125,axiom,
    join(A2,join(B2,C)) = join(join(A2,B2),C),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).

cnf(c126,plain,
    join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
    inference(substitution,[status(thm)],[c125]) ).

cnf(c127,plain,
    top = join(X,complement(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c128,plain,
    join(X,complement(X)) = top,
    inference(symmetry,[status(thm)],[c127]) ).

cnf(c129,plain,
    join(join(X2,complement(X2)),X) = join(top,X),
    inference(congruence,[status(thm)],[c128]) ).

cnf(c130,plain,
    join(top,X) = join(X,top),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c131,plain,
    join(join(X2,complement(X2)),X) = join(X,top),
    inference(transitivity,[status(thm)],[c129,c130]) ).

cnf(c132,plain,
    join(X2,join(complement(X2),X)) = join(X,top),
    inference(transitivity,[status(thm)],[c126,c131]) ).

cnf(c133,plain,
    join(X2,join(X,complement(X2))) = join(X,top),
    inference(transitivity,[status(thm)],[c124,c132]) ).

cnf(c134,plain,
    join(complement(X),top) = join(top,complement(X)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c135,plain,
    join(top,complement(X)) = join(complement(X),top),
    inference(symmetry,[status(thm)],[c134]) ).

cnf(c136,plain,
    join(X,join(complement(X),complement(X))) = join(complement(X),top),
    inference(substitution,[status(thm)],[c133]) ).

cnf(c137,plain,
    join(complement(X),top) = join(X,join(complement(X),complement(X))),
    inference(symmetry,[status(thm)],[c136]) ).

cnf(c138,plain,
    join(X,join(complement(X),complement(X))) = join(X,complement(X)),
    inference(congruence,[status(thm)],[c71]) ).

cnf(c139,plain,
    top = join(X,complement(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c140,plain,
    join(X,complement(X)) = top,
    inference(symmetry,[status(thm)],[c139]) ).

cnf(c141,plain,
    join(X,join(complement(X),complement(X))) = top,
    inference(transitivity,[status(thm)],[c138,c140]) ).

cnf(c142,plain,
    join(complement(X),top) = top,
    inference(transitivity,[status(thm)],[c137,c141]) ).

cnf(c143,plain,
    join(top,complement(X)) = top,
    inference(transitivity,[status(thm)],[c135,c142]) ).

cnf(c144,plain,
    top = join(top,complement(X)),
    inference(symmetry,[status(thm)],[c143]) ).

cnf(c145,plain,
    join(X,top) = join(X,join(top,complement(X))),
    inference(congruence,[status(thm)],[c144]) ).

cnf(c146,plain,
    join(X,join(top,complement(X))) = join(top,top),
    inference(substitution,[status(thm)],[c133]) ).

cnf(c147,plain,
    join(X,join(top,complement(X))) = join(top,top),
    inference(substitution,[status(thm)],[c133]) ).

cnf(c148,plain,
    join(top,top) = join(X,join(top,complement(X))),
    inference(symmetry,[status(thm)],[c147]) ).

cnf(c149,plain,
    join(X,join(top,complement(X))) = join(X,top),
    inference(congruence,[status(thm)],[c143]) ).

cnf(c150,plain,
    join(top,top) = join(X,top),
    inference(transitivity,[status(thm)],[c148,c149]) ).

cnf(c151,plain,
    join(X,join(top,complement(X))) = join(X2,top),
    inference(transitivity,[status(thm)],[c146,c150]) ).

cnf(c152,plain,
    join(X2,top) = join(X,top),
    inference(transitivity,[status(thm)],[c145,c151]) ).

cnf(c153,plain,
    join(X2,top) = join(X,top),
    inference(symmetry,[status(thm)],[c152]) ).

cnf(c154,plain,
    join(X3,join(X2,complement(X3))) = join(X,top),
    inference(transitivity,[status(thm)],[c133,c153]) ).

cnf(c155,plain,
    join(X3,join(complement(X3),X2)) = join(X,top),
    inference(transitivity,[status(thm)],[c121,c154]) ).

cnf(c156,plain,
    join(X2,join(complement(X2),converse(complement(converse(complement(X2)))))) = join(X,top),
    inference(substitution,[status(thm)],[c155]) ).

cnf(c157,plain,
    join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = join(X3,top),
    inference(substitution,[status(thm)],[c155]) ).

cnf(c158,plain,
    join(X3,top) = join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))),
    inference(symmetry,[status(thm)],[c157]) ).

cnf(c159,plain,
    join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = join(X2,complement(X2)),
    inference(congruence,[status(thm)],[c68]) ).

cnf(c160,plain,
    top = join(X,complement(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c161,plain,
    join(X,complement(X)) = top,
    inference(symmetry,[status(thm)],[c160]) ).

cnf(c162,plain,
    join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = top,
    inference(transitivity,[status(thm)],[c159,c161]) ).

cnf(c163,plain,
    join(X,top) = top,
    inference(transitivity,[status(thm)],[c158,c162]) ).

cnf(c164,plain,
    join(X,join(complement(X),converse(complement(converse(complement(X)))))) = top,
    inference(transitivity,[status(thm)],[c156,c163]) ).

cnf(c165,plain,
    join(X,converse(top)) = top,
    inference(transitivity,[status(thm)],[c118,c164]) ).

cnf(c166,plain,
    top = join(X,converse(top)),
    inference(symmetry,[status(thm)],[c165]) ).

cnf(c167,plain,
    converse(top) = converse(join(X,converse(top))),
    inference(congruence,[status(thm)],[c166]) ).

cnf(c168,plain,
    converse(join(X,converse(top))) = join(converse(X),converse(converse(top))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c169,plain,
    converse(converse(top)) = top,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c170,plain,
    join(converse(X),converse(converse(top))) = join(converse(X),top),
    inference(congruence,[status(thm)],[c169]) ).

cnf(c171,plain,
    join(converse(X),top) = top,
    inference(substitution,[status(thm)],[c163]) ).

cnf(c172,plain,
    join(converse(X),converse(converse(top))) = top,
    inference(transitivity,[status(thm)],[c170,c171]) ).

cnf(c173,plain,
    converse(join(X,converse(top))) = top,
    inference(transitivity,[status(thm)],[c168,c172]) ).

cnf(c174,plain,
    converse(top) = top,
    inference(transitivity,[status(thm)],[c167,c173]) ).

cnf(c175,plain,
    top = converse(top),
    inference(symmetry,[status(thm)],[c174]) ).

cnf(c176,plain,
    meet(X,top) = meet(X,converse(top)),
    inference(congruence,[status(thm)],[c175]) ).

cnf(c177,plain,
    join(meet(X,top),complement(top)) = join(meet(X,converse(top)),complement(top)),
    inference(congruence,[status(thm)],[c176]) ).

cnf(c178,plain,
    join(complement(X),converse(top)) = top,
    inference(substitution,[status(thm)],[c165]) ).

cnf(c179,plain,
    top = join(complement(X),converse(top)),
    inference(symmetry,[status(thm)],[c178]) ).

cnf(c180,plain,
    complement(top) = complement(join(complement(X),converse(top))),
    inference(congruence,[status(thm)],[c179]) ).

cnf(c181,plain,
    join(meet(X,converse(top)),complement(top)) = join(meet(X,converse(top)),complement(join(complement(X),converse(top)))),
    inference(congruence,[status(thm)],[c180]) ).

cnf(c182,plain,
    join(meet(X,converse(top)),complement(join(complement(X),converse(top)))) = X,
    inference(substitution,[status(thm)],[c88]) ).

cnf(c183,plain,
    join(meet(X,converse(top)),complement(top)) = X,
    inference(transitivity,[status(thm)],[c181,c182]) ).

cnf(c184,plain,
    join(meet(X,top),complement(top)) = X,
    inference(transitivity,[status(thm)],[c177,c183]) ).

cnf(c185,plain,
    join(meet(X,top),zero) = X,
    inference(transitivity,[status(thm)],[c103,c184]) ).

cnf(c186,plain,
    join(zero,meet(X,top)) = X,
    inference(transitivity,[status(thm)],[c101,c185]) ).

cnf(c187,plain,
    join(zero,meet(top,X)) = X,
    inference(transitivity,[status(thm)],[c99,c186]) ).

cnf(c188,plain,
    join(zero,meet(top,complement(X))) = complement(X),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c189,plain,
    join(zero,complement(X)) = complement(X),
    inference(transitivity,[status(thm)],[c97,c188]) ).

cnf(c190,plain,
    join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
    inference(substitution,[status(thm)],[c189]) ).

cnf(c191,plain,
    complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
    inference(symmetry,[status(thm)],[c190]) ).

cnf(c192,plain,
    join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
    inference(congruence,[status(thm)],[c30]) ).

cnf(c193,plain,
    join(zero,complement(join(zero,complement(X)))) = X,
    inference(transitivity,[status(thm)],[c192,c186]) ).

cnf(c194,plain,
    complement(join(zero,complement(X))) = X,
    inference(transitivity,[status(thm)],[c191,c193]) ).

cnf(c195,plain,
    meet(X,top) = X,
    inference(transitivity,[status(thm)],[c31,c194]) ).

cnf(c196,plain,
    meet(join(X,composition(composition(X,converse(X)),X)),top) = join(X,composition(composition(X,converse(X)),X)),
    inference(substitution,[status(thm)],[c195]) ).

cnf(c197,plain,
    join(X,composition(composition(X,converse(X)),X)) = meet(join(X,composition(composition(X,converse(X)),X)),top),
    inference(symmetry,[status(thm)],[c196]) ).

cnf(c198,plain,
    meet(X2,complement(X)) = meet(complement(X),X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c199,plain,
    complement(meet(X2,complement(X))) = complement(meet(complement(X),X2)),
    inference(congruence,[status(thm)],[c198]) ).

cnf(c200,plain,
    complement(X) = join(zero,complement(X)),
    inference(symmetry,[status(thm)],[c189]) ).

cnf(c201,plain,
    meet(complement(X),X2) = meet(join(zero,complement(X)),X2),
    inference(congruence,[status(thm)],[c200]) ).

cnf(c202,plain,
    complement(meet(complement(X),X2)) = complement(meet(join(zero,complement(X)),X2)),
    inference(congruence,[status(thm)],[c201]) ).

cnf(c203,plain,
    join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c204,plain,
    join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
    inference(symmetry,[status(thm)],[c203]) ).

cnf(c205,plain,
    meet(top,X) = meet(X,top),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c206,plain,
    meet(top,X) = X,
    inference(transitivity,[status(thm)],[c205,c195]) ).

cnf(c207,plain,
    meet(top,join(complement(X),complement(X2))) = join(complement(X),complement(X2)),
    inference(substitution,[status(thm)],[c206]) ).

cnf(c208,plain,
    join(complement(X),complement(X2)) = meet(top,join(complement(X),complement(X2))),
    inference(symmetry,[status(thm)],[c207]) ).

cnf(c209,plain,
    meet(X2,X) = meet(X,X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c210,plain,
    join(complement(X3),meet(X2,X)) = join(complement(X3),meet(X,X2)),
    inference(congruence,[status(thm)],[c209]) ).

cnf(c211,plain,
    complement(join(complement(X3),meet(X2,X))) = complement(join(complement(X3),meet(X,X2))),
    inference(congruence,[status(thm)],[c210]) ).

cnf(c212,plain,
    join(meet(X,X2),complement(X3)) = join(complement(X3),meet(X,X2)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c213,plain,
    join(complement(X3),meet(X,X2)) = join(meet(X,X2),complement(X3)),
    inference(symmetry,[status(thm)],[c212]) ).

cnf(c214,plain,
    complement(join(complement(X3),meet(X,X2))) = complement(join(meet(X,X2),complement(X3))),
    inference(congruence,[status(thm)],[c213]) ).

cnf(c215,plain,
    meet(X,X2) = complement(join(complement(X),complement(X2))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c216,plain,
    join(meet(X,X2),complement(X3)) = join(complement(join(complement(X),complement(X2))),complement(X3)),
    inference(congruence,[status(thm)],[c215]) ).

cnf(c217,plain,
    complement(join(meet(X,X2),complement(X3))) = complement(join(complement(join(complement(X),complement(X2))),complement(X3))),
    inference(congruence,[status(thm)],[c216]) ).

cnf(c218,plain,
    meet(join(complement(X),complement(X2)),X3) = complement(join(complement(join(complement(X),complement(X2))),complement(X3))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c219,plain,
    complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = meet(join(complement(X),complement(X2)),X3),
    inference(symmetry,[status(thm)],[c218]) ).

cnf(c220,plain,
    meet(X3,join(complement(X),complement(X2))) = meet(join(complement(X),complement(X2)),X3),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c221,plain,
    meet(join(complement(X),complement(X2)),X3) = meet(X3,join(complement(X),complement(X2))),
    inference(symmetry,[status(thm)],[c220]) ).

cnf(c222,plain,
    join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c223,plain,
    meet(X3,join(complement(X),complement(X2))) = meet(X3,join(complement(X2),complement(X))),
    inference(congruence,[status(thm)],[c222]) ).

cnf(c224,plain,
    meet(join(complement(X),complement(X2)),X3) = meet(X3,join(complement(X2),complement(X))),
    inference(transitivity,[status(thm)],[c221,c223]) ).

cnf(c225,plain,
    complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = meet(X3,join(complement(X2),complement(X))),
    inference(transitivity,[status(thm)],[c219,c224]) ).

cnf(c226,plain,
    complement(join(meet(X,X2),complement(X3))) = meet(X3,join(complement(X2),complement(X))),
    inference(transitivity,[status(thm)],[c217,c225]) ).

cnf(c227,plain,
    complement(join(complement(X3),meet(X,X2))) = meet(X3,join(complement(X2),complement(X))),
    inference(transitivity,[status(thm)],[c214,c226]) ).

cnf(c228,plain,
    complement(join(complement(X3),meet(X2,X))) = meet(X3,join(complement(X2),complement(X))),
    inference(transitivity,[status(thm)],[c211,c227]) ).

cnf(c229,plain,
    complement(join(complement(top),meet(X,X2))) = meet(top,join(complement(X),complement(X2))),
    inference(substitution,[status(thm)],[c228]) ).

cnf(c230,plain,
    meet(top,join(complement(X),complement(X2))) = complement(join(complement(top),meet(X,X2))),
    inference(symmetry,[status(thm)],[c229]) ).

cnf(c231,plain,
    join(complement(top),meet(X,X2)) = join(zero,meet(X,X2)),
    inference(congruence,[status(thm)],[c12]) ).

cnf(c232,plain,
    complement(join(complement(top),meet(X,X2))) = complement(join(zero,meet(X,X2))),
    inference(congruence,[status(thm)],[c231]) ).

cnf(c233,plain,
    join(X,zero) = join(zero,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c234,plain,
    join(zero,X) = join(X,zero),
    inference(symmetry,[status(thm)],[c233]) ).

cnf(c235,plain,
    zero = complement(top),
    inference(symmetry,[status(thm)],[c12]) ).

cnf(c236,plain,
    join(X,zero) = join(X,complement(top)),
    inference(congruence,[status(thm)],[c235]) ).

cnf(c237,plain,
    join(complement(X),top) = top,
    inference(substitution,[status(thm)],[c163]) ).

cnf(c238,plain,
    top = join(complement(X),top),
    inference(symmetry,[status(thm)],[c237]) ).

cnf(c239,plain,
    complement(top) = complement(join(complement(X),top)),
    inference(congruence,[status(thm)],[c238]) ).

cnf(c240,plain,
    join(X,complement(top)) = join(X,complement(join(complement(X),top))),
    inference(congruence,[status(thm)],[c239]) ).

cnf(c241,plain,
    X = meet(X,top),
    inference(symmetry,[status(thm)],[c195]) ).

cnf(c242,plain,
    join(X,complement(join(complement(X),top))) = join(meet(X,top),complement(join(complement(X),top))),
    inference(congruence,[status(thm)],[c241]) ).

cnf(c243,plain,
    join(meet(X,top),complement(join(complement(X),top))) = X,
    inference(substitution,[status(thm)],[c88]) ).

cnf(c244,plain,
    join(X,complement(join(complement(X),top))) = X,
    inference(transitivity,[status(thm)],[c242,c243]) ).

cnf(c245,plain,
    join(X,complement(top)) = X,
    inference(transitivity,[status(thm)],[c240,c244]) ).

cnf(c246,plain,
    join(X,zero) = X,
    inference(transitivity,[status(thm)],[c236,c245]) ).

cnf(c247,plain,
    join(zero,X) = X,
    inference(transitivity,[status(thm)],[c234,c246]) ).

cnf(c248,plain,
    join(zero,meet(X,X2)) = meet(X,X2),
    inference(substitution,[status(thm)],[c247]) ).

cnf(c249,plain,
    complement(join(zero,meet(X,X2))) = complement(meet(X,X2)),
    inference(congruence,[status(thm)],[c248]) ).

cnf(c250,plain,
    meet(X2,X) = meet(X,X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c251,plain,
    meet(X,X2) = meet(X2,X),
    inference(symmetry,[status(thm)],[c250]) ).

cnf(c252,plain,
    complement(meet(X,X2)) = complement(meet(X2,X)),
    inference(congruence,[status(thm)],[c251]) ).

cnf(c253,plain,
    complement(join(zero,meet(X,X2))) = complement(meet(X2,X)),
    inference(transitivity,[status(thm)],[c249,c252]) ).

cnf(c254,plain,
    complement(join(complement(top),meet(X,X2))) = complement(meet(X2,X)),
    inference(transitivity,[status(thm)],[c232,c253]) ).

cnf(c255,plain,
    meet(top,join(complement(X),complement(X2))) = complement(meet(X2,X)),
    inference(transitivity,[status(thm)],[c230,c254]) ).

cnf(c256,plain,
    join(complement(X),complement(X2)) = complement(meet(X2,X)),
    inference(transitivity,[status(thm)],[c208,c255]) ).

cnf(c257,plain,
    join(complement(X2),complement(X)) = complement(meet(X2,X)),
    inference(transitivity,[status(thm)],[c204,c256]) ).

cnf(c258,plain,
    join(complement(join(zero,complement(X))),complement(X2)) = complement(meet(join(zero,complement(X)),X2)),
    inference(substitution,[status(thm)],[c257]) ).

cnf(c259,plain,
    complement(meet(join(zero,complement(X)),X2)) = join(complement(join(zero,complement(X))),complement(X2)),
    inference(symmetry,[status(thm)],[c258]) ).

cnf(c260,plain,
    join(complement(join(zero,complement(X))),complement(X2)) = join(meet(X,top),complement(X2)),
    inference(congruence,[status(thm)],[c30]) ).

cnf(c261,plain,
    join(meet(X,top),complement(X2)) = join(X,complement(X2)),
    inference(congruence,[status(thm)],[c195]) ).

cnf(c262,plain,
    join(complement(join(zero,complement(X))),complement(X2)) = join(X,complement(X2)),
    inference(transitivity,[status(thm)],[c260,c261]) ).

cnf(c263,plain,
    complement(meet(join(zero,complement(X)),X2)) = join(X,complement(X2)),
    inference(transitivity,[status(thm)],[c259,c262]) ).

cnf(c264,plain,
    complement(meet(complement(X),X2)) = join(X,complement(X2)),
    inference(transitivity,[status(thm)],[c202,c263]) ).

cnf(c265,plain,
    complement(meet(X2,complement(X))) = join(X,complement(X2)),
    inference(transitivity,[status(thm)],[c199,c264]) ).

cnf(c266,plain,
    complement(meet(join(X,X2),complement(X2))) = join(X2,complement(join(X,X2))),
    inference(substitution,[status(thm)],[c265]) ).

cnf(c267,plain,
    join(X2,complement(join(X,X2))) = complement(meet(join(X,X2),complement(X2))),
    inference(symmetry,[status(thm)],[c266]) ).

cnf(c268,plain,
    meet(join(X2,X),complement(X)) = meet(complement(X),join(X2,X)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c269,plain,
    join(X2,X) = join(X,X2),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c270,plain,
    meet(complement(X),join(X2,X)) = meet(complement(X),join(X,X2)),
    inference(congruence,[status(thm)],[c269]) ).

cnf(c271,plain,
    join(X,X2) = join(X2,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c272,plain,
    join(X2,X) = join(X,X2),
    inference(symmetry,[status(thm)],[c271]) ).

cnf(c273,plain,
    meet(complement(X2),join(X2,X)) = meet(complement(X2),join(X,X2)),
    inference(congruence,[status(thm)],[c272]) ).

cnf(c274,plain,
    X = meet(X,top),
    inference(symmetry,[status(thm)],[c195]) ).

cnf(c275,plain,
    join(X,X2) = join(X,meet(X2,top)),
    inference(congruence,[status(thm)],[c274]) ).

cnf(c276,plain,
    meet(complement(X2),join(X,X2)) = meet(complement(X2),join(X,meet(X2,top))),
    inference(congruence,[status(thm)],[c275]) ).

cnf(c277,plain,
    complement(X) = join(zero,complement(X)),
    inference(symmetry,[status(thm)],[c189]) ).

cnf(c278,plain,
    meet(complement(X2),join(X,meet(X2,top))) = meet(join(zero,complement(X2)),join(X,meet(X2,top))),
    inference(congruence,[status(thm)],[c277]) ).

cnf(c279,plain,
    meet(X,top) = complement(join(zero,complement(X))),
    inference(symmetry,[status(thm)],[c30]) ).

cnf(c280,plain,
    join(X,meet(X2,top)) = join(X,complement(join(zero,complement(X2)))),
    inference(congruence,[status(thm)],[c279]) ).

cnf(c281,plain,
    meet(join(zero,complement(X2)),join(X,meet(X2,top))) = meet(join(zero,complement(X2)),join(X,complement(join(zero,complement(X2))))),
    inference(congruence,[status(thm)],[c280]) ).

cnf(c282,plain,
    meet(complement(X2),X) = meet(X,complement(X2)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c283,plain,
    complement(meet(complement(X2),X)) = complement(meet(X,complement(X2))),
    inference(congruence,[status(thm)],[c282]) ).

cnf(c284,plain,
    complement(meet(X,complement(X2))) = join(X2,complement(X)),
    inference(substitution,[status(thm)],[c265]) ).

cnf(c285,plain,
    complement(meet(complement(X2),X)) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c283,c284]) ).

cnf(c286,plain,
    complement(meet(complement(X),X2)) = join(X,complement(X2)),
    inference(substitution,[status(thm)],[c285]) ).

cnf(c287,plain,
    join(X,complement(X2)) = complement(meet(complement(X),X2)),
    inference(symmetry,[status(thm)],[c286]) ).

cnf(c288,plain,
    meet(X2,join(X,complement(X2))) = meet(X2,complement(meet(complement(X),X2))),
    inference(congruence,[status(thm)],[c287]) ).

cnf(c289,plain,
    meet(complement(X),X2) = meet(X2,complement(X)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c290,plain,
    join(meet(X2,X),meet(complement(X),X2)) = join(meet(X2,X),meet(X2,complement(X))),
    inference(congruence,[status(thm)],[c289]) ).

cnf(c291,plain,
    join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,X),meet(X2,complement(X))),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c292,plain,
    join(meet(X2,X),meet(X2,complement(X))) = join(meet(X2,complement(X)),meet(X2,X)),
    inference(symmetry,[status(thm)],[c291]) ).

cnf(c293,plain,
    meet(X2,X) = complement(join(complement(X2),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c294,plain,
    join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))),
    inference(congruence,[status(thm)],[c293]) ).

cnf(c295,plain,
    join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))) = X2,
    inference(substitution,[status(thm)],[c88]) ).

cnf(c296,plain,
    join(meet(X2,complement(X)),meet(X2,X)) = X2,
    inference(transitivity,[status(thm)],[c294,c295]) ).

cnf(c297,plain,
    join(meet(X2,X),meet(X2,complement(X))) = X2,
    inference(transitivity,[status(thm)],[c292,c296]) ).

cnf(c298,plain,
    join(meet(X2,X),meet(complement(X),X2)) = X2,
    inference(transitivity,[status(thm)],[c290,c297]) ).

cnf(c299,plain,
    join(meet(meet(X2,complement(meet(complement(X),X2))),X),meet(complement(X),meet(X2,complement(meet(complement(X),X2))))) = meet(X2,complement(meet(complement(X),X2))),
    inference(substitution,[status(thm)],[c298]) ).

cnf(c300,plain,
    meet(X2,complement(meet(complement(X),X2))) = join(meet(meet(X2,complement(meet(complement(X),X2))),X),meet(complement(X),meet(X2,complement(meet(complement(X),X2))))),
    inference(symmetry,[status(thm)],[c299]) ).

cnf(c301,plain,
    meet(X,complement(meet(X2,X))) = meet(complement(meet(X2,X)),X),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c302,plain,
    meet(X2,meet(X,complement(meet(X2,X)))) = meet(X2,meet(complement(meet(X2,X)),X)),
    inference(congruence,[status(thm)],[c301]) ).

cnf(c303,plain,
    meet(X2,X) = meet(X,X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c304,plain,
    meet(X2,meet(X3,X)) = meet(X2,meet(X,X3)),
    inference(congruence,[status(thm)],[c303]) ).

cnf(c305,plain,
    meet(meet(X2,meet(X,X3)),top) = meet(X2,meet(X,X3)),
    inference(substitution,[status(thm)],[c195]) ).

cnf(c306,plain,
    meet(X2,meet(X,X3)) = meet(meet(X2,meet(X,X3)),top),
    inference(symmetry,[status(thm)],[c305]) ).

cnf(c307,plain,
    complement(join(zero,complement(meet(X2,meet(X,X3))))) = meet(meet(X2,meet(X,X3)),top),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c308,plain,
    meet(meet(X2,meet(X,X3)),top) = complement(join(zero,complement(meet(X2,meet(X,X3))))),
    inference(symmetry,[status(thm)],[c307]) ).

cnf(c309,plain,
    meet(X2,meet(X,X3)) = meet(X2,meet(X3,X)),
    inference(congruence,[status(thm)],[c26]) ).

cnf(c310,plain,
    complement(meet(X2,meet(X,X3))) = complement(meet(X2,meet(X3,X))),
    inference(congruence,[status(thm)],[c309]) ).

cnf(c311,plain,
    meet(X2,X) = complement(join(complement(X2),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c312,plain,
    meet(X2,meet(X3,X)) = meet(X2,complement(join(complement(X3),complement(X)))),
    inference(congruence,[status(thm)],[c311]) ).

cnf(c313,plain,
    complement(meet(X2,meet(X3,X))) = complement(meet(X2,complement(join(complement(X3),complement(X))))),
    inference(congruence,[status(thm)],[c312]) ).

cnf(c314,plain,
    complement(meet(X2,complement(join(complement(X3),complement(X))))) = join(join(complement(X3),complement(X)),complement(X2)),
    inference(substitution,[status(thm)],[c265]) ).

cnf(c315,plain,
    join(complement(X3),join(complement(X),complement(X2))) = join(join(complement(X3),complement(X)),complement(X2)),
    inference(substitution,[status(thm)],[c125]) ).

cnf(c316,plain,
    join(join(complement(X3),complement(X)),complement(X2)) = join(complement(X3),join(complement(X),complement(X2))),
    inference(symmetry,[status(thm)],[c315]) ).

cnf(c317,plain,
    join(complement(X),complement(X2)) = complement(meet(X,X2)),
    inference(substitution,[status(thm)],[c257]) ).

cnf(c318,plain,
    join(complement(X3),join(complement(X),complement(X2))) = join(complement(X3),complement(meet(X,X2))),
    inference(congruence,[status(thm)],[c317]) ).

cnf(c319,plain,
    join(complement(X3),complement(meet(X,X2))) = complement(meet(X3,meet(X,X2))),
    inference(substitution,[status(thm)],[c257]) ).

cnf(c320,plain,
    meet(X2,X) = meet(X,X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c321,plain,
    meet(X,X2) = meet(X2,X),
    inference(symmetry,[status(thm)],[c320]) ).

cnf(c322,plain,
    meet(X3,meet(X,X2)) = meet(X3,meet(X2,X)),
    inference(congruence,[status(thm)],[c321]) ).

cnf(c323,plain,
    complement(meet(X3,meet(X,X2))) = complement(meet(X3,meet(X2,X))),
    inference(congruence,[status(thm)],[c322]) ).

cnf(c324,plain,
    join(complement(X3),complement(meet(X,X2))) = complement(meet(X3,meet(X2,X))),
    inference(transitivity,[status(thm)],[c319,c323]) ).

cnf(c325,plain,
    join(complement(X3),join(complement(X),complement(X2))) = complement(meet(X3,meet(X2,X))),
    inference(transitivity,[status(thm)],[c318,c324]) ).

cnf(c326,plain,
    join(join(complement(X3),complement(X)),complement(X2)) = complement(meet(X3,meet(X2,X))),
    inference(transitivity,[status(thm)],[c316,c325]) ).

cnf(c327,plain,
    complement(meet(X2,complement(join(complement(X3),complement(X))))) = complement(meet(X3,meet(X2,X))),
    inference(transitivity,[status(thm)],[c314,c326]) ).

cnf(c328,plain,
    complement(meet(X2,meet(X3,X))) = complement(meet(X3,meet(X2,X))),
    inference(transitivity,[status(thm)],[c313,c327]) ).

cnf(c329,plain,
    complement(meet(X2,meet(X,X3))) = complement(meet(X3,meet(X2,X))),
    inference(transitivity,[status(thm)],[c310,c328]) ).

cnf(c330,plain,
    join(zero,complement(meet(X2,meet(X,X3)))) = join(zero,complement(meet(X3,meet(X2,X)))),
    inference(congruence,[status(thm)],[c329]) ).

cnf(c331,plain,
    complement(join(zero,complement(meet(X2,meet(X,X3))))) = complement(join(zero,complement(meet(X3,meet(X2,X))))),
    inference(congruence,[status(thm)],[c330]) ).

cnf(c332,plain,
    complement(join(zero,complement(meet(X3,meet(X2,X))))) = meet(meet(X3,meet(X2,X)),top),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c333,plain,
    meet(meet(X3,meet(X2,X)),top) = meet(X3,meet(X2,X)),
    inference(substitution,[status(thm)],[c195]) ).

cnf(c334,plain,
    complement(join(zero,complement(meet(X3,meet(X2,X))))) = meet(X3,meet(X2,X)),
    inference(transitivity,[status(thm)],[c332,c333]) ).

cnf(c335,plain,
    complement(join(zero,complement(meet(X2,meet(X,X3))))) = meet(X3,meet(X2,X)),
    inference(transitivity,[status(thm)],[c331,c334]) ).

cnf(c336,plain,
    meet(meet(X2,meet(X,X3)),top) = meet(X3,meet(X2,X)),
    inference(transitivity,[status(thm)],[c308,c335]) ).

cnf(c337,plain,
    meet(X2,meet(X,X3)) = meet(X3,meet(X2,X)),
    inference(transitivity,[status(thm)],[c306,c336]) ).

cnf(c338,plain,
    meet(X2,meet(X3,X)) = meet(X3,meet(X2,X)),
    inference(transitivity,[status(thm)],[c304,c337]) ).

cnf(c339,plain,
    meet(X2,meet(complement(meet(X2,X)),X)) = meet(complement(meet(X2,X)),meet(X2,X)),
    inference(substitution,[status(thm)],[c338]) ).

cnf(c340,plain,
    complement(meet(X2,X)) = join(complement(X2),complement(X)),
    inference(symmetry,[status(thm)],[c257]) ).

cnf(c341,plain,
    meet(complement(meet(X2,X)),meet(X2,X)) = meet(join(complement(X2),complement(X)),meet(X2,X)),
    inference(congruence,[status(thm)],[c340]) ).

cnf(c342,plain,
    meet(X2,X) = complement(join(complement(X2),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c343,plain,
    meet(join(complement(X2),complement(X)),meet(X2,X)) = meet(join(complement(X2),complement(X)),complement(join(complement(X2),complement(X)))),
    inference(congruence,[status(thm)],[c342]) ).

cnf(c344,plain,
    zero = meet(join(complement(X2),complement(X)),complement(join(complement(X2),complement(X)))),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c345,plain,
    meet(join(complement(X2),complement(X)),complement(join(complement(X2),complement(X)))) = zero,
    inference(symmetry,[status(thm)],[c344]) ).

cnf(c346,plain,
    meet(join(complement(X2),complement(X)),meet(X2,X)) = zero,
    inference(transitivity,[status(thm)],[c343,c345]) ).

cnf(c347,plain,
    meet(complement(meet(X2,X)),meet(X2,X)) = zero,
    inference(transitivity,[status(thm)],[c341,c346]) ).

cnf(c348,plain,
    meet(X2,meet(complement(meet(X2,X)),X)) = zero,
    inference(transitivity,[status(thm)],[c339,c347]) ).

cnf(c349,plain,
    meet(X2,meet(X,complement(meet(X2,X)))) = zero,
    inference(transitivity,[status(thm)],[c302,c348]) ).

cnf(c350,plain,
    meet(complement(X),meet(X2,complement(meet(complement(X),X2)))) = zero,
    inference(substitution,[status(thm)],[c349]) ).

cnf(c351,plain,
    join(meet(meet(X2,complement(meet(complement(X),X2))),X),meet(complement(X),meet(X2,complement(meet(complement(X),X2))))) = join(meet(meet(X2,complement(meet(complement(X),X2))),X),zero),
    inference(congruence,[status(thm)],[c350]) ).

cnf(c352,plain,
    join(meet(meet(X2,complement(meet(complement(X),X2))),X),zero) = meet(meet(X2,complement(meet(complement(X),X2))),X),
    inference(substitution,[status(thm)],[c246]) ).

cnf(c353,plain,
    meet(meet(X3,X2),X) = meet(X,meet(X3,X2)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c354,plain,
    meet(X3,meet(X,X2)) = meet(X,meet(X3,X2)),
    inference(substitution,[status(thm)],[c338]) ).

cnf(c355,plain,
    meet(X,meet(X3,X2)) = meet(X3,meet(X,X2)),
    inference(symmetry,[status(thm)],[c354]) ).

cnf(c356,plain,
    meet(meet(X3,X2),X) = meet(X3,meet(X,X2)),
    inference(transitivity,[status(thm)],[c353,c355]) ).

cnf(c357,plain,
    meet(meet(X2,complement(meet(complement(X),X2))),X) = meet(X2,meet(X,complement(meet(complement(X),X2)))),
    inference(substitution,[status(thm)],[c356]) ).

cnf(c358,plain,
    complement(meet(complement(X),X2)) = join(X,complement(X2)),
    inference(substitution,[status(thm)],[c285]) ).

cnf(c359,plain,
    meet(X,complement(meet(complement(X),X2))) = meet(X,join(X,complement(X2))),
    inference(congruence,[status(thm)],[c358]) ).

cnf(c360,plain,
    meet(X2,meet(X,complement(meet(complement(X),X2)))) = meet(X2,meet(X,join(X,complement(X2)))),
    inference(congruence,[status(thm)],[c359]) ).

cnf(c361,plain,
    complement(meet(X,complement(X2))) = join(X2,complement(X)),
    inference(substitution,[status(thm)],[c265]) ).

cnf(c362,plain,
    join(X2,complement(X)) = complement(meet(X,complement(X2))),
    inference(symmetry,[status(thm)],[c361]) ).

cnf(c363,plain,
    meet(X2,join(X2,complement(X))) = meet(X2,complement(meet(X,complement(X2)))),
    inference(congruence,[status(thm)],[c362]) ).

cnf(c364,plain,
    join(complement(X),complement(complement(X2))) = complement(meet(X,complement(X2))),
    inference(substitution,[status(thm)],[c257]) ).

cnf(c365,plain,
    complement(meet(X,complement(X2))) = join(complement(X),complement(complement(X2))),
    inference(symmetry,[status(thm)],[c364]) ).

cnf(c366,plain,
    meet(X2,complement(meet(X,complement(X2)))) = meet(X2,join(complement(X),complement(complement(X2)))),
    inference(congruence,[status(thm)],[c365]) ).

cnf(c367,plain,
    complement(join(complement(X2),meet(X,complement(X2)))) = meet(X2,join(complement(X),complement(complement(X2)))),
    inference(substitution,[status(thm)],[c228]) ).

cnf(c368,plain,
    meet(X2,join(complement(X),complement(complement(X2)))) = complement(join(complement(X2),meet(X,complement(X2)))),
    inference(symmetry,[status(thm)],[c367]) ).

cnf(c369,plain,
    join(zero,complement(join(complement(X2),meet(X,complement(X2))))) = complement(join(complement(X2),meet(X,complement(X2)))),
    inference(substitution,[status(thm)],[c189]) ).

cnf(c370,plain,
    complement(join(complement(X2),meet(X,complement(X2)))) = join(zero,complement(join(complement(X2),meet(X,complement(X2))))),
    inference(symmetry,[status(thm)],[c369]) ).

cnf(c371,plain,
    meet(X,complement(X2)) = meet(complement(X2),X),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c372,plain,
    meet(X2,meet(X,complement(X2))) = meet(X2,meet(complement(X2),X)),
    inference(congruence,[status(thm)],[c371]) ).

cnf(c373,plain,
    meet(X2,meet(complement(X2),X)) = complement(join(complement(X2),complement(meet(complement(X2),X)))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c374,plain,
    meet(X2,X) = meet(X,X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c375,plain,
    complement(meet(X2,X)) = complement(meet(X,X2)),
    inference(congruence,[status(thm)],[c374]) ).

cnf(c376,plain,
    join(X2,complement(meet(X2,X))) = join(X2,complement(meet(X,X2))),
    inference(congruence,[status(thm)],[c375]) ).

cnf(c377,plain,
    join(complement(X),complement(X2)) = complement(meet(X,X2)),
    inference(substitution,[status(thm)],[c257]) ).

cnf(c378,plain,
    complement(meet(X,X2)) = join(complement(X),complement(X2)),
    inference(symmetry,[status(thm)],[c377]) ).

cnf(c379,plain,
    join(X2,complement(meet(X,X2))) = join(X2,join(complement(X),complement(X2))),
    inference(congruence,[status(thm)],[c378]) ).

cnf(c380,plain,
    join(X2,join(complement(X),complement(X2))) = join(complement(X),top),
    inference(substitution,[status(thm)],[c133]) ).

cnf(c381,plain,
    join(complement(X),top) = top,
    inference(substitution,[status(thm)],[c163]) ).

cnf(c382,plain,
    join(X2,join(complement(X),complement(X2))) = top,
    inference(transitivity,[status(thm)],[c380,c381]) ).

cnf(c383,plain,
    join(X2,complement(meet(X,X2))) = top,
    inference(transitivity,[status(thm)],[c379,c382]) ).

cnf(c384,plain,
    join(X2,complement(meet(X2,X))) = top,
    inference(transitivity,[status(thm)],[c376,c383]) ).

cnf(c385,plain,
    join(complement(X2),complement(meet(complement(X2),X))) = top,
    inference(substitution,[status(thm)],[c384]) ).

cnf(c386,plain,
    complement(join(complement(X2),complement(meet(complement(X2),X)))) = complement(top),
    inference(congruence,[status(thm)],[c385]) ).

cnf(c387,plain,
    complement(join(complement(X2),complement(meet(complement(X2),X)))) = zero,
    inference(transitivity,[status(thm)],[c386,c12]) ).

cnf(c388,plain,
    meet(X2,meet(complement(X2),X)) = zero,
    inference(transitivity,[status(thm)],[c373,c387]) ).

cnf(c389,plain,
    meet(X2,meet(X,complement(X2))) = zero,
    inference(transitivity,[status(thm)],[c372,c388]) ).

cnf(c390,plain,
    zero = meet(X2,meet(X,complement(X2))),
    inference(symmetry,[status(thm)],[c389]) ).

cnf(c391,plain,
    join(zero,complement(join(complement(X2),meet(X,complement(X2))))) = join(meet(X2,meet(X,complement(X2))),complement(join(complement(X2),meet(X,complement(X2))))),
    inference(congruence,[status(thm)],[c390]) ).

cnf(c392,plain,
    join(meet(X2,meet(X,complement(X2))),complement(join(complement(X2),meet(X,complement(X2))))) = X2,
    inference(substitution,[status(thm)],[c88]) ).

cnf(c393,plain,
    join(zero,complement(join(complement(X2),meet(X,complement(X2))))) = X2,
    inference(transitivity,[status(thm)],[c391,c392]) ).

cnf(c394,plain,
    complement(join(complement(X2),meet(X,complement(X2)))) = X2,
    inference(transitivity,[status(thm)],[c370,c393]) ).

cnf(c395,plain,
    meet(X2,join(complement(X),complement(complement(X2)))) = X2,
    inference(transitivity,[status(thm)],[c368,c394]) ).

cnf(c396,plain,
    meet(X2,complement(meet(X,complement(X2)))) = X2,
    inference(transitivity,[status(thm)],[c366,c395]) ).

cnf(c397,plain,
    meet(X2,join(X2,complement(X))) = X2,
    inference(transitivity,[status(thm)],[c363,c396]) ).

cnf(c398,plain,
    meet(X,join(X,complement(X2))) = X,
    inference(substitution,[status(thm)],[c397]) ).

cnf(c399,plain,
    meet(X2,meet(X,join(X,complement(X2)))) = meet(X2,X),
    inference(congruence,[status(thm)],[c398]) ).

cnf(c400,plain,
    meet(X2,meet(X,complement(meet(complement(X),X2)))) = meet(X2,X),
    inference(transitivity,[status(thm)],[c360,c399]) ).

cnf(c401,plain,
    meet(meet(X2,complement(meet(complement(X),X2))),X) = meet(X2,X),
    inference(transitivity,[status(thm)],[c357,c400]) ).

cnf(c402,plain,
    join(meet(meet(X2,complement(meet(complement(X),X2))),X),zero) = meet(X2,X),
    inference(transitivity,[status(thm)],[c352,c401]) ).

cnf(c403,plain,
    join(meet(meet(X2,complement(meet(complement(X),X2))),X),meet(complement(X),meet(X2,complement(meet(complement(X),X2))))) = meet(X2,X),
    inference(transitivity,[status(thm)],[c351,c402]) ).

cnf(c404,plain,
    meet(X2,complement(meet(complement(X),X2))) = meet(X2,X),
    inference(transitivity,[status(thm)],[c300,c403]) ).

cnf(c405,plain,
    meet(X2,join(X,complement(X2))) = meet(X2,X),
    inference(transitivity,[status(thm)],[c288,c404]) ).

cnf(c406,plain,
    meet(join(zero,complement(X2)),join(X,complement(join(zero,complement(X2))))) = meet(join(zero,complement(X2)),X),
    inference(substitution,[status(thm)],[c405]) ).

cnf(c407,plain,
    meet(join(zero,complement(X2)),X) = meet(complement(X2),X),
    inference(congruence,[status(thm)],[c189]) ).

cnf(c408,plain,
    meet(X,complement(X2)) = meet(complement(X2),X),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c409,plain,
    meet(complement(X2),X) = meet(X,complement(X2)),
    inference(symmetry,[status(thm)],[c408]) ).

cnf(c410,plain,
    meet(join(zero,complement(X2)),X) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c407,c409]) ).

cnf(c411,plain,
    meet(join(zero,complement(X2)),join(X,complement(join(zero,complement(X2))))) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c406,c410]) ).

cnf(c412,plain,
    meet(join(zero,complement(X2)),join(X,meet(X2,top))) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c281,c411]) ).

cnf(c413,plain,
    meet(complement(X2),join(X,meet(X2,top))) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c278,c412]) ).

cnf(c414,plain,
    meet(complement(X2),join(X,X2)) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c276,c413]) ).

cnf(c415,plain,
    meet(complement(X2),join(X2,X)) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c273,c414]) ).

cnf(c416,plain,
    meet(complement(X),join(X,X2)) = meet(X2,complement(X)),
    inference(substitution,[status(thm)],[c415]) ).

cnf(c417,plain,
    meet(complement(X),join(X2,X)) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c270,c416]) ).

cnf(c418,plain,
    meet(join(X2,X),complement(X)) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c268,c417]) ).

cnf(c419,plain,
    meet(join(X,X2),complement(X2)) = meet(X,complement(X2)),
    inference(substitution,[status(thm)],[c418]) ).

cnf(c420,plain,
    complement(meet(join(X,X2),complement(X2))) = complement(meet(X,complement(X2))),
    inference(congruence,[status(thm)],[c419]) ).

cnf(c421,plain,
    complement(meet(X,complement(X2))) = join(X2,complement(X)),
    inference(substitution,[status(thm)],[c265]) ).

cnf(c422,plain,
    complement(meet(join(X,X2),complement(X2))) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c420,c421]) ).

cnf(c423,plain,
    join(X2,complement(join(X,X2))) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c267,c422]) ).

cnf(c424,plain,
    join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))) = join(composition(composition(X,converse(X)),X),complement(X)),
    inference(substitution,[status(thm)],[c423]) ).

cnf(c425,plain,
    meet(complement(X2),X) = meet(X,complement(X2)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c426,plain,
    join(meet(X2,X),meet(complement(X2),X)) = join(meet(X2,X),meet(X,complement(X2))),
    inference(congruence,[status(thm)],[c425]) ).

cnf(c427,plain,
    meet(X2,X) = meet(X,X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c428,plain,
    join(meet(X2,X),meet(X,complement(X2))) = join(meet(X,X2),meet(X,complement(X2))),
    inference(congruence,[status(thm)],[c427]) ).

cnf(c429,plain,
    join(meet(X,X2),meet(X,complement(X2))) = X,
    inference(substitution,[status(thm)],[c297]) ).

cnf(c430,plain,
    join(meet(X2,X),meet(X,complement(X2))) = X,
    inference(transitivity,[status(thm)],[c428,c429]) ).

cnf(c431,plain,
    join(meet(X2,X),meet(complement(X2),X)) = X,
    inference(transitivity,[status(thm)],[c426,c430]) ).

cnf(c432,plain,
    join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))) = converse(complement(converse(X))),
    inference(substitution,[status(thm)],[c431]) ).

cnf(c433,plain,
    converse(complement(converse(X))) = join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))),
    inference(symmetry,[status(thm)],[c432]) ).

cnf(c434,plain,
    join(zero,complement(complement(X))) = complement(complement(X)),
    inference(substitution,[status(thm)],[c189]) ).

cnf(c435,plain,
    complement(complement(X)) = join(zero,complement(complement(X))),
    inference(symmetry,[status(thm)],[c434]) ).

cnf(c436,plain,
    join(zero,complement(complement(X))) = join(zero,meet(X,X)),
    inference(congruence,[status(thm)],[c76]) ).

cnf(c437,plain,
    join(zero,complement(complement(X))) = X,
    inference(transitivity,[status(thm)],[c436,c91]) ).

cnf(c438,plain,
    complement(complement(X)) = X,
    inference(transitivity,[status(thm)],[c435,c437]) ).

cnf(c439,plain,
    X = complement(complement(X)),
    inference(symmetry,[status(thm)],[c438]) ).

cnf(c440,plain,
    converse(X) = converse(complement(complement(X))),
    inference(congruence,[status(thm)],[c439]) ).

cnf(c441,plain,
    complement(converse(X)) = complement(converse(complement(complement(X)))),
    inference(congruence,[status(thm)],[c440]) ).

cnf(c442,plain,
    converse(complement(converse(X))) = converse(complement(converse(complement(complement(X))))),
    inference(congruence,[status(thm)],[c441]) ).

cnf(c443,plain,
    meet(X,converse(complement(converse(X)))) = meet(X,converse(complement(converse(complement(complement(X)))))),
    inference(congruence,[status(thm)],[c442]) ).

cnf(c444,plain,
    join(X,complement(X2)) = join(complement(X2),X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c445,plain,
    join(complement(X2),X) = join(X,complement(X2)),
    inference(symmetry,[status(thm)],[c444]) ).

cnf(c446,plain,
    meet(X2,join(complement(X2),X)) = meet(X2,join(X,complement(X2))),
    inference(congruence,[status(thm)],[c445]) ).

cnf(c447,plain,
    meet(X2,join(complement(X2),X)) = meet(X2,X),
    inference(transitivity,[status(thm)],[c446,c405]) ).

cnf(c448,plain,
    meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))) = meet(X,converse(complement(converse(complement(complement(X)))))),
    inference(substitution,[status(thm)],[c447]) ).

cnf(c449,plain,
    meet(X,converse(complement(converse(complement(complement(X)))))) = meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))),
    inference(symmetry,[status(thm)],[c448]) ).

cnf(c450,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c451,plain,
    X = converse(converse(X)),
    inference(symmetry,[status(thm)],[c450]) ).

cnf(c452,plain,
    join(X,converse(complement(converse(complement(X))))) = join(converse(converse(X)),converse(complement(converse(complement(X))))),
    inference(congruence,[status(thm)],[c451]) ).

cnf(c453,plain,
    converse(join(converse(X),complement(converse(complement(X))))) = join(converse(converse(X)),converse(complement(converse(complement(X))))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c454,plain,
    join(converse(converse(X)),converse(complement(converse(complement(X))))) = converse(join(converse(X),complement(converse(complement(X))))),
    inference(symmetry,[status(thm)],[c453]) ).

cnf(c455,plain,
    meet(complement(X2),complement(X)) = meet(complement(X),complement(X2)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c456,plain,
    complement(X) = join(zero,complement(X)),
    inference(symmetry,[status(thm)],[c189]) ).

cnf(c457,plain,
    meet(complement(X),complement(X2)) = meet(join(zero,complement(X)),complement(X2)),
    inference(congruence,[status(thm)],[c456]) ).

cnf(c458,plain,
    join(zero,join(X2,complement(X))) = join(X2,complement(X)),
    inference(substitution,[status(thm)],[c247]) ).

cnf(c459,plain,
    join(X2,complement(X)) = join(zero,join(X2,complement(X))),
    inference(symmetry,[status(thm)],[c458]) ).

cnf(c460,plain,
    complement(join(X2,complement(X))) = complement(join(zero,join(X2,complement(X)))),
    inference(congruence,[status(thm)],[c459]) ).

cnf(c461,plain,
    complement(meet(X,complement(X2))) = join(X2,complement(X)),
    inference(substitution,[status(thm)],[c265]) ).

cnf(c462,plain,
    join(X2,complement(X)) = complement(meet(X,complement(X2))),
    inference(symmetry,[status(thm)],[c461]) ).

cnf(c463,plain,
    join(zero,join(X2,complement(X))) = join(zero,complement(meet(X,complement(X2)))),
    inference(congruence,[status(thm)],[c462]) ).

cnf(c464,plain,
    complement(join(zero,join(X2,complement(X)))) = complement(join(zero,complement(meet(X,complement(X2))))),
    inference(congruence,[status(thm)],[c463]) ).

cnf(c465,plain,
    complement(join(zero,complement(meet(X,complement(X2))))) = meet(meet(X,complement(X2)),top),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c466,plain,
    meet(meet(X,complement(X2)),top) = meet(X,complement(X2)),
    inference(substitution,[status(thm)],[c195]) ).

cnf(c467,plain,
    complement(join(zero,complement(meet(X,complement(X2))))) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c465,c466]) ).

cnf(c468,plain,
    complement(join(zero,join(X2,complement(X)))) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c464,c467]) ).

cnf(c469,plain,
    complement(join(X2,complement(X))) = meet(X,complement(X2)),
    inference(transitivity,[status(thm)],[c460,c468]) ).

cnf(c470,plain,
    complement(join(X2,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X2)),
    inference(substitution,[status(thm)],[c469]) ).

cnf(c471,plain,
    meet(join(zero,complement(X)),complement(X2)) = complement(join(X2,complement(join(zero,complement(X))))),
    inference(symmetry,[status(thm)],[c470]) ).

cnf(c472,plain,
    join(X2,complement(join(zero,complement(X)))) = join(X2,meet(X,top)),
    inference(congruence,[status(thm)],[c30]) ).

cnf(c473,plain,
    complement(join(X2,complement(join(zero,complement(X))))) = complement(join(X2,meet(X,top))),
    inference(congruence,[status(thm)],[c472]) ).

cnf(c474,plain,
    join(X2,meet(X,top)) = join(X2,X),
    inference(congruence,[status(thm)],[c195]) ).

cnf(c475,plain,
    complement(join(X2,meet(X,top))) = complement(join(X2,X)),
    inference(congruence,[status(thm)],[c474]) ).

cnf(c476,plain,
    complement(join(X2,complement(join(zero,complement(X))))) = complement(join(X2,X)),
    inference(transitivity,[status(thm)],[c473,c475]) ).

cnf(c477,plain,
    meet(join(zero,complement(X)),complement(X2)) = complement(join(X2,X)),
    inference(transitivity,[status(thm)],[c471,c476]) ).

cnf(c478,plain,
    meet(complement(X),complement(X2)) = complement(join(X2,X)),
    inference(transitivity,[status(thm)],[c457,c477]) ).

cnf(c479,plain,
    meet(complement(X2),complement(X)) = complement(join(X2,X)),
    inference(transitivity,[status(thm)],[c455,c478]) ).

cnf(c480,plain,
    complement(join(X2,X)) = meet(complement(X2),complement(X)),
    inference(symmetry,[status(thm)],[c479]) ).

cnf(c481,plain,
    join(X2,complement(join(X2,X))) = join(X2,meet(complement(X2),complement(X))),
    inference(congruence,[status(thm)],[c480]) ).

cnf(c482,plain,
    X2 = meet(X2,join(X2,complement(X))),
    inference(symmetry,[status(thm)],[c397]) ).

cnf(c483,plain,
    join(X2,meet(complement(X2),complement(X))) = join(meet(X2,join(X2,complement(X))),meet(complement(X2),complement(X))),
    inference(congruence,[status(thm)],[c482]) ).

cnf(c484,plain,
    join(X2,complement(X)) = complement(meet(complement(X2),X)),
    inference(symmetry,[status(thm)],[c285]) ).

cnf(c485,plain,
    meet(X2,join(X2,complement(X))) = meet(X2,complement(meet(complement(X2),X))),
    inference(congruence,[status(thm)],[c484]) ).

cnf(c486,plain,
    join(meet(X2,join(X2,complement(X))),meet(complement(X2),complement(X))) = join(meet(X2,complement(meet(complement(X2),X))),meet(complement(X2),complement(X))),
    inference(congruence,[status(thm)],[c485]) ).

cnf(c487,plain,
    meet(X2,X) = meet(X,X2),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c488,plain,
    complement(meet(X2,X)) = complement(meet(X,X2)),
    inference(congruence,[status(thm)],[c487]) ).

cnf(c489,plain,
    meet(X2,complement(meet(X2,X))) = meet(X2,complement(meet(X,X2))),
    inference(congruence,[status(thm)],[c488]) ).

cnf(c490,plain,
    join(meet(X,meet(X2,complement(meet(X,X2)))),meet(meet(X2,complement(meet(X,X2))),complement(X))) = meet(X2,complement(meet(X,X2))),
    inference(substitution,[status(thm)],[c430]) ).

cnf(c491,plain,
    meet(X2,complement(meet(X,X2))) = join(meet(X,meet(X2,complement(meet(X,X2)))),meet(meet(X2,complement(meet(X,X2))),complement(X))),
    inference(symmetry,[status(thm)],[c490]) ).

cnf(c492,plain,
    meet(X,meet(X2,complement(meet(X,X2)))) = zero,
    inference(substitution,[status(thm)],[c349]) ).

cnf(c493,plain,
    join(meet(X,meet(X2,complement(meet(X,X2)))),meet(meet(X2,complement(meet(X,X2))),complement(X))) = join(zero,meet(meet(X2,complement(meet(X,X2))),complement(X))),
    inference(congruence,[status(thm)],[c492]) ).

cnf(c494,plain,
    join(zero,meet(meet(X2,complement(meet(X,X2))),complement(X))) = meet(meet(X2,complement(meet(X,X2))),complement(X)),
    inference(substitution,[status(thm)],[c247]) ).

cnf(c495,plain,
    meet(meet(X2,complement(meet(X,X2))),complement(X)) = meet(X2,meet(complement(X),complement(meet(X,X2)))),
    inference(substitution,[status(thm)],[c356]) ).

cnf(c496,plain,
    meet(complement(X),complement(meet(X,X2))) = complement(join(X,meet(X,X2))),
    inference(substitution,[status(thm)],[c479]) ).

cnf(c497,plain,
    meet(X2,meet(complement(X),complement(meet(X,X2)))) = meet(X2,complement(join(X,meet(X,X2)))),
    inference(congruence,[status(thm)],[c496]) ).

cnf(c498,plain,
    meet(X2,X) = complement(join(complement(X2),complement(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c499,plain,
    join(X2,meet(X2,X)) = join(X2,complement(join(complement(X2),complement(X)))),
    inference(congruence,[status(thm)],[c498]) ).

cnf(c500,plain,
    complement(meet(complement(X2),join(complement(X2),complement(X)))) = join(X2,complement(join(complement(X2),complement(X)))),
    inference(substitution,[status(thm)],[c285]) ).

cnf(c501,plain,
    join(X2,complement(join(complement(X2),complement(X)))) = complement(meet(complement(X2),join(complement(X2),complement(X)))),
    inference(symmetry,[status(thm)],[c500]) ).

cnf(c502,plain,
    meet(complement(X2),join(complement(X2),complement(X))) = complement(X2),
    inference(substitution,[status(thm)],[c397]) ).

cnf(c503,plain,
    complement(meet(complement(X2),join(complement(X2),complement(X)))) = complement(complement(X2)),
    inference(congruence,[status(thm)],[c502]) ).

cnf(c504,plain,
    complement(meet(complement(X2),join(complement(X2),complement(X)))) = X2,
    inference(transitivity,[status(thm)],[c503,c438]) ).

cnf(c505,plain,
    join(X2,complement(join(complement(X2),complement(X)))) = X2,
    inference(transitivity,[status(thm)],[c501,c504]) ).

cnf(c506,plain,
    join(X2,meet(X2,X)) = X2,
    inference(transitivity,[status(thm)],[c499,c505]) ).

cnf(c507,plain,
    join(X,meet(X,X2)) = X,
    inference(substitution,[status(thm)],[c506]) ).

cnf(c508,plain,
    complement(join(X,meet(X,X2))) = complement(X),
    inference(congruence,[status(thm)],[c507]) ).

cnf(c509,plain,
    meet(X2,complement(join(X,meet(X,X2)))) = meet(X2,complement(X)),
    inference(congruence,[status(thm)],[c508]) ).

cnf(c510,plain,
    meet(X2,meet(complement(X),complement(meet(X,X2)))) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c497,c509]) ).

cnf(c511,plain,
    meet(meet(X2,complement(meet(X,X2))),complement(X)) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c495,c510]) ).

cnf(c512,plain,
    join(zero,meet(meet(X2,complement(meet(X,X2))),complement(X))) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c494,c511]) ).

cnf(c513,plain,
    join(meet(X,meet(X2,complement(meet(X,X2)))),meet(meet(X2,complement(meet(X,X2))),complement(X))) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c493,c512]) ).

cnf(c514,plain,
    meet(X2,complement(meet(X,X2))) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c491,c513]) ).

cnf(c515,plain,
    meet(X2,complement(meet(X2,X))) = meet(X2,complement(X)),
    inference(transitivity,[status(thm)],[c489,c514]) ).

cnf(c516,plain,
    meet(complement(X2),complement(meet(complement(X2),X))) = meet(complement(X2),complement(X)),
    inference(substitution,[status(thm)],[c515]) ).

cnf(c517,plain,
    meet(complement(X2),complement(X)) = meet(complement(X2),complement(meet(complement(X2),X))),
    inference(symmetry,[status(thm)],[c516]) ).

cnf(c518,plain,
    join(meet(X2,complement(meet(complement(X2),X))),meet(complement(X2),complement(X))) = join(meet(X2,complement(meet(complement(X2),X))),meet(complement(X2),complement(meet(complement(X2),X)))),
    inference(congruence,[status(thm)],[c517]) ).

cnf(c519,plain,
    join(meet(X2,complement(meet(complement(X2),X))),meet(complement(X2),complement(meet(complement(X2),X)))) = complement(meet(complement(X2),X)),
    inference(substitution,[status(thm)],[c431]) ).

cnf(c520,plain,
    join(meet(X2,complement(meet(complement(X2),X))),meet(complement(X2),complement(meet(complement(X2),X)))) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c519,c285]) ).

cnf(c521,plain,
    join(meet(X2,complement(meet(complement(X2),X))),meet(complement(X2),complement(X))) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c518,c520]) ).

cnf(c522,plain,
    join(meet(X2,join(X2,complement(X))),meet(complement(X2),complement(X))) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c486,c521]) ).

cnf(c523,plain,
    join(X2,meet(complement(X2),complement(X))) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c483,c522]) ).

cnf(c524,plain,
    join(X2,complement(join(X2,X))) = join(X2,complement(X)),
    inference(transitivity,[status(thm)],[c481,c523]) ).

cnf(c525,plain,
    join(converse(X),complement(join(converse(X),converse(complement(X))))) = join(converse(X),complement(converse(complement(X)))),
    inference(substitution,[status(thm)],[c524]) ).

cnf(c526,plain,
    join(converse(X),complement(converse(complement(X)))) = join(converse(X),complement(join(converse(X),converse(complement(X))))),
    inference(symmetry,[status(thm)],[c525]) ).

cnf(c527,plain,
    complement(join(converse(X),converse(complement(X)))) = complement(converse(top)),
    inference(congruence,[status(thm)],[c113]) ).

cnf(c528,plain,
    join(converse(X),complement(join(converse(X),converse(complement(X))))) = join(converse(X),complement(converse(top))),
    inference(congruence,[status(thm)],[c527]) ).

cnf(c529,plain,
    complement(converse(top)) = complement(top),
    inference(congruence,[status(thm)],[c174]) ).

cnf(c530,plain,
    join(converse(X),complement(converse(top))) = join(converse(X),complement(top)),
    inference(congruence,[status(thm)],[c529]) ).

cnf(c531,plain,
    join(converse(X),complement(top)) = join(converse(X),zero),
    inference(congruence,[status(thm)],[c12]) ).

cnf(c532,plain,
    join(converse(X),zero) = converse(X),
    inference(substitution,[status(thm)],[c246]) ).

cnf(c533,plain,
    join(converse(X),complement(top)) = converse(X),
    inference(transitivity,[status(thm)],[c531,c532]) ).

cnf(c534,plain,
    join(converse(X),complement(converse(top))) = converse(X),
    inference(transitivity,[status(thm)],[c530,c533]) ).

cnf(c535,plain,
    join(converse(X),complement(join(converse(X),converse(complement(X))))) = converse(X),
    inference(transitivity,[status(thm)],[c528,c534]) ).

cnf(c536,plain,
    join(converse(X),complement(converse(complement(X)))) = converse(X),
    inference(transitivity,[status(thm)],[c526,c535]) ).

cnf(c537,plain,
    converse(join(converse(X),complement(converse(complement(X))))) = converse(converse(X)),
    inference(congruence,[status(thm)],[c536]) ).

cnf(c538,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c539,plain,
    converse(join(converse(X),complement(converse(complement(X))))) = X,
    inference(transitivity,[status(thm)],[c537,c538]) ).

cnf(c540,plain,
    join(converse(converse(X)),converse(complement(converse(complement(X))))) = X,
    inference(transitivity,[status(thm)],[c454,c539]) ).

cnf(c541,plain,
    join(X,converse(complement(converse(complement(X))))) = X,
    inference(transitivity,[status(thm)],[c452,c540]) ).

cnf(c542,plain,
    join(complement(X),converse(complement(converse(complement(complement(X)))))) = complement(X),
    inference(substitution,[status(thm)],[c541]) ).

cnf(c543,plain,
    meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))) = meet(X,complement(X)),
    inference(congruence,[status(thm)],[c542]) ).

cnf(c544,plain,
    zero = meet(X,complement(X)),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c545,plain,
    meet(X,complement(X)) = zero,
    inference(symmetry,[status(thm)],[c544]) ).

cnf(c546,plain,
    meet(X,join(complement(X),converse(complement(converse(complement(complement(X))))))) = zero,
    inference(transitivity,[status(thm)],[c543,c545]) ).

cnf(c547,plain,
    meet(X,converse(complement(converse(complement(complement(X)))))) = zero,
    inference(transitivity,[status(thm)],[c449,c546]) ).

cnf(c548,plain,
    meet(X,converse(complement(converse(X)))) = zero,
    inference(transitivity,[status(thm)],[c443,c547]) ).

cnf(c549,plain,
    join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))) = join(zero,meet(complement(X),converse(complement(converse(X))))),
    inference(congruence,[status(thm)],[c548]) ).

cnf(c550,plain,
    join(zero,meet(complement(X),converse(complement(converse(X))))) = meet(complement(X),converse(complement(converse(X)))),
    inference(substitution,[status(thm)],[c247]) ).

cnf(c551,plain,
    meet(complement(X),converse(complement(converse(X)))) = meet(converse(complement(converse(X))),complement(X)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c552,plain,
    meet(complement(X),join(X,converse(complement(converse(X))))) = meet(converse(complement(converse(X))),complement(X)),
    inference(substitution,[status(thm)],[c415]) ).

cnf(c553,plain,
    meet(converse(complement(converse(X))),complement(X)) = meet(complement(X),join(X,converse(complement(converse(X))))),
    inference(symmetry,[status(thm)],[c552]) ).

cnf(c554,plain,
    meet(complement(X),join(X,converse(complement(converse(X))))) = meet(complement(X),converse(top)),
    inference(congruence,[status(thm)],[c115]) ).

cnf(c555,plain,
    meet(complement(X),converse(top)) = meet(complement(X),top),
    inference(congruence,[status(thm)],[c174]) ).

cnf(c556,plain,
    meet(complement(X),top) = complement(X),
    inference(substitution,[status(thm)],[c195]) ).

cnf(c557,plain,
    meet(complement(X),converse(top)) = complement(X),
    inference(transitivity,[status(thm)],[c555,c556]) ).

cnf(c558,plain,
    meet(complement(X),join(X,converse(complement(converse(X))))) = complement(X),
    inference(transitivity,[status(thm)],[c554,c557]) ).

cnf(c559,plain,
    meet(converse(complement(converse(X))),complement(X)) = complement(X),
    inference(transitivity,[status(thm)],[c553,c558]) ).

cnf(c560,plain,
    meet(complement(X),converse(complement(converse(X)))) = complement(X),
    inference(transitivity,[status(thm)],[c551,c559]) ).

cnf(c561,plain,
    join(zero,meet(complement(X),converse(complement(converse(X))))) = complement(X),
    inference(transitivity,[status(thm)],[c550,c560]) ).

cnf(c562,plain,
    join(meet(X,converse(complement(converse(X)))),meet(complement(X),converse(complement(converse(X))))) = complement(X),
    inference(transitivity,[status(thm)],[c549,c561]) ).

cnf(c563,plain,
    converse(complement(converse(X))) = complement(X),
    inference(transitivity,[status(thm)],[c433,c562]) ).

cnf(c564,plain,
    complement(X) = converse(complement(converse(X))),
    inference(symmetry,[status(thm)],[c563]) ).

cnf(c565,plain,
    join(composition(composition(X,converse(X)),X),complement(X)) = join(composition(composition(X,converse(X)),X),converse(complement(converse(X)))),
    inference(congruence,[status(thm)],[c564]) ).

cnf(c566,plain,
    converse(converse(composition(composition(X,converse(X)),X))) = composition(composition(X,converse(X)),X),
    inference(substitution,[status(thm)],[c35]) ).

cnf(c567,plain,
    composition(composition(X,converse(X)),X) = converse(converse(composition(composition(X,converse(X)),X))),
    inference(symmetry,[status(thm)],[c566]) ).

cnf(c568,plain,
    join(composition(composition(X,converse(X)),X),converse(complement(converse(X)))) = join(converse(converse(composition(composition(X,converse(X)),X))),converse(complement(converse(X)))),
    inference(congruence,[status(thm)],[c567]) ).

cnf(c569,plain,
    converse(join(converse(composition(composition(X,converse(X)),X)),complement(converse(X)))) = join(converse(converse(composition(composition(X,converse(X)),X))),converse(complement(converse(X)))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c570,plain,
    join(converse(converse(composition(composition(X,converse(X)),X))),converse(complement(converse(X)))) = converse(join(converse(composition(composition(X,converse(X)),X)),complement(converse(X)))),
    inference(symmetry,[status(thm)],[c569]) ).

cnf(c571,plain,
    join(composition(converse(X),complement(composition(X,X3))),X2) = join(X2,composition(converse(X),complement(composition(X,X3)))),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c572,plain,
    join(X2,composition(converse(X),complement(composition(X,X3)))) = join(composition(converse(X),complement(composition(X,X3))),X2),
    inference(symmetry,[status(thm)],[c571]) ).

cnf(c573,plain,
    join(complement(X3),join(X2,composition(converse(X),complement(composition(X,X3))))) = join(complement(X3),join(composition(converse(X),complement(composition(X,X3))),X2)),
    inference(congruence,[status(thm)],[c572]) ).

cnf(c574,plain,
    join(complement(X3),join(composition(converse(X),complement(composition(X,X3))),X2)) = join(join(complement(X3),composition(converse(X),complement(composition(X,X3)))),X2),
    inference(substitution,[status(thm)],[c125]) ).

cnf(c575,plain,
    join(join(complement(X3),composition(converse(X),complement(composition(X,X3)))),X2) = join(complement(X3),X2),
    inference(congruence,[status(thm)],[c68]) ).

cnf(c576,plain,
    join(complement(X2),X) = join(X,complement(X2)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c577,plain,
    join(join(complement(X3),composition(converse(X),complement(composition(X,X3)))),X2) = join(X2,complement(X3)),
    inference(transitivity,[status(thm)],[c575,c576]) ).

cnf(c578,plain,
    join(complement(X3),join(composition(converse(X),complement(composition(X,X3))),X2)) = join(X2,complement(X3)),
    inference(transitivity,[status(thm)],[c574,c577]) ).

cnf(c579,plain,
    join(complement(X3),join(X2,composition(converse(X),complement(composition(X,X3))))) = join(X2,complement(X3)),
    inference(transitivity,[status(thm)],[c573,c578]) ).

cnf(c580,plain,
    join(complement(converse(X)),join(converse(composition(composition(X,converse(X)),X)),composition(converse(X),complement(composition(X,converse(X)))))) = join(converse(composition(composition(X,converse(X)),X)),complement(converse(X))),
    inference(substitution,[status(thm)],[c579]) ).

cnf(c581,plain,
    join(converse(composition(composition(X,converse(X)),X)),complement(converse(X))) = join(complement(converse(X)),join(converse(composition(composition(X,converse(X)),X)),composition(converse(X),complement(composition(X,converse(X)))))),
    inference(symmetry,[status(thm)],[c580]) ).

cnf(c582,plain,
    meet(X,complement(X2)) = meet(complement(X2),X),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c583,plain,
    join(X2,meet(X,complement(X2))) = join(X2,meet(complement(X2),X)),
    inference(congruence,[status(thm)],[c582]) ).

cnf(c584,plain,
    join(X2,X) = join(X,X2),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c585,plain,
    join(X,X2) = join(X2,X),
    inference(symmetry,[status(thm)],[c584]) ).

cnf(c586,plain,
    meet(X2,join(X,X2)) = meet(X2,join(X2,X)),
    inference(congruence,[status(thm)],[c585]) ).

cnf(c587,plain,
    X = meet(X,top),
    inference(symmetry,[status(thm)],[c195]) ).

cnf(c588,plain,
    join(X2,X) = join(X2,meet(X,top)),
    inference(congruence,[status(thm)],[c587]) ).

cnf(c589,plain,
    meet(X2,join(X2,X)) = meet(X2,join(X2,meet(X,top))),
    inference(congruence,[status(thm)],[c588]) ).

cnf(c590,plain,
    meet(X,top) = complement(join(zero,complement(X))),
    inference(symmetry,[status(thm)],[c30]) ).

cnf(c591,plain,
    join(X2,meet(X,top)) = join(X2,complement(join(zero,complement(X)))),
    inference(congruence,[status(thm)],[c590]) ).

cnf(c592,plain,
    meet(X2,join(X2,meet(X,top))) = meet(X2,join(X2,complement(join(zero,complement(X))))),
    inference(congruence,[status(thm)],[c591]) ).

cnf(c593,plain,
    meet(X2,join(X2,complement(join(zero,complement(X))))) = X2,
    inference(substitution,[status(thm)],[c397]) ).

cnf(c594,plain,
    meet(X2,join(X2,meet(X,top))) = X2,
    inference(transitivity,[status(thm)],[c592,c593]) ).

cnf(c595,plain,
    meet(X2,join(X2,X)) = X2,
    inference(transitivity,[status(thm)],[c589,c594]) ).

cnf(c596,plain,
    meet(X2,join(X,X2)) = X2,
    inference(transitivity,[status(thm)],[c586,c595]) ).

cnf(c597,plain,
    X2 = meet(X2,join(X,X2)),
    inference(symmetry,[status(thm)],[c596]) ).

cnf(c598,plain,
    join(X2,meet(complement(X2),X)) = join(meet(X2,join(X,X2)),meet(complement(X2),X)),
    inference(congruence,[status(thm)],[c597]) ).

cnf(c599,plain,
    X = complement(complement(X)),
    inference(symmetry,[status(thm)],[c438]) ).

cnf(c600,plain,
    join(X,X2) = join(X,complement(complement(X2))),
    inference(congruence,[status(thm)],[c599]) ).

cnf(c601,plain,
    meet(X2,join(X,X2)) = meet(X2,join(X,complement(complement(X2)))),
    inference(congruence,[status(thm)],[c600]) ).

cnf(c602,plain,
    join(meet(X2,join(X,X2)),meet(complement(X2),X)) = join(meet(X2,join(X,complement(complement(X2)))),meet(complement(X2),X)),
    inference(congruence,[status(thm)],[c601]) ).

cnf(c603,plain,
    meet(complement(X2),join(X,complement(complement(X2)))) = meet(complement(X2),X),
    inference(substitution,[status(thm)],[c405]) ).

cnf(c604,plain,
    meet(complement(X2),X) = meet(complement(X2),join(X,complement(complement(X2)))),
    inference(symmetry,[status(thm)],[c603]) ).

cnf(c605,plain,
    join(meet(X2,join(X,complement(complement(X2)))),meet(complement(X2),X)) = join(meet(X2,join(X,complement(complement(X2)))),meet(complement(X2),join(X,complement(complement(X2))))),
    inference(congruence,[status(thm)],[c604]) ).

cnf(c606,plain,
    join(meet(X2,join(X,complement(complement(X2)))),meet(complement(X2),join(X,complement(complement(X2))))) = join(X,complement(complement(X2))),
    inference(substitution,[status(thm)],[c431]) ).

cnf(c607,plain,
    join(X,complement(complement(X2))) = join(X,X2),
    inference(congruence,[status(thm)],[c438]) ).

cnf(c608,plain,
    join(X,X2) = join(X2,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c609,plain,
    join(X,complement(complement(X2))) = join(X2,X),
    inference(transitivity,[status(thm)],[c607,c608]) ).

cnf(c610,plain,
    join(meet(X2,join(X,complement(complement(X2)))),meet(complement(X2),join(X,complement(complement(X2))))) = join(X2,X),
    inference(transitivity,[status(thm)],[c606,c609]) ).

cnf(c611,plain,
    join(meet(X2,join(X,complement(complement(X2)))),meet(complement(X2),X)) = join(X2,X),
    inference(transitivity,[status(thm)],[c605,c610]) ).

cnf(c612,plain,
    join(meet(X2,join(X,X2)),meet(complement(X2),X)) = join(X2,X),
    inference(transitivity,[status(thm)],[c602,c611]) ).

cnf(c613,plain,
    join(X2,meet(complement(X2),X)) = join(X2,X),
    inference(transitivity,[status(thm)],[c598,c612]) ).

cnf(c614,plain,
    join(X2,meet(X,complement(X2))) = join(X2,X),
    inference(transitivity,[status(thm)],[c583,c613]) ).

cnf(c615,plain,
    join(complement(composition(X2,converse(X))),meet(converse(complement(composition(X,converse(X2)))),complement(complement(composition(X2,converse(X)))))) = join(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))),
    inference(substitution,[status(thm)],[c614]) ).

cnf(c616,plain,
    join(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))) = join(complement(composition(X2,converse(X))),meet(converse(complement(composition(X,converse(X2)))),complement(complement(composition(X2,converse(X)))))),
    inference(symmetry,[status(thm)],[c615]) ).

cnf(c617,plain,
    meet(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))) = meet(converse(complement(composition(X,converse(X2)))),complement(composition(X2,converse(X)))),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c618,plain,
    meet(complement(composition(X2,converse(X))),join(composition(X2,converse(X)),converse(complement(composition(X,converse(X2)))))) = meet(converse(complement(composition(X,converse(X2)))),complement(composition(X2,converse(X)))),
    inference(substitution,[status(thm)],[c415]) ).

cnf(c619,plain,
    meet(converse(complement(composition(X,converse(X2)))),complement(composition(X2,converse(X)))) = meet(complement(composition(X2,converse(X))),join(composition(X2,converse(X)),converse(complement(composition(X,converse(X2)))))),
    inference(symmetry,[status(thm)],[c618]) ).

cnf(c620,plain,
    converse(composition(X2,converse(X))) = composition(converse(converse(X)),converse(X2)),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c621,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c622,plain,
    composition(converse(converse(X)),converse(X2)) = composition(X,converse(X2)),
    inference(congruence,[status(thm)],[c621]) ).

cnf(c623,plain,
    converse(composition(X2,converse(X))) = composition(X,converse(X2)),
    inference(transitivity,[status(thm)],[c620,c622]) ).

cnf(c624,plain,
    converse(composition(X,converse(X2))) = composition(X2,converse(X)),
    inference(substitution,[status(thm)],[c623]) ).

cnf(c625,plain,
    composition(X2,converse(X)) = converse(composition(X,converse(X2))),
    inference(symmetry,[status(thm)],[c624]) ).

cnf(c626,plain,
    join(composition(X2,converse(X)),converse(complement(composition(X,converse(X2))))) = join(converse(composition(X,converse(X2))),converse(complement(composition(X,converse(X2))))),
    inference(congruence,[status(thm)],[c625]) ).

cnf(c627,plain,
    join(converse(composition(X,converse(X2))),converse(complement(composition(X,converse(X2))))) = converse(top),
    inference(substitution,[status(thm)],[c113]) ).

cnf(c628,plain,
    join(composition(X2,converse(X)),converse(complement(composition(X,converse(X2))))) = converse(top),
    inference(transitivity,[status(thm)],[c626,c627]) ).

cnf(c629,plain,
    meet(complement(composition(X2,converse(X))),join(composition(X2,converse(X)),converse(complement(composition(X,converse(X2)))))) = meet(complement(composition(X2,converse(X))),converse(top)),
    inference(congruence,[status(thm)],[c628]) ).

cnf(c630,plain,
    meet(complement(composition(X2,converse(X))),converse(top)) = meet(complement(composition(X2,converse(X))),top),
    inference(congruence,[status(thm)],[c174]) ).

cnf(c631,plain,
    meet(complement(composition(X2,converse(X))),top) = complement(composition(X2,converse(X))),
    inference(substitution,[status(thm)],[c195]) ).

cnf(c632,plain,
    meet(complement(composition(X2,converse(X))),converse(top)) = complement(composition(X2,converse(X))),
    inference(transitivity,[status(thm)],[c630,c631]) ).

cnf(c633,plain,
    meet(complement(composition(X2,converse(X))),join(composition(X2,converse(X)),converse(complement(composition(X,converse(X2)))))) = complement(composition(X2,converse(X))),
    inference(transitivity,[status(thm)],[c629,c632]) ).

cnf(c634,plain,
    meet(converse(complement(composition(X,converse(X2)))),complement(composition(X2,converse(X)))) = complement(composition(X2,converse(X))),
    inference(transitivity,[status(thm)],[c619,c633]) ).

cnf(c635,plain,
    meet(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))) = complement(composition(X2,converse(X))),
    inference(transitivity,[status(thm)],[c617,c634]) ).

cnf(c636,plain,
    complement(composition(X2,converse(X))) = meet(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))),
    inference(symmetry,[status(thm)],[c635]) ).

cnf(c637,plain,
    join(complement(composition(X2,converse(X))),meet(converse(complement(composition(X,converse(X2)))),complement(complement(composition(X2,converse(X)))))) = join(meet(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))),meet(converse(complement(composition(X,converse(X2)))),complement(complement(composition(X2,converse(X)))))),
    inference(congruence,[status(thm)],[c636]) ).

cnf(c638,plain,
    join(meet(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))),meet(converse(complement(composition(X,converse(X2)))),complement(complement(composition(X2,converse(X)))))) = converse(complement(composition(X,converse(X2)))),
    inference(substitution,[status(thm)],[c430]) ).

cnf(c639,plain,
    join(complement(composition(X2,converse(X))),meet(converse(complement(composition(X,converse(X2)))),complement(complement(composition(X2,converse(X)))))) = converse(complement(composition(X,converse(X2)))),
    inference(transitivity,[status(thm)],[c637,c638]) ).

cnf(c640,plain,
    join(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2))))) = converse(complement(composition(X,converse(X2)))),
    inference(transitivity,[status(thm)],[c616,c639]) ).

cnf(c641,plain,
    join(complement(composition(X,converse(X2))),converse(complement(composition(X2,converse(X))))) = converse(complement(composition(X2,converse(X)))),
    inference(substitution,[status(thm)],[c640]) ).

cnf(c642,plain,
    converse(complement(composition(X2,converse(X)))) = join(complement(composition(X,converse(X2))),converse(complement(composition(X2,converse(X))))),
    inference(symmetry,[status(thm)],[c641]) ).

cnf(c643,plain,
    join(converse(complement(composition(X2,converse(X)))),complement(composition(X,converse(X2)))) = join(complement(composition(X,converse(X2))),converse(complement(composition(X2,converse(X))))),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c644,plain,
    join(complement(composition(X,converse(X2))),converse(complement(composition(X2,converse(X))))) = join(converse(complement(composition(X2,converse(X)))),complement(composition(X,converse(X2)))),
    inference(symmetry,[status(thm)],[c643]) ).

cnf(c645,plain,
    converse(converse(complement(composition(X,converse(X2))))) = complement(composition(X,converse(X2))),
    inference(substitution,[status(thm)],[c35]) ).

cnf(c646,plain,
    complement(composition(X,converse(X2))) = converse(converse(complement(composition(X,converse(X2))))),
    inference(symmetry,[status(thm)],[c645]) ).

cnf(c647,plain,
    join(converse(complement(composition(X2,converse(X)))),complement(composition(X,converse(X2)))) = join(converse(complement(composition(X2,converse(X)))),converse(converse(complement(composition(X,converse(X2)))))),
    inference(congruence,[status(thm)],[c646]) ).

cnf(c648,plain,
    converse(join(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2)))))) = join(converse(complement(composition(X2,converse(X)))),converse(converse(complement(composition(X,converse(X2)))))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c649,plain,
    join(converse(complement(composition(X2,converse(X)))),converse(converse(complement(composition(X,converse(X2)))))) = converse(join(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2)))))),
    inference(symmetry,[status(thm)],[c648]) ).

cnf(c650,plain,
    converse(join(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2)))))) = converse(converse(complement(composition(X,converse(X2))))),
    inference(congruence,[status(thm)],[c640]) ).

cnf(c651,plain,
    converse(converse(complement(composition(X,converse(X2))))) = complement(composition(X,converse(X2))),
    inference(substitution,[status(thm)],[c35]) ).

cnf(c652,plain,
    converse(join(complement(composition(X2,converse(X))),converse(complement(composition(X,converse(X2)))))) = complement(composition(X,converse(X2))),
    inference(transitivity,[status(thm)],[c650,c651]) ).

cnf(c653,plain,
    join(converse(complement(composition(X2,converse(X)))),converse(converse(complement(composition(X,converse(X2)))))) = complement(composition(X,converse(X2))),
    inference(transitivity,[status(thm)],[c649,c652]) ).

cnf(c654,plain,
    join(converse(complement(composition(X2,converse(X)))),complement(composition(X,converse(X2)))) = complement(composition(X,converse(X2))),
    inference(transitivity,[status(thm)],[c647,c653]) ).

cnf(c655,plain,
    join(complement(composition(X,converse(X2))),converse(complement(composition(X2,converse(X))))) = complement(composition(X,converse(X2))),
    inference(transitivity,[status(thm)],[c644,c654]) ).

cnf(c656,plain,
    converse(complement(composition(X2,converse(X)))) = complement(composition(X,converse(X2))),
    inference(transitivity,[status(thm)],[c642,c655]) ).

cnf(c657,plain,
    complement(composition(X,converse(X2))) = converse(complement(composition(X2,converse(X)))),
    inference(symmetry,[status(thm)],[c656]) ).

cnf(c658,plain,
    composition(converse(X),complement(composition(X2,converse(X3)))) = composition(converse(X),converse(complement(composition(X3,converse(X2))))),
    inference(congruence,[status(thm)],[c657]) ).

cnf(c659,plain,
    join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),complement(composition(X2,converse(X3))))) = join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),converse(complement(composition(X3,converse(X2)))))),
    inference(congruence,[status(thm)],[c658]) ).

cnf(c660,plain,
    converse(composition(complement(composition(X3,converse(X2))),X)) = composition(converse(X),converse(complement(composition(X3,converse(X2))))),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c661,plain,
    composition(converse(X),converse(complement(composition(X3,converse(X2))))) = converse(composition(complement(composition(X3,converse(X2))),X)),
    inference(symmetry,[status(thm)],[c660]) ).

cnf(c662,plain,
    join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),converse(complement(composition(X3,converse(X2)))))) = join(converse(composition(composition(X3,converse(X2)),X)),converse(composition(complement(composition(X3,converse(X2))),X))),
    inference(congruence,[status(thm)],[c661]) ).

cnf(c663,plain,
    converse(join(composition(composition(X3,converse(X2)),X),composition(complement(composition(X3,converse(X2))),X))) = join(converse(composition(composition(X3,converse(X2)),X)),converse(composition(complement(composition(X3,converse(X2))),X))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c664,plain,
    join(converse(composition(composition(X3,converse(X2)),X)),converse(composition(complement(composition(X3,converse(X2))),X))) = converse(join(composition(composition(X3,converse(X2)),X),composition(complement(composition(X3,converse(X2))),X))),
    inference(symmetry,[status(thm)],[c663]) ).

cnf(c665,axiom,
    composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).

cnf(c666,plain,
    composition(join(X2,complement(X2)),X) = join(composition(X2,X),composition(complement(X2),X)),
    inference(substitution,[status(thm)],[c665]) ).

cnf(c667,plain,
    join(composition(X2,X),composition(complement(X2),X)) = composition(join(X2,complement(X2)),X),
    inference(symmetry,[status(thm)],[c666]) ).

cnf(c668,plain,
    top = join(X,complement(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c669,plain,
    join(X,complement(X)) = top,
    inference(symmetry,[status(thm)],[c668]) ).

cnf(c670,plain,
    composition(join(X2,complement(X2)),X) = composition(top,X),
    inference(congruence,[status(thm)],[c669]) ).

cnf(c671,plain,
    converse(converse(join(X2,composition(X,X2)))) = join(X2,composition(X,X2)),
    inference(substitution,[status(thm)],[c35]) ).

cnf(c672,plain,
    join(X2,composition(X,X2)) = converse(converse(join(X2,composition(X,X2)))),
    inference(symmetry,[status(thm)],[c671]) ).

cnf(c673,plain,
    composition(top,join(X2,composition(X,X2))) = composition(top,converse(converse(join(X2,composition(X,X2))))),
    inference(congruence,[status(thm)],[c672]) ).

cnf(c674,plain,
    top = converse(top),
    inference(symmetry,[status(thm)],[c174]) ).

cnf(c675,plain,
    composition(top,converse(converse(join(X2,composition(X,X2))))) = composition(converse(top),converse(converse(join(X2,composition(X,X2))))),
    inference(congruence,[status(thm)],[c674]) ).

cnf(c676,plain,
    converse(composition(converse(join(X2,composition(X,X2))),top)) = composition(converse(top),converse(converse(join(X2,composition(X,X2))))),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c677,plain,
    composition(converse(top),converse(converse(join(X2,composition(X,X2))))) = converse(composition(converse(join(X2,composition(X,X2))),top)),
    inference(symmetry,[status(thm)],[c676]) ).

cnf(c678,plain,
    converse(join(X2,composition(X,X2))) = join(converse(X2),converse(composition(X,X2))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c679,plain,
    composition(converse(join(X2,composition(X,X2))),top) = composition(join(converse(X2),converse(composition(X,X2))),top),
    inference(congruence,[status(thm)],[c678]) ).

cnf(c680,plain,
    composition(join(converse(X2),converse(composition(X,X2))),top) = join(composition(converse(X2),top),composition(converse(composition(X,X2)),top)),
    inference(substitution,[status(thm)],[c665]) ).

cnf(c681,plain,
    join(zero,meet(top,complement(zero))) = complement(zero),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c682,plain,
    complement(zero) = join(zero,meet(top,complement(zero))),
    inference(symmetry,[status(thm)],[c681]) ).

cnf(c683,plain,
    meet(top,zero) = zero,
    inference(substitution,[status(thm)],[c206]) ).

cnf(c684,plain,
    zero = meet(top,zero),
    inference(symmetry,[status(thm)],[c683]) ).

cnf(c685,plain,
    join(zero,meet(top,complement(zero))) = join(meet(top,zero),meet(top,complement(zero))),
    inference(congruence,[status(thm)],[c684]) ).

cnf(c686,plain,
    join(meet(top,zero),meet(top,complement(zero))) = top,
    inference(substitution,[status(thm)],[c297]) ).

cnf(c687,plain,
    join(zero,meet(top,complement(zero))) = top,
    inference(transitivity,[status(thm)],[c685,c686]) ).

cnf(c688,plain,
    complement(zero) = top,
    inference(transitivity,[status(thm)],[c682,c687]) ).

cnf(c689,plain,
    top = complement(zero),
    inference(symmetry,[status(thm)],[c688]) ).

cnf(c690,plain,
    composition(converse(composition(X,X2)),top) = composition(converse(composition(X,X2)),complement(zero)),
    inference(congruence,[status(thm)],[c689]) ).

cnf(c691,plain,
    join(composition(converse(X2),top),composition(converse(composition(X,X2)),top)) = join(composition(converse(X2),top),composition(converse(composition(X,X2)),complement(zero))),
    inference(congruence,[status(thm)],[c690]) ).

cnf(c692,plain,
    complement(complement(composition(converse(X),top))) = composition(converse(X),top),
    inference(substitution,[status(thm)],[c438]) ).

cnf(c693,plain,
    composition(converse(X),top) = complement(complement(composition(converse(X),top))),
    inference(symmetry,[status(thm)],[c692]) ).

cnf(c694,plain,
    join(composition(converse(X2),top),composition(converse(composition(X,X2)),complement(zero))) = join(complement(complement(composition(converse(X2),top))),composition(converse(composition(X,X2)),complement(zero))),
    inference(congruence,[status(thm)],[c693]) ).

cnf(c695,axiom,
    composition(A2,composition(B2,C2)) = composition(composition(A2,B2),C2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).

cnf(c696,plain,
    composition(X2,composition(X,complement(composition(converse(X),top)))) = composition(composition(X2,X),complement(composition(converse(X),top))),
    inference(substitution,[status(thm)],[c695]) ).

cnf(c697,plain,
    composition(composition(X2,X),complement(composition(converse(X),top))) = composition(X2,composition(X,complement(composition(converse(X),top)))),
    inference(symmetry,[status(thm)],[c696]) ).

cnf(c698,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c699,plain,
    X = converse(converse(X)),
    inference(symmetry,[status(thm)],[c698]) ).

cnf(c700,plain,
    composition(X,complement(composition(converse(X),top))) = composition(converse(converse(X)),complement(composition(converse(X),top))),
    inference(congruence,[status(thm)],[c699]) ).

cnf(c701,plain,
    join(zero,composition(converse(X),complement(composition(X,top)))) = composition(converse(X),complement(composition(X,top))),
    inference(substitution,[status(thm)],[c247]) ).

cnf(c702,plain,
    composition(converse(X),complement(composition(X,top))) = join(zero,composition(converse(X),complement(composition(X,top)))),
    inference(symmetry,[status(thm)],[c701]) ).

cnf(c703,plain,
    zero = complement(top),
    inference(symmetry,[status(thm)],[c12]) ).

cnf(c704,plain,
    join(zero,composition(converse(X),complement(composition(X,top)))) = join(complement(top),composition(converse(X),complement(composition(X,top)))),
    inference(congruence,[status(thm)],[c703]) ).

cnf(c705,plain,
    join(complement(top),composition(converse(X),complement(composition(X,top)))) = complement(top),
    inference(substitution,[status(thm)],[c68]) ).

cnf(c706,plain,
    join(complement(top),composition(converse(X),complement(composition(X,top)))) = zero,
    inference(transitivity,[status(thm)],[c705,c12]) ).

cnf(c707,plain,
    join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
    inference(transitivity,[status(thm)],[c704,c706]) ).

cnf(c708,plain,
    composition(converse(X),complement(composition(X,top))) = zero,
    inference(transitivity,[status(thm)],[c702,c707]) ).

cnf(c709,plain,
    composition(converse(converse(X)),complement(composition(converse(X),top))) = zero,
    inference(substitution,[status(thm)],[c708]) ).

cnf(c710,plain,
    composition(X,complement(composition(converse(X),top))) = zero,
    inference(transitivity,[status(thm)],[c700,c709]) ).

cnf(c711,plain,
    composition(X2,composition(X,complement(composition(converse(X),top)))) = composition(X2,zero),
    inference(congruence,[status(thm)],[c710]) ).

cnf(c712,plain,
    join(composition(X,zero),zero) = composition(X,zero),
    inference(substitution,[status(thm)],[c246]) ).

cnf(c713,plain,
    composition(X,zero) = join(composition(X,zero),zero),
    inference(symmetry,[status(thm)],[c712]) ).

cnf(c714,plain,
    top = converse(top),
    inference(symmetry,[status(thm)],[c174]) ).

cnf(c715,plain,
    composition(top,X) = composition(converse(top),X),
    inference(congruence,[status(thm)],[c714]) ).

cnf(c716,plain,
    join(X,composition(top,X)) = join(X,composition(converse(top),X)),
    inference(congruence,[status(thm)],[c715]) ).

cnf(c717,plain,
    join(X,one) = join(one,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c718,plain,
    join(one,X) = join(X,one),
    inference(symmetry,[status(thm)],[c717]) ).

cnf(c719,plain,
    composition(join(one,X),X2) = composition(join(X,one),X2),
    inference(congruence,[status(thm)],[c718]) ).

cnf(c720,plain,
    join(one,X) = join(X,one),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c721,plain,
    join(X,one) = join(one,X),
    inference(symmetry,[status(thm)],[c720]) ).

cnf(c722,plain,
    composition(join(X2,one),X) = composition(join(one,X2),X),
    inference(congruence,[status(thm)],[c721]) ).

cnf(c723,plain,
    one = converse(one),
    inference(symmetry,[status(thm)],[c56]) ).

cnf(c724,plain,
    join(one,X) = join(converse(one),X),
    inference(congruence,[status(thm)],[c723]) ).

cnf(c725,plain,
    composition(join(one,X2),X) = composition(join(converse(one),X2),X),
    inference(congruence,[status(thm)],[c724]) ).

cnf(c726,plain,
    composition(join(converse(one),X2),X) = join(composition(converse(one),X),composition(X2,X)),
    inference(substitution,[status(thm)],[c665]) ).

cnf(c727,plain,
    join(composition(converse(one),X),composition(X2,X)) = join(X,composition(X2,X)),
    inference(congruence,[status(thm)],[c49]) ).

cnf(c728,plain,
    composition(join(converse(one),X2),X) = join(X,composition(X2,X)),
    inference(transitivity,[status(thm)],[c726,c727]) ).

cnf(c729,plain,
    composition(join(one,X2),X) = join(X,composition(X2,X)),
    inference(transitivity,[status(thm)],[c725,c728]) ).

cnf(c730,plain,
    composition(join(X2,one),X) = join(X,composition(X2,X)),
    inference(transitivity,[status(thm)],[c722,c729]) ).

cnf(c731,plain,
    composition(join(X,one),X2) = join(X2,composition(X,X2)),
    inference(substitution,[status(thm)],[c730]) ).

cnf(c732,plain,
    composition(join(one,X),X2) = join(X2,composition(X,X2)),
    inference(transitivity,[status(thm)],[c719,c731]) ).

cnf(c733,plain,
    composition(join(one,converse(top)),X) = join(X,composition(converse(top),X)),
    inference(substitution,[status(thm)],[c732]) ).

cnf(c734,plain,
    join(X,composition(converse(top),X)) = composition(join(one,converse(top)),X),
    inference(symmetry,[status(thm)],[c733]) ).

cnf(c735,plain,
    join(one,converse(top)) = top,
    inference(substitution,[status(thm)],[c165]) ).

cnf(c736,plain,
    composition(join(one,converse(top)),X) = composition(top,X),
    inference(congruence,[status(thm)],[c735]) ).

cnf(c737,plain,
    join(X,composition(converse(top),X)) = composition(top,X),
    inference(transitivity,[status(thm)],[c734,c736]) ).

cnf(c738,plain,
    join(X,composition(top,X)) = composition(top,X),
    inference(transitivity,[status(thm)],[c716,c737]) ).

cnf(c739,plain,
    join(zero,composition(top,zero)) = composition(top,zero),
    inference(substitution,[status(thm)],[c738]) ).

cnf(c740,plain,
    composition(top,zero) = join(zero,composition(top,zero)),
    inference(symmetry,[status(thm)],[c739]) ).

cnf(c741,plain,
    top = converse(top),
    inference(symmetry,[status(thm)],[c174]) ).

cnf(c742,plain,
    composition(top,zero) = composition(converse(top),zero),
    inference(congruence,[status(thm)],[c741]) ).

cnf(c743,plain,
    join(zero,composition(top,zero)) = join(zero,composition(converse(top),zero)),
    inference(congruence,[status(thm)],[c742]) ).

cnf(c744,plain,
    zero = complement(top),
    inference(symmetry,[status(thm)],[c12]) ).

cnf(c745,plain,
    join(zero,composition(converse(top),zero)) = join(complement(top),composition(converse(top),zero)),
    inference(congruence,[status(thm)],[c744]) ).

cnf(c746,plain,
    zero = complement(top),
    inference(symmetry,[status(thm)],[c12]) ).

cnf(c747,plain,
    composition(converse(top),zero) = composition(converse(top),complement(top)),
    inference(congruence,[status(thm)],[c746]) ).

cnf(c748,plain,
    join(complement(top),composition(converse(top),zero)) = join(complement(top),composition(converse(top),complement(top))),
    inference(congruence,[status(thm)],[c747]) ).

cnf(c749,plain,
    join(top,composition(top,top)) = composition(top,top),
    inference(substitution,[status(thm)],[c738]) ).

cnf(c750,plain,
    composition(top,top) = join(top,composition(top,top)),
    inference(symmetry,[status(thm)],[c749]) ).

cnf(c751,plain,
    join(complement(X),join(X2,X)) = join(join(X2,X),complement(X)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c752,plain,
    join(join(X2,X),complement(X)) = join(complement(X),join(X2,X)),
    inference(symmetry,[status(thm)],[c751]) ).

cnf(c753,plain,
    join(join(X,X3),X2) = join(X2,join(X,X3)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c754,plain,
    join(X2,join(X,X3)) = join(join(X,X3),X2),
    inference(symmetry,[status(thm)],[c753]) ).

cnf(c755,plain,
    join(X,X2) = join(X2,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c756,plain,
    join(join(X,X3),X2) = join(join(X3,X),X2),
    inference(congruence,[status(thm)],[c755]) ).

cnf(c757,plain,
    join(X3,join(X,X2)) = join(join(X3,X),X2),
    inference(substitution,[status(thm)],[c125]) ).

cnf(c758,plain,
    join(join(X3,X),X2) = join(X3,join(X,X2)),
    inference(symmetry,[status(thm)],[c757]) ).

cnf(c759,plain,
    join(X,X2) = join(X2,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c760,plain,
    join(X3,join(X,X2)) = join(X3,join(X2,X)),
    inference(congruence,[status(thm)],[c759]) ).

cnf(c761,plain,
    join(join(X3,X),X2) = join(X3,join(X2,X)),
    inference(transitivity,[status(thm)],[c758,c760]) ).

cnf(c762,plain,
    join(join(X,X3),X2) = join(X3,join(X2,X)),
    inference(transitivity,[status(thm)],[c756,c761]) ).

cnf(c763,plain,
    join(X2,join(X,X3)) = join(X3,join(X2,X)),
    inference(transitivity,[status(thm)],[c754,c762]) ).

cnf(c764,plain,
    join(X,join(X2,X3)) = join(X3,join(X,X2)),
    inference(substitution,[status(thm)],[c763]) ).

cnf(c765,plain,
    join(X,X2) = join(X2,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c766,plain,
    join(X3,join(X,X2)) = join(X3,join(X2,X)),
    inference(congruence,[status(thm)],[c765]) ).

cnf(c767,plain,
    join(X,join(X2,X3)) = join(X3,join(X2,X)),
    inference(transitivity,[status(thm)],[c764,c766]) ).

cnf(c768,plain,
    join(complement(X),join(X2,X)) = join(X,join(X2,complement(X))),
    inference(substitution,[status(thm)],[c767]) ).

cnf(c769,plain,
    join(X,join(X2,complement(X))) = join(X2,top),
    inference(substitution,[status(thm)],[c133]) ).

cnf(c770,plain,
    join(X,top) = join(top,X),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c771,plain,
    join(X,join(X2,complement(X))) = join(top,X2),
    inference(transitivity,[status(thm)],[c769,c770]) ).

cnf(c772,plain,
    join(complement(X),join(X2,X)) = join(top,X2),
    inference(transitivity,[status(thm)],[c768,c771]) ).

cnf(c773,plain,
    join(join(X2,X),complement(X)) = join(top,X2),
    inference(transitivity,[status(thm)],[c752,c772]) ).

cnf(c774,plain,
    join(top,X2) = join(join(X2,X),complement(X)),
    inference(symmetry,[status(thm)],[c773]) ).

cnf(c775,plain,
    join(complement(X),join(X2,X)) = join(join(X2,X),complement(X)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c776,plain,
    join(join(X2,X),complement(X)) = join(complement(X),join(X2,X)),
    inference(symmetry,[status(thm)],[c775]) ).

cnf(c777,plain,
    join(complement(X),join(X2,X)) = join(X,join(complement(X),X2)),
    inference(substitution,[status(thm)],[c763]) ).

cnf(c778,plain,
    join(X2,join(complement(X2),X3)) = join(X,top),
    inference(substitution,[status(thm)],[c155]) ).

cnf(c779,plain,
    join(X,join(complement(X),X2)) = top,
    inference(transitivity,[status(thm)],[c778,c163]) ).

cnf(c780,plain,
    join(complement(X),join(X2,X)) = top,
    inference(transitivity,[status(thm)],[c777,c779]) ).

cnf(c781,plain,
    join(join(X2,X),complement(X)) = top,
    inference(transitivity,[status(thm)],[c776,c780]) ).

cnf(c782,plain,
    join(top,X) = top,
    inference(transitivity,[status(thm)],[c774,c781]) ).

cnf(c783,plain,
    join(top,composition(top,top)) = top,
    inference(substitution,[status(thm)],[c782]) ).

cnf(c784,plain,
    composition(top,top) = top,
    inference(transitivity,[status(thm)],[c750,c783]) ).

cnf(c785,plain,
    top = composition(top,top),
    inference(symmetry,[status(thm)],[c784]) ).

cnf(c786,plain,
    complement(top) = complement(composition(top,top)),
    inference(congruence,[status(thm)],[c785]) ).

cnf(c787,plain,
    composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
    inference(congruence,[status(thm)],[c786]) ).

cnf(c788,plain,
    join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
    inference(congruence,[status(thm)],[c787]) ).

cnf(c789,plain,
    join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
    inference(substitution,[status(thm)],[c68]) ).

cnf(c790,plain,
    join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
    inference(transitivity,[status(thm)],[c789,c12]) ).

cnf(c791,plain,
    join(complement(top),composition(converse(top),complement(top))) = zero,
    inference(transitivity,[status(thm)],[c788,c790]) ).

cnf(c792,plain,
    join(complement(top),composition(converse(top),zero)) = zero,
    inference(transitivity,[status(thm)],[c748,c791]) ).

cnf(c793,plain,
    join(zero,composition(converse(top),zero)) = zero,
    inference(transitivity,[status(thm)],[c745,c792]) ).

cnf(c794,plain,
    join(zero,composition(top,zero)) = zero,
    inference(transitivity,[status(thm)],[c743,c793]) ).

cnf(c795,plain,
    composition(top,zero) = zero,
    inference(transitivity,[status(thm)],[c740,c794]) ).

cnf(c796,plain,
    zero = composition(top,zero),
    inference(symmetry,[status(thm)],[c795]) ).

cnf(c797,plain,
    join(composition(X,zero),zero) = join(composition(X,zero),composition(top,zero)),
    inference(congruence,[status(thm)],[c796]) ).

cnf(c798,plain,
    composition(join(X,top),zero) = join(composition(X,zero),composition(top,zero)),
    inference(substitution,[status(thm)],[c665]) ).

cnf(c799,plain,
    join(composition(X,zero),composition(top,zero)) = composition(join(X,top),zero),
    inference(symmetry,[status(thm)],[c798]) ).

cnf(c800,plain,
    join(X2,top) = join(X,top),
    inference(symmetry,[status(thm)],[c152]) ).

cnf(c801,plain,
    composition(join(X2,top),zero) = composition(join(X,top),zero),
    inference(congruence,[status(thm)],[c800]) ).

cnf(c802,plain,
    composition(join(X,top),zero) = composition(top,zero),
    inference(congruence,[status(thm)],[c163]) ).

cnf(c803,plain,
    composition(join(X,top),zero) = zero,
    inference(transitivity,[status(thm)],[c802,c795]) ).

cnf(c804,plain,
    composition(join(X,top),zero) = zero,
    inference(transitivity,[status(thm)],[c801,c803]) ).

cnf(c805,plain,
    join(composition(X,zero),composition(top,zero)) = zero,
    inference(transitivity,[status(thm)],[c799,c804]) ).

cnf(c806,plain,
    join(composition(X,zero),zero) = zero,
    inference(transitivity,[status(thm)],[c797,c805]) ).

cnf(c807,plain,
    composition(X,zero) = zero,
    inference(transitivity,[status(thm)],[c713,c806]) ).

cnf(c808,plain,
    composition(X2,composition(X,complement(composition(converse(X),top)))) = zero,
    inference(transitivity,[status(thm)],[c711,c807]) ).

cnf(c809,plain,
    composition(composition(X2,X),complement(composition(converse(X),top))) = zero,
    inference(transitivity,[status(thm)],[c697,c808]) ).

cnf(c810,plain,
    composition(composition(X,X2),complement(composition(converse(X2),top))) = zero,
    inference(substitution,[status(thm)],[c809]) ).

cnf(c811,plain,
    zero = composition(composition(X,X2),complement(composition(converse(X2),top))),
    inference(symmetry,[status(thm)],[c810]) ).

cnf(c812,plain,
    complement(zero) = complement(composition(composition(X,X2),complement(composition(converse(X2),top)))),
    inference(congruence,[status(thm)],[c811]) ).

cnf(c813,plain,
    composition(converse(composition(X,X2)),complement(zero)) = composition(converse(composition(X,X2)),complement(composition(composition(X,X2),complement(composition(converse(X2),top))))),
    inference(congruence,[status(thm)],[c812]) ).

cnf(c814,plain,
    join(complement(complement(composition(converse(X2),top))),composition(converse(composition(X,X2)),complement(zero))) = join(complement(complement(composition(converse(X2),top))),composition(converse(composition(X,X2)),complement(composition(composition(X,X2),complement(composition(converse(X2),top)))))),
    inference(congruence,[status(thm)],[c813]) ).

cnf(c815,plain,
    join(complement(complement(composition(converse(X2),top))),composition(converse(composition(X,X2)),complement(composition(composition(X,X2),complement(composition(converse(X2),top)))))) = complement(complement(composition(converse(X2),top))),
    inference(substitution,[status(thm)],[c68]) ).

cnf(c816,plain,
    complement(complement(composition(converse(X),top))) = composition(converse(X),top),
    inference(substitution,[status(thm)],[c438]) ).

cnf(c817,plain,
    join(complement(complement(composition(converse(X2),top))),composition(converse(composition(X,X2)),complement(composition(composition(X,X2),complement(composition(converse(X2),top)))))) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c815,c816]) ).

cnf(c818,plain,
    join(complement(complement(composition(converse(X2),top))),composition(converse(composition(X,X2)),complement(zero))) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c814,c817]) ).

cnf(c819,plain,
    join(composition(converse(X2),top),composition(converse(composition(X,X2)),complement(zero))) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c694,c818]) ).

cnf(c820,plain,
    join(composition(converse(X2),top),composition(converse(composition(X,X2)),top)) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c691,c819]) ).

cnf(c821,plain,
    composition(join(converse(X2),converse(composition(X,X2))),top) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c680,c820]) ).

cnf(c822,plain,
    composition(converse(join(X2,composition(X,X2))),top) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c679,c821]) ).

cnf(c823,plain,
    converse(composition(converse(join(X2,composition(X,X2))),top)) = converse(composition(converse(X2),top)),
    inference(congruence,[status(thm)],[c822]) ).

cnf(c824,plain,
    converse(composition(converse(X),top)) = composition(converse(top),converse(converse(X))),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c825,plain,
    composition(converse(top),converse(converse(X))) = composition(top,converse(converse(X))),
    inference(congruence,[status(thm)],[c174]) ).

cnf(c826,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c827,plain,
    composition(top,converse(converse(X))) = composition(top,X),
    inference(congruence,[status(thm)],[c826]) ).

cnf(c828,plain,
    composition(converse(top),converse(converse(X))) = composition(top,X),
    inference(transitivity,[status(thm)],[c825,c827]) ).

cnf(c829,plain,
    converse(composition(converse(X),top)) = composition(top,X),
    inference(transitivity,[status(thm)],[c824,c828]) ).

cnf(c830,plain,
    converse(composition(converse(join(X2,composition(X,X2))),top)) = composition(top,X2),
    inference(transitivity,[status(thm)],[c823,c829]) ).

cnf(c831,plain,
    composition(converse(top),converse(converse(join(X2,composition(X,X2))))) = composition(top,X2),
    inference(transitivity,[status(thm)],[c677,c830]) ).

cnf(c832,plain,
    composition(top,converse(converse(join(X2,composition(X,X2))))) = composition(top,X2),
    inference(transitivity,[status(thm)],[c675,c831]) ).

cnf(c833,plain,
    composition(top,join(X2,composition(X,X2))) = composition(top,X2),
    inference(transitivity,[status(thm)],[c673,c832]) ).

cnf(c834,plain,
    composition(top,X2) = composition(top,join(X2,composition(X,X2))),
    inference(symmetry,[status(thm)],[c833]) ).

cnf(c835,plain,
    composition(join(X3,complement(X3)),X2) = composition(top,join(X2,composition(X,X2))),
    inference(transitivity,[status(thm)],[c670,c834]) ).

cnf(c836,plain,
    join(composition(X3,X2),composition(complement(X3),X2)) = composition(top,join(X2,composition(X,X2))),
    inference(transitivity,[status(thm)],[c667,c835]) ).

cnf(c837,plain,
    join(composition(composition(X3,converse(X2)),X),composition(complement(composition(X3,converse(X2))),X)) = composition(top,join(X,composition(X4,X))),
    inference(substitution,[status(thm)],[c836]) ).

cnf(c838,plain,
    converse(join(composition(composition(X4,converse(X3)),X2),composition(complement(composition(X4,converse(X3))),X2))) = converse(composition(top,join(X2,composition(X,X2)))),
    inference(congruence,[status(thm)],[c837]) ).

cnf(c839,plain,
    converse(composition(top,join(X2,composition(X,X2)))) = composition(converse(join(X2,composition(X,X2))),converse(top)),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c840,plain,
    composition(converse(join(X2,composition(X,X2))),converse(top)) = composition(converse(join(X2,composition(X,X2))),top),
    inference(congruence,[status(thm)],[c174]) ).

cnf(c841,plain,
    composition(converse(join(X2,composition(X,X2))),converse(top)) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c840,c822]) ).

cnf(c842,plain,
    converse(composition(top,join(X2,composition(X,X2)))) = composition(converse(X2),top),
    inference(transitivity,[status(thm)],[c839,c841]) ).

cnf(c843,plain,
    converse(join(composition(composition(X3,converse(X2)),X),composition(complement(composition(X3,converse(X2))),X))) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c838,c842]) ).

cnf(c844,plain,
    join(converse(composition(composition(X3,converse(X2)),X)),converse(composition(complement(composition(X3,converse(X2))),X))) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c664,c843]) ).

cnf(c845,plain,
    join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),converse(complement(composition(X3,converse(X2)))))) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c662,c844]) ).

cnf(c846,plain,
    join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),complement(composition(X2,converse(X3))))) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c659,c845]) ).

cnf(c847,plain,
    join(converse(composition(composition(X,converse(X)),X)),composition(converse(X),complement(composition(X,converse(X))))) = composition(converse(X),top),
    inference(substitution,[status(thm)],[c846]) ).

cnf(c848,plain,
    join(complement(converse(X)),join(converse(composition(composition(X,converse(X)),X)),composition(converse(X),complement(composition(X,converse(X)))))) = join(complement(converse(X)),composition(converse(X),top)),
    inference(congruence,[status(thm)],[c847]) ).

cnf(c849,plain,
    join(composition(X,top),complement(X)) = join(complement(X),composition(X,top)),
    inference(substitution,[status(thm)],[c19]) ).

cnf(c850,plain,
    join(complement(X),composition(X,top)) = join(composition(X,top),complement(X)),
    inference(symmetry,[status(thm)],[c849]) ).

cnf(c851,plain,
    join(composition(X,top),complement(join(X,composition(X,top)))) = join(composition(X,top),complement(X)),
    inference(substitution,[status(thm)],[c423]) ).

cnf(c852,plain,
    join(composition(X,top),complement(X)) = join(composition(X,top),complement(join(X,composition(X,top)))),
    inference(symmetry,[status(thm)],[c851]) ).

cnf(c853,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c854,plain,
    X = converse(converse(X)),
    inference(symmetry,[status(thm)],[c853]) ).

cnf(c855,plain,
    composition(X,top) = composition(converse(converse(X)),top),
    inference(congruence,[status(thm)],[c854]) ).

cnf(c856,plain,
    join(X,composition(X,top)) = join(X,composition(converse(converse(X)),top)),
    inference(congruence,[status(thm)],[c855]) ).

cnf(c857,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c858,plain,
    X = converse(converse(X)),
    inference(symmetry,[status(thm)],[c857]) ).

cnf(c859,plain,
    join(X,composition(converse(converse(X)),top)) = join(converse(converse(X)),composition(converse(converse(X)),top)),
    inference(congruence,[status(thm)],[c858]) ).

cnf(c860,plain,
    top = converse(top),
    inference(symmetry,[status(thm)],[c174]) ).

cnf(c861,plain,
    composition(converse(X),top) = composition(converse(X),converse(top)),
    inference(congruence,[status(thm)],[c860]) ).

cnf(c862,plain,
    join(converse(X),composition(converse(X),top)) = join(converse(X),composition(converse(X),converse(top))),
    inference(congruence,[status(thm)],[c861]) ).

cnf(c863,plain,
    converse(composition(top,X)) = composition(converse(X),converse(top)),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c864,plain,
    composition(converse(X),converse(top)) = converse(composition(top,X)),
    inference(symmetry,[status(thm)],[c863]) ).

cnf(c865,plain,
    join(converse(X),composition(converse(X),converse(top))) = join(converse(X),converse(composition(top,X))),
    inference(congruence,[status(thm)],[c864]) ).

cnf(c866,plain,
    converse(join(X,composition(top,X))) = join(converse(X),converse(composition(top,X))),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c867,plain,
    join(converse(X),converse(composition(top,X))) = converse(join(X,composition(top,X))),
    inference(symmetry,[status(thm)],[c866]) ).

cnf(c868,plain,
    converse(join(X,composition(top,X))) = converse(composition(top,X)),
    inference(congruence,[status(thm)],[c738]) ).

cnf(c869,plain,
    converse(composition(top,X)) = composition(converse(X),converse(top)),
    inference(substitution,[status(thm)],[c39]) ).

cnf(c870,plain,
    composition(converse(X),converse(top)) = composition(converse(X),top),
    inference(congruence,[status(thm)],[c174]) ).

cnf(c871,plain,
    converse(composition(top,X)) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c869,c870]) ).

cnf(c872,plain,
    converse(join(X,composition(top,X))) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c868,c871]) ).

cnf(c873,plain,
    join(converse(X),converse(composition(top,X))) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c867,c872]) ).

cnf(c874,plain,
    join(converse(X),composition(converse(X),converse(top))) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c865,c873]) ).

cnf(c875,plain,
    join(converse(X),composition(converse(X),top)) = composition(converse(X),top),
    inference(transitivity,[status(thm)],[c862,c874]) ).

cnf(c876,plain,
    join(converse(converse(X)),composition(converse(converse(X)),top)) = composition(converse(converse(X)),top),
    inference(substitution,[status(thm)],[c875]) ).

cnf(c877,plain,
    converse(converse(X)) = X,
    inference(substitution,[status(thm)],[c35]) ).

cnf(c878,plain,
    composition(converse(converse(X)),top) = composition(X,top),
    inference(congruence,[status(thm)],[c877]) ).

cnf(c879,plain,
    join(converse(converse(X)),composition(converse(converse(X)),top)) = composition(X,top),
    inference(transitivity,[status(thm)],[c876,c878]) ).

cnf(c880,plain,
    join(X,composition(converse(converse(X)),top)) = composition(X,top),
    inference(transitivity,[status(thm)],[c859,c879]) ).

cnf(c881,plain,
    join(X,composition(X,top)) = composition(X,top),
    inference(transitivity,[status(thm)],[c856,c880]) ).

cnf(c882,plain,
    complement(join(X,composition(X,top))) = complement(composition(X,top)),
    inference(congruence,[status(thm)],[c881]) ).

cnf(c883,plain,
    join(composition(X,top),complement(join(X,composition(X,top)))) = join(composition(X,top),complement(composition(X,top))),
    inference(congruence,[status(thm)],[c882]) ).

cnf(c884,plain,
    top = join(composition(X,top),complement(composition(X,top))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c885,plain,
    join(composition(X,top),complement(composition(X,top))) = top,
    inference(symmetry,[status(thm)],[c884]) ).

cnf(c886,plain,
    join(composition(X,top),complement(join(X,composition(X,top)))) = top,
    inference(transitivity,[status(thm)],[c883,c885]) ).

cnf(c887,plain,
    join(composition(X,top),complement(X)) = top,
    inference(transitivity,[status(thm)],[c852,c886]) ).

cnf(c888,plain,
    join(complement(X),composition(X,top)) = top,
    inference(transitivity,[status(thm)],[c850,c887]) ).

cnf(c889,plain,
    join(complement(converse(X)),composition(converse(X),top)) = top,
    inference(substitution,[status(thm)],[c888]) ).

cnf(c890,plain,
    join(complement(converse(X)),join(converse(composition(composition(X,converse(X)),X)),composition(converse(X),complement(composition(X,converse(X)))))) = top,
    inference(transitivity,[status(thm)],[c848,c889]) ).

cnf(c891,plain,
    join(converse(composition(composition(X,converse(X)),X)),complement(converse(X))) = top,
    inference(transitivity,[status(thm)],[c581,c890]) ).

cnf(c892,plain,
    converse(join(converse(composition(composition(X,converse(X)),X)),complement(converse(X)))) = converse(top),
    inference(congruence,[status(thm)],[c891]) ).

cnf(c893,plain,
    converse(join(converse(composition(composition(X,converse(X)),X)),complement(converse(X)))) = top,
    inference(transitivity,[status(thm)],[c892,c174]) ).

cnf(c894,plain,
    join(converse(converse(composition(composition(X,converse(X)),X))),converse(complement(converse(X)))) = top,
    inference(transitivity,[status(thm)],[c570,c893]) ).

cnf(c895,plain,
    join(composition(composition(X,converse(X)),X),converse(complement(converse(X)))) = top,
    inference(transitivity,[status(thm)],[c568,c894]) ).

cnf(c896,plain,
    join(composition(composition(X,converse(X)),X),complement(X)) = top,
    inference(transitivity,[status(thm)],[c565,c895]) ).

cnf(c897,plain,
    join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))) = top,
    inference(transitivity,[status(thm)],[c424,c896]) ).

cnf(c898,plain,
    top = join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))),
    inference(symmetry,[status(thm)],[c897]) ).

cnf(c899,plain,
    meet(join(X,composition(composition(X,converse(X)),X)),top) = meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X))))),
    inference(congruence,[status(thm)],[c898]) ).

cnf(c900,plain,
    meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X))))) = meet(join(X,composition(composition(X,converse(X)),X)),composition(composition(X,converse(X)),X)),
    inference(substitution,[status(thm)],[c405]) ).

cnf(c901,plain,
    meet(join(X2,X),X) = meet(X,join(X2,X)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c902,plain,
    meet(X,join(X2,X)) = complement(join(complement(X),complement(join(X2,X)))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c903,plain,
    join(zero,complement(join(complement(X),complement(join(X2,X))))) = complement(join(complement(X),complement(join(X2,X)))),
    inference(substitution,[status(thm)],[c189]) ).

cnf(c904,plain,
    complement(join(complement(X),complement(join(X2,X)))) = join(zero,complement(join(complement(X),complement(join(X2,X))))),
    inference(symmetry,[status(thm)],[c903]) ).

cnf(c905,plain,
    complement(join(join(X,X2),complement(X2))) = meet(X2,complement(join(X,X2))),
    inference(substitution,[status(thm)],[c469]) ).

cnf(c906,plain,
    meet(X2,complement(join(X,X2))) = complement(join(join(X,X2),complement(X2))),
    inference(symmetry,[status(thm)],[c905]) ).

cnf(c907,plain,
    join(join(X,X2),complement(X2)) = join(top,X),
    inference(substitution,[status(thm)],[c773]) ).

cnf(c908,plain,
    complement(join(join(X,X2),complement(X2))) = complement(join(top,X)),
    inference(congruence,[status(thm)],[c907]) ).

cnf(c909,plain,
    complement(join(top,X)) = complement(top),
    inference(congruence,[status(thm)],[c782]) ).

cnf(c910,plain,
    complement(join(top,X)) = zero,
    inference(transitivity,[status(thm)],[c909,c12]) ).

cnf(c911,plain,
    complement(join(join(X,X2),complement(X2))) = zero,
    inference(transitivity,[status(thm)],[c908,c910]) ).

cnf(c912,plain,
    meet(X2,complement(join(X,X2))) = zero,
    inference(transitivity,[status(thm)],[c906,c911]) ).

cnf(c913,plain,
    meet(X,complement(join(X2,X))) = zero,
    inference(substitution,[status(thm)],[c912]) ).

cnf(c914,plain,
    zero = meet(X,complement(join(X2,X))),
    inference(symmetry,[status(thm)],[c913]) ).

cnf(c915,plain,
    join(zero,complement(join(complement(X),complement(join(X2,X))))) = join(meet(X,complement(join(X2,X))),complement(join(complement(X),complement(join(X2,X))))),
    inference(congruence,[status(thm)],[c914]) ).

cnf(c916,plain,
    join(meet(X,complement(join(X2,X))),complement(join(complement(X),complement(join(X2,X))))) = X,
    inference(substitution,[status(thm)],[c88]) ).

cnf(c917,plain,
    join(zero,complement(join(complement(X),complement(join(X2,X))))) = X,
    inference(transitivity,[status(thm)],[c915,c916]) ).

cnf(c918,plain,
    complement(join(complement(X),complement(join(X2,X)))) = X,
    inference(transitivity,[status(thm)],[c904,c917]) ).

cnf(c919,plain,
    meet(X,join(X2,X)) = X,
    inference(transitivity,[status(thm)],[c902,c918]) ).

cnf(c920,plain,
    meet(join(X2,X),X) = X,
    inference(transitivity,[status(thm)],[c901,c919]) ).

cnf(c921,plain,
    meet(join(X,composition(composition(X,converse(X)),X)),composition(composition(X,converse(X)),X)) = composition(composition(X,converse(X)),X),
    inference(substitution,[status(thm)],[c920]) ).

cnf(c922,plain,
    meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X))))) = composition(composition(X,converse(X)),X),
    inference(transitivity,[status(thm)],[c900,c921]) ).

cnf(c923,plain,
    meet(join(X,composition(composition(X,converse(X)),X)),top) = composition(composition(X,converse(X)),X),
    inference(transitivity,[status(thm)],[c899,c922]) ).

cnf(c924,plain,
    join(X,composition(composition(X,converse(X)),X)) = composition(composition(X,converse(X)),X),
    inference(transitivity,[status(thm)],[c197,c923]) ).

cnf(c925,plain,
    join(sk1,composition(composition(sk1,converse(sk1)),sk1)) = composition(composition(sk1,converse(sk1)),sk1),
    inference(substitution,[status(thm)],[c924]) ).

cnf(c926,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c925]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : REL045-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44  % Computer : n005.cluster.edu
% 0.16/0.44  % Model    : x86_64 x86_64
% 0.16/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44  % Memory   : 8046.5625MB
% 0.16/0.44  % OS       : Linux 6.8.0-71-generic
% 0.16/0.44  % CPULimit : 300
% 0.16/0.44  % WCLimit  : 300
% 0.16/0.44  % DateTime : Sun Sep 27 22:56:31 UTC 2026
% 0.16/0.44  % CPUTime  : 
% 0.16/0.44  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.13/3.23  Command-line arguments: --flatten --complete-subsets
% 21.13/3.23  
% 21.13/3.23  % SZS status Unsatisfiable
% 21.13/3.23  
% 21.13/3.37  % SZS output start CNFRefutation
% See solution above
% 28.32/4.18  
% 28.32/4.18  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------