%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL045-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:33:33 PM UTC 2026
% Result : Unsatisfiable 17.15s 2.68s
% Output : CNFRefutation 22.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 126
% Number of leaves : 15
% Syntax : Number of clauses : 1052 (1052 unt; 0 nHn; 78 RR)
% Number of literals : 1052 (1051 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 1642 ( 122 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_17) ).
cnf(c2,axiom,
meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c3,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
join(A2,B2) = join(B2,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c5,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
complement(join(complement(X2),complement(X))) = meet(X2,X),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
complement(join(complement(X),complement(X2))) = meet(X2,X),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
meet(X,X2) = meet(X2,X),
inference(transitivity,[status(thm)],[c3,c10]) ).
cnf(c12,plain,
meet(join(X2,X),X) = meet(X,join(X2,X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
meet(X,join(X2,X)) = complement(join(complement(X),complement(join(X2,X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c11]) ).
cnf(c15,axiom,
top = join(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
cnf(c16,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c21,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c19,c22]) ).
cnf(c24,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c17,c23]) ).
cnf(c25,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c31,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c37,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c39,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c43,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c46,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c44,c47]) ).
cnf(c49,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c51,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c49,c50]) ).
cnf(c52,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c41,c51]) ).
cnf(c53,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
composition(converse(one),one) = converse(one),
inference(substitution,[status(thm)],[c45]) ).
cnf(c57,plain,
converse(one) = composition(converse(one),one),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
composition(converse(one),one) = one,
inference(substitution,[status(thm)],[c52]) ).
cnf(c59,plain,
converse(one) = one,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
composition(one,X) = composition(converse(one),X),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c61,c52]) ).
cnf(c63,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,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)],[c4]) ).
cnf(c68,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)],[c67]) ).
cnf(c69,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c70,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c68,c70]) ).
cnf(c72,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c66,c72]) ).
cnf(c74,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c55,c73]) ).
cnf(c75,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c79,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)],[c78]) ).
cnf(c80,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(c81,plain,
X2 = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))) = X2,
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
join(meet(X2,X),complement(join(complement(X2),X))) = X2,
inference(transitivity,[status(thm)],[c79,c82]) ).
cnf(c84,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c77,c84]) ).
cnf(c86,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c37,c85]) ).
cnf(c87,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c35,c87]) ).
cnf(c89,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c14,c88]) ).
cnf(c90,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c11]) ).
cnf(c93,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c95,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c97,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c99,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,axiom,
converse(join(A2,B2)) = join(converse(A2),converse(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(c102,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c105,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c103,c106]) ).
cnf(c108,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c100,c108]) ).
cnf(c110,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
converse(top) = join(complement(X),converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(complement(converse(complement(X)))))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c114,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
join(X2,join(complement(X2),X)) = join(X2,join(X,complement(X2))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c117,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c120,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c122,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c4]) ).
cnf(c125,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c120,c125]) ).
cnf(c127,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c118,c126]) ).
cnf(c128,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c129,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c127]) ).
cnf(c131,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c133,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c134,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c132,c134]) ).
cnf(c136,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c131,c135]) ).
cnf(c137,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c129,c136]) ).
cnf(c138,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c127]) ).
cnf(c141,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c127]) ).
cnf(c142,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c137]) ).
cnf(c144,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
join(X,join(top,complement(X))) = join(X2,top),
inference(transitivity,[status(thm)],[c140,c144]) ).
cnf(c146,plain,
join(X2,top) = join(X,top),
inference(transitivity,[status(thm)],[c139,c145]) ).
cnf(c147,plain,
join(X2,top) = join(X,top),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
join(X3,join(X2,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c127,c147]) ).
cnf(c149,plain,
join(X3,join(complement(X3),X2)) = join(X,top),
inference(transitivity,[status(thm)],[c115,c148]) ).
cnf(c150,plain,
join(X2,join(complement(X2),converse(complement(converse(complement(X2)))))) = join(X,top),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = join(X3,top),
inference(substitution,[status(thm)],[c149]) ).
cnf(c152,plain,
join(X3,top) = join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = join(X2,complement(X2)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c154,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c155,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = top,
inference(transitivity,[status(thm)],[c153,c155]) ).
cnf(c157,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c152,c156]) ).
cnf(c158,plain,
join(X,join(complement(X),converse(complement(converse(complement(X)))))) = top,
inference(transitivity,[status(thm)],[c150,c157]) ).
cnf(c159,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c112,c158]) ).
cnf(c160,plain,
top = join(X,converse(top)),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
converse(top) = converse(join(X,converse(top))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
converse(join(X,converse(top))) = join(converse(X),converse(converse(top))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c163,plain,
converse(converse(top)) = top,
inference(substitution,[status(thm)],[c38]) ).
cnf(c164,plain,
join(converse(X),converse(converse(top))) = join(converse(X),top),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
join(converse(X),top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c166,plain,
join(converse(X),converse(converse(top))) = top,
inference(transitivity,[status(thm)],[c164,c165]) ).
cnf(c167,plain,
converse(join(X,converse(top))) = top,
inference(transitivity,[status(thm)],[c162,c166]) ).
cnf(c168,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c161,c167]) ).
cnf(c169,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
meet(X,top) = meet(X,converse(top)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
join(meet(X,top),complement(top)) = join(meet(X,converse(top)),complement(top)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
join(complement(X),converse(top)) = top,
inference(substitution,[status(thm)],[c159]) ).
cnf(c173,plain,
top = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
complement(top) = complement(join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
join(meet(X,converse(top)),complement(top)) = join(meet(X,converse(top)),complement(join(complement(X),converse(top)))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
join(meet(X,converse(top)),complement(join(complement(X),converse(top)))) = X,
inference(substitution,[status(thm)],[c83]) ).
cnf(c177,plain,
join(meet(X,converse(top)),complement(top)) = X,
inference(transitivity,[status(thm)],[c175,c176]) ).
cnf(c178,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c171,c177]) ).
cnf(c179,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c97,c178]) ).
cnf(c180,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c95,c179]) ).
cnf(c181,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c93,c180]) ).
cnf(c182,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c91,c182]) ).
cnf(c184,plain,
join(zero,complement(join(complement(X),complement(join(X2,X))))) = complement(join(complement(X),complement(join(X2,X)))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
complement(join(complement(X),complement(join(X2,X)))) = join(zero,complement(join(complement(X),complement(join(X2,X))))),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c187,plain,
join(X2,complement(X)) = join(complement(X),X2),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
complement(join(X2,complement(X))) = complement(join(complement(X),X2)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c11]) ).
cnf(c190,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c191,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c192,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c194,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c193,c180]) ).
cnf(c195,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c192,c194]) ).
cnf(c196,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c190,c195]) ).
cnf(c197,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c189,c196]) ).
cnf(c198,plain,
X = meet(top,X),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
join(complement(X),X2) = join(complement(X),meet(top,X2)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
complement(join(complement(X),X2)) = complement(join(complement(X),meet(top,X2))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c202,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
meet(X3,join(complement(X2),complement(X))) = meet(X3,join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
meet(X3,join(complement(X),complement(X2))) = meet(join(complement(X),complement(X2)),X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c205,plain,
meet(join(complement(X),complement(X2)),X3) = complement(join(complement(join(complement(X),complement(X2))),complement(X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c206,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c207,plain,
complement(join(complement(X),complement(X2))) = meet(X,X2),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
join(complement(join(complement(X),complement(X2))),complement(X3)) = join(meet(X,X2),complement(X3)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = complement(join(meet(X,X2),complement(X3))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
join(meet(X,X2),complement(X3)) = join(complement(X3),meet(X,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c211,plain,
complement(join(meet(X,X2),complement(X3))) = complement(join(complement(X3),meet(X,X2))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c213,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
join(complement(X3),meet(X,X2)) = join(complement(X3),meet(X2,X)),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
complement(join(complement(X3),meet(X,X2))) = complement(join(complement(X3),meet(X2,X))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
complement(join(meet(X,X2),complement(X3))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c211,c215]) ).
cnf(c217,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c209,c216]) ).
cnf(c218,plain,
meet(join(complement(X),complement(X2)),X3) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c205,c217]) ).
cnf(c219,plain,
meet(X3,join(complement(X),complement(X2))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c204,c218]) ).
cnf(c220,plain,
meet(X3,join(complement(X2),complement(X))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c203,c219]) ).
cnf(c221,plain,
meet(X,join(complement(top),complement(X2))) = complement(join(complement(X),meet(top,X2))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
complement(join(complement(X),meet(top,X2))) = meet(X,join(complement(top),complement(X2))),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c223,plain,
join(complement(top),complement(X)) = join(zero,complement(X)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c224,plain,
meet(X,join(complement(top),complement(X2))) = meet(X,join(zero,complement(X2))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
meet(X,join(zero,complement(X2))) = meet(X,complement(X2)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c226,plain,
meet(X,join(complement(top),complement(X2))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c224,c225]) ).
cnf(c227,plain,
complement(join(complement(X),meet(top,X2))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c222,c226]) ).
cnf(c228,plain,
complement(join(complement(X),X2)) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c200,c227]) ).
cnf(c229,plain,
complement(join(X2,complement(X))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c188,c228]) ).
cnf(c230,plain,
complement(join(join(X,X2),complement(X2))) = meet(X2,complement(join(X,X2))),
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
meet(X2,complement(join(X,X2))) = complement(join(join(X,X2),complement(X2))),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
join(complement(X),join(X2,X)) = join(join(X2,X),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c233,plain,
join(join(X2,X),complement(X)) = join(complement(X),join(X2,X)),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
join(join(X,X3),X2) = join(X2,join(X,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c235,plain,
join(X2,join(X,X3)) = join(join(X,X3),X2),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c237,plain,
join(join(X,X3),X2) = join(join(X3,X),X2),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
join(X3,join(X,X2)) = join(join(X3,X),X2),
inference(substitution,[status(thm)],[c119]) ).
cnf(c239,plain,
join(join(X3,X),X2) = join(X3,join(X,X2)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c241,plain,
join(X3,join(X,X2)) = join(X3,join(X2,X)),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
join(join(X3,X),X2) = join(X3,join(X2,X)),
inference(transitivity,[status(thm)],[c239,c241]) ).
cnf(c243,plain,
join(join(X,X3),X2) = join(X3,join(X2,X)),
inference(transitivity,[status(thm)],[c237,c242]) ).
cnf(c244,plain,
join(X2,join(X,X3)) = join(X3,join(X2,X)),
inference(transitivity,[status(thm)],[c235,c243]) ).
cnf(c245,plain,
join(X,join(X2,X3)) = join(X3,join(X,X2)),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c247,plain,
join(X3,join(X,X2)) = join(X3,join(X2,X)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
join(X,join(X2,X3)) = join(X3,join(X2,X)),
inference(transitivity,[status(thm)],[c245,c247]) ).
cnf(c249,plain,
join(complement(X),join(X2,X)) = join(X,join(X2,complement(X))),
inference(substitution,[status(thm)],[c248]) ).
cnf(c250,plain,
join(X,join(X2,complement(X))) = join(X2,top),
inference(substitution,[status(thm)],[c127]) ).
cnf(c251,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c252,plain,
join(X,join(X2,complement(X))) = join(top,X2),
inference(transitivity,[status(thm)],[c250,c251]) ).
cnf(c253,plain,
join(complement(X),join(X2,X)) = join(top,X2),
inference(transitivity,[status(thm)],[c249,c252]) ).
cnf(c254,plain,
join(join(X2,X),complement(X)) = join(top,X2),
inference(transitivity,[status(thm)],[c233,c253]) ).
cnf(c255,plain,
join(join(X,X2),complement(X2)) = join(top,X),
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
complement(join(join(X,X2),complement(X2))) = complement(join(top,X)),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
join(top,X2) = join(join(X2,X),complement(X)),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c258,plain,
join(complement(X),join(X2,X)) = join(join(X2,X),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c259,plain,
join(join(X2,X),complement(X)) = join(complement(X),join(X2,X)),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
join(complement(X),join(X2,X)) = join(X,join(complement(X),X2)),
inference(substitution,[status(thm)],[c244]) ).
cnf(c261,plain,
join(X2,join(complement(X2),X3)) = join(X,top),
inference(substitution,[status(thm)],[c149]) ).
cnf(c262,plain,
join(X,join(complement(X),X2)) = top,
inference(transitivity,[status(thm)],[c261,c157]) ).
cnf(c263,plain,
join(complement(X),join(X2,X)) = top,
inference(transitivity,[status(thm)],[c260,c262]) ).
cnf(c264,plain,
join(join(X2,X),complement(X)) = top,
inference(transitivity,[status(thm)],[c259,c263]) ).
cnf(c265,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c257,c264]) ).
cnf(c266,plain,
complement(join(top,X)) = complement(top),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
complement(join(top,X)) = zero,
inference(transitivity,[status(thm)],[c266,c24]) ).
cnf(c268,plain,
complement(join(join(X,X2),complement(X2))) = zero,
inference(transitivity,[status(thm)],[c256,c267]) ).
cnf(c269,plain,
meet(X2,complement(join(X,X2))) = zero,
inference(transitivity,[status(thm)],[c231,c268]) ).
cnf(c270,plain,
meet(X,complement(join(X2,X))) = zero,
inference(substitution,[status(thm)],[c269]) ).
cnf(c271,plain,
zero = meet(X,complement(join(X2,X))),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,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)],[c271]) ).
cnf(c273,plain,
join(meet(X,complement(join(X2,X))),complement(join(complement(X),complement(join(X2,X))))) = X,
inference(substitution,[status(thm)],[c83]) ).
cnf(c274,plain,
join(zero,complement(join(complement(X),complement(join(X2,X))))) = X,
inference(transitivity,[status(thm)],[c272,c273]) ).
cnf(c275,plain,
complement(join(complement(X),complement(join(X2,X)))) = X,
inference(transitivity,[status(thm)],[c185,c274]) ).
cnf(c276,plain,
meet(X,join(X2,X)) = X,
inference(transitivity,[status(thm)],[c13,c275]) ).
cnf(c277,plain,
meet(join(X2,X),X) = X,
inference(transitivity,[status(thm)],[c12,c276]) ).
cnf(c278,plain,
meet(join(X,X2),X2) = X2,
inference(substitution,[status(thm)],[c277]) ).
cnf(c279,plain,
X2 = meet(join(X,X2),X2),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
join(X2,meet(join(X,X2),complement(X2))) = join(meet(join(X,X2),X2),meet(join(X,X2),complement(X2))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,X),meet(X2,complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c282,plain,
join(meet(X2,X),meet(X2,complement(X))) = join(meet(X2,complement(X)),meet(X2,X)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c284,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))) = X2,
inference(substitution,[status(thm)],[c83]) ).
cnf(c286,plain,
join(meet(X2,complement(X)),meet(X2,X)) = X2,
inference(transitivity,[status(thm)],[c284,c285]) ).
cnf(c287,plain,
join(meet(X2,X),meet(X2,complement(X))) = X2,
inference(transitivity,[status(thm)],[c282,c286]) ).
cnf(c288,plain,
join(meet(join(X,X2),X2),meet(join(X,X2),complement(X2))) = join(X,X2),
inference(substitution,[status(thm)],[c287]) ).
cnf(c289,plain,
join(X2,meet(join(X,X2),complement(X2))) = join(X,X2),
inference(transitivity,[status(thm)],[c280,c288]) ).
cnf(c290,plain,
join(composition(composition(X,converse(X)),X),meet(join(X,composition(composition(X,converse(X)),X)),complement(composition(composition(X,converse(X)),X)))) = join(X,composition(composition(X,converse(X)),X)),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
join(X,composition(composition(X,converse(X)),X)) = join(composition(composition(X,converse(X)),X),meet(join(X,composition(composition(X,converse(X)),X)),complement(composition(composition(X,converse(X)),X)))),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c293,plain,
join(X,X2) = join(X2,X),
inference(symmetry,[status(thm)],[c292]) ).
cnf(c294,plain,
meet(complement(X),join(X,X2)) = meet(complement(X),join(X2,X)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
join(X2,meet(complement(X),join(X,X2))) = join(X2,meet(complement(X),join(X2,X))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
meet(complement(X),join(X2,X)) = meet(join(X2,X),complement(X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c297,plain,
join(X2,meet(complement(X),join(X2,X))) = join(X2,meet(join(X2,X),complement(X))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
complement(join(X,complement(join(X2,X)))) = meet(join(X2,X),complement(X)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c299,plain,
meet(join(X2,X),complement(X)) = complement(join(X,complement(join(X2,X)))),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
join(X2,meet(join(X2,X),complement(X))) = join(X2,complement(join(X,complement(join(X2,X))))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
meet(complement(X2),complement(X)) = meet(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c302,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c303,plain,
meet(complement(X),complement(X2)) = meet(join(zero,complement(X)),complement(X2)),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
complement(join(X2,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X2)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c305,plain,
meet(join(zero,complement(X)),complement(X2)) = complement(join(X2,complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
join(X2,complement(join(zero,complement(X)))) = join(X2,meet(X,top)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c307,plain,
complement(join(X2,complement(join(zero,complement(X))))) = complement(join(X2,meet(X,top))),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
join(X2,meet(X,top)) = join(X2,X),
inference(congruence,[status(thm)],[c196]) ).
cnf(c309,plain,
complement(join(X2,meet(X,top))) = complement(join(X2,X)),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
complement(join(X2,complement(join(zero,complement(X))))) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c307,c309]) ).
cnf(c311,plain,
meet(join(zero,complement(X)),complement(X2)) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c305,c310]) ).
cnf(c312,plain,
meet(complement(X),complement(X2)) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c303,c311]) ).
cnf(c313,plain,
meet(complement(X2),complement(X)) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c301,c312]) ).
cnf(c314,plain,
complement(join(X2,X)) = meet(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
join(X,complement(join(X2,X))) = join(X,meet(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
complement(join(X,complement(join(X2,X)))) = complement(join(X,meet(complement(X2),complement(X)))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
join(X2,complement(join(X,complement(join(X2,X))))) = join(X2,complement(join(X,meet(complement(X2),complement(X))))),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
meet(complement(X2),X) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c319,plain,
complement(meet(complement(X2),X)) = complement(meet(X,complement(X2))),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c321,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c320]) ).
cnf(c322,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c4]) ).
cnf(c323,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
join(complement(complement(X)),X2) = join(X2,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c325,plain,
join(X2,complement(complement(X))) = join(complement(complement(X)),X2),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
join(zero,join(X2,complement(complement(X)))) = join(zero,join(complement(complement(X)),X2)),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c328,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c329,plain,
meet(X,X) = complement(complement(X)),
inference(transitivity,[status(thm)],[c327,c328]) ).
cnf(c330,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
join(complement(complement(X)),X2) = join(meet(X,X),X2),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
join(zero,join(complement(complement(X)),X2)) = join(zero,join(meet(X,X),X2)),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
join(zero,join(meet(X,X),X2)) = join(join(zero,meet(X,X)),X2),
inference(substitution,[status(thm)],[c119]) ).
cnf(c334,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c335,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c337,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c83]) ).
cnf(c339,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c337,c338]) ).
cnf(c340,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c335,c339]) ).
cnf(c341,plain,
join(join(zero,meet(X,X)),X2) = join(X,X2),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c343,plain,
join(join(zero,meet(X,X)),X2) = join(X2,X),
inference(transitivity,[status(thm)],[c341,c342]) ).
cnf(c344,plain,
join(zero,join(meet(X,X),X2)) = join(X2,X),
inference(transitivity,[status(thm)],[c333,c343]) ).
cnf(c345,plain,
join(zero,join(complement(complement(X)),X2)) = join(X2,X),
inference(transitivity,[status(thm)],[c332,c344]) ).
cnf(c346,plain,
join(zero,join(X2,complement(complement(X)))) = join(X2,X),
inference(transitivity,[status(thm)],[c326,c345]) ).
cnf(c347,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,X),
inference(substitution,[status(thm)],[c346]) ).
cnf(c348,plain,
join(zero,X) = join(zero,join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c183]) ).
cnf(c350,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
join(zero,join(zero,complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c350,c86]) ).
cnf(c352,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c348,c351]) ).
cnf(c353,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c323,c352]) ).
cnf(c354,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c321,c353]) ).
cnf(c355,plain,
join(zero,meet(X2,complement(X))) = meet(X2,complement(X)),
inference(substitution,[status(thm)],[c354]) ).
cnf(c356,plain,
meet(X2,complement(X)) = join(zero,meet(X2,complement(X))),
inference(symmetry,[status(thm)],[c355]) ).
cnf(c357,plain,
complement(meet(X2,complement(X))) = complement(join(zero,meet(X2,complement(X)))),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
complement(join(X,complement(X2))) = meet(X2,complement(X)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c359,plain,
meet(X2,complement(X)) = complement(join(X,complement(X2))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
join(zero,meet(X2,complement(X))) = join(zero,complement(join(X,complement(X2)))),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
complement(join(zero,meet(X2,complement(X)))) = complement(join(zero,complement(join(X,complement(X2))))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
complement(join(zero,complement(join(X,complement(X2))))) = meet(join(X,complement(X2)),top),
inference(substitution,[status(thm)],[c33]) ).
cnf(c363,plain,
meet(join(X,complement(X2)),top) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c364,plain,
complement(join(zero,complement(join(X,complement(X2))))) = join(X,complement(X2)),
inference(transitivity,[status(thm)],[c362,c363]) ).
cnf(c365,plain,
complement(join(zero,meet(X2,complement(X)))) = join(X,complement(X2)),
inference(transitivity,[status(thm)],[c361,c364]) ).
cnf(c366,plain,
complement(meet(X2,complement(X))) = join(X,complement(X2)),
inference(transitivity,[status(thm)],[c357,c365]) ).
cnf(c367,plain,
complement(meet(X,complement(X2))) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c366]) ).
cnf(c368,plain,
complement(meet(complement(X2),X)) = join(X2,complement(X)),
inference(transitivity,[status(thm)],[c319,c367]) ).
cnf(c369,plain,
complement(meet(complement(X2),join(X,meet(complement(X2),complement(X))))) = join(X2,complement(join(X,meet(complement(X2),complement(X))))),
inference(substitution,[status(thm)],[c368]) ).
cnf(c370,plain,
join(X2,complement(join(X,meet(complement(X2),complement(X))))) = complement(meet(complement(X2),join(X,meet(complement(X2),complement(X))))),
inference(symmetry,[status(thm)],[c369]) ).
cnf(c371,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c372,plain,
meet(X2,complement(X)) = meet(X2,join(zero,complement(X))),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
join(X,meet(X2,complement(X))) = join(X,meet(X2,join(zero,complement(X)))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
meet(X2,join(X,meet(X2,complement(X)))) = meet(X2,join(X,meet(X2,join(zero,complement(X))))),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c376,plain,
join(X,meet(X2,join(zero,complement(X)))) = join(meet(X,top),meet(X2,join(zero,complement(X)))),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
meet(X2,join(X,meet(X2,join(zero,complement(X))))) = meet(X2,join(meet(X,top),meet(X2,join(zero,complement(X))))),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c379,plain,
join(meet(X,top),meet(X2,join(zero,complement(X)))) = join(complement(join(zero,complement(X))),meet(X2,join(zero,complement(X)))),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
meet(X2,join(meet(X,top),meet(X2,join(zero,complement(X))))) = meet(X2,join(complement(join(zero,complement(X))),meet(X2,join(zero,complement(X))))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
join(meet(X2,join(complement(X),meet(X2,X))),zero) = meet(X2,join(complement(X),meet(X2,X))),
inference(substitution,[status(thm)],[c353]) ).
cnf(c382,plain,
meet(X2,join(complement(X),meet(X2,X))) = join(meet(X2,join(complement(X),meet(X2,X))),zero),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c384,plain,
join(meet(X2,join(complement(X),meet(X2,X))),zero) = join(meet(X2,join(complement(X),meet(X2,X))),complement(top)),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
join(complement(X2),join(complement(X),meet(X2,X))) = join(join(complement(X2),complement(X)),meet(X2,X)),
inference(substitution,[status(thm)],[c119]) ).
cnf(c386,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c387,plain,
join(join(complement(X2),complement(X)),meet(X2,X)) = join(join(complement(X2),complement(X)),complement(join(complement(X2),complement(X)))),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
top = join(join(complement(X2),complement(X)),complement(join(complement(X2),complement(X)))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c389,plain,
join(join(complement(X2),complement(X)),complement(join(complement(X2),complement(X)))) = top,
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
join(join(complement(X2),complement(X)),meet(X2,X)) = top,
inference(transitivity,[status(thm)],[c387,c389]) ).
cnf(c391,plain,
join(complement(X2),join(complement(X),meet(X2,X))) = top,
inference(transitivity,[status(thm)],[c385,c390]) ).
cnf(c392,plain,
top = join(complement(X2),join(complement(X),meet(X2,X))),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
complement(top) = complement(join(complement(X2),join(complement(X),meet(X2,X)))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
join(meet(X2,join(complement(X),meet(X2,X))),complement(top)) = join(meet(X2,join(complement(X),meet(X2,X))),complement(join(complement(X2),join(complement(X),meet(X2,X))))),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
join(meet(X2,join(complement(X),meet(X2,X))),complement(join(complement(X2),join(complement(X),meet(X2,X))))) = X2,
inference(substitution,[status(thm)],[c83]) ).
cnf(c396,plain,
join(meet(X2,join(complement(X),meet(X2,X))),complement(top)) = X2,
inference(transitivity,[status(thm)],[c394,c395]) ).
cnf(c397,plain,
join(meet(X2,join(complement(X),meet(X2,X))),zero) = X2,
inference(transitivity,[status(thm)],[c384,c396]) ).
cnf(c398,plain,
meet(X2,join(complement(X),meet(X2,X))) = X2,
inference(transitivity,[status(thm)],[c382,c397]) ).
cnf(c399,plain,
meet(X2,join(complement(join(zero,complement(X))),meet(X2,join(zero,complement(X))))) = X2,
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
meet(X2,join(meet(X,top),meet(X2,join(zero,complement(X))))) = X2,
inference(transitivity,[status(thm)],[c380,c399]) ).
cnf(c401,plain,
meet(X2,join(X,meet(X2,join(zero,complement(X))))) = X2,
inference(transitivity,[status(thm)],[c377,c400]) ).
cnf(c402,plain,
meet(X2,join(X,meet(X2,complement(X)))) = X2,
inference(transitivity,[status(thm)],[c374,c401]) ).
cnf(c403,plain,
meet(complement(X2),join(X,meet(complement(X2),complement(X)))) = complement(X2),
inference(substitution,[status(thm)],[c402]) ).
cnf(c404,plain,
complement(meet(complement(X2),join(X,meet(complement(X2),complement(X))))) = complement(complement(X2)),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c183]) ).
cnf(c406,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c406,c86]) ).
cnf(c408,plain,
complement(meet(complement(X2),join(X,meet(complement(X2),complement(X))))) = X2,
inference(transitivity,[status(thm)],[c404,c407]) ).
cnf(c409,plain,
join(X2,complement(join(X,meet(complement(X2),complement(X))))) = X2,
inference(transitivity,[status(thm)],[c370,c408]) ).
cnf(c410,plain,
join(X2,complement(join(X,complement(join(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c317,c409]) ).
cnf(c411,plain,
join(X2,meet(join(X2,X),complement(X))) = X2,
inference(transitivity,[status(thm)],[c300,c410]) ).
cnf(c412,plain,
join(X2,meet(complement(X),join(X2,X))) = X2,
inference(transitivity,[status(thm)],[c297,c411]) ).
cnf(c413,plain,
join(X2,meet(complement(X),join(X,X2))) = X2,
inference(transitivity,[status(thm)],[c295,c412]) ).
cnf(c414,plain,
join(complement(join(X,composition(composition(X,converse(X)),X))),meet(complement(composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))))) = complement(join(X,composition(composition(X,converse(X)),X))),
inference(substitution,[status(thm)],[c413]) ).
cnf(c415,plain,
complement(join(X,composition(composition(X,converse(X)),X))) = join(complement(join(X,composition(composition(X,converse(X)),X))),meet(complement(composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))))),
inference(symmetry,[status(thm)],[c414]) ).
cnf(c416,plain,
complement(meet(join(X,X2),complement(X2))) = join(X2,complement(join(X,X2))),
inference(substitution,[status(thm)],[c366]) ).
cnf(c417,plain,
join(X2,complement(join(X,X2))) = complement(meet(join(X,X2),complement(X2))),
inference(symmetry,[status(thm)],[c416]) ).
cnf(c418,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c419,plain,
join(X,X2) = join(X2,X),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
meet(X2,join(X,X2)) = meet(X2,join(X2,X)),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c422,plain,
join(X2,X) = join(X2,meet(X,top)),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
meet(X2,join(X2,X)) = meet(X2,join(X2,meet(X,top))),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c425,plain,
join(X2,meet(X,top)) = join(X2,complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
meet(X2,join(X2,meet(X,top))) = meet(X2,join(X2,complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
complement(meet(X,complement(X2))) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c366]) ).
cnf(c428,plain,
join(X2,complement(X)) = complement(meet(X,complement(X2))),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
meet(X2,join(X2,complement(X))) = meet(X2,complement(meet(X,complement(X2)))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c431,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c430]) ).
cnf(c432,plain,
complement(join(complement(X2),X)) = complement(join(X,complement(X2))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
complement(join(X,complement(X2))) = meet(X2,complement(X)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c434,plain,
complement(join(complement(X2),X)) = meet(X2,complement(X)),
inference(transitivity,[status(thm)],[c432,c433]) ).
cnf(c435,plain,
complement(join(complement(X2),meet(X,complement(X2)))) = meet(X2,complement(meet(X,complement(X2)))),
inference(substitution,[status(thm)],[c434]) ).
cnf(c436,plain,
meet(X2,complement(meet(X,complement(X2)))) = complement(join(complement(X2),meet(X,complement(X2)))),
inference(symmetry,[status(thm)],[c435]) ).
cnf(c437,plain,
join(zero,complement(join(complement(X2),meet(X,complement(X2))))) = complement(join(complement(X2),meet(X,complement(X2)))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c438,plain,
complement(join(complement(X2),meet(X,complement(X2)))) = join(zero,complement(join(complement(X2),meet(X,complement(X2))))),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
meet(X,complement(X2)) = meet(complement(X2),X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c440,plain,
meet(X2,meet(X,complement(X2))) = meet(X2,meet(complement(X2),X)),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
meet(X2,meet(complement(X2),X)) = complement(join(complement(X2),complement(meet(complement(X2),X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c442,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c443,plain,
complement(meet(X2,X)) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
join(X2,complement(meet(X2,X))) = join(X2,complement(meet(X,X2))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c446,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c445]) ).
cnf(c447,plain,
join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c340]) ).
cnf(c448,plain,
join(complement(X),complement(X2)) = join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))),
inference(symmetry,[status(thm)],[c447]) ).
cnf(c449,plain,
meet(join(complement(X),complement(X2)),join(complement(X),complement(X2))) = complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c450,plain,
join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))) = join(zero,complement(join(complement(join(complement(X),complement(X2))),meet(X,X2)))),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
join(zero,complement(join(complement(join(complement(X),complement(X2))),meet(X,X2)))) = complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c452,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c453,plain,
complement(join(complement(X),complement(X2))) = meet(X,X2),
inference(symmetry,[status(thm)],[c452]) ).
cnf(c454,plain,
join(complement(join(complement(X),complement(X2))),meet(X,X2)) = join(meet(X,X2),meet(X,X2)),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))) = complement(join(meet(X,X2),meet(X,X2))),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c457,plain,
join(X,X) = join(X,complement(complement(X))),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
join(complement(complement(X)),X) = join(X,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c459,plain,
join(X,complement(complement(X))) = join(complement(complement(X)),X),
inference(symmetry,[status(thm)],[c458]) ).
cnf(c460,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(complement(complement(X)),X),
inference(substitution,[status(thm)],[c346]) ).
cnf(c461,plain,
join(complement(complement(X)),X) = join(zero,join(complement(complement(X)),complement(complement(X)))),
inference(symmetry,[status(thm)],[c460]) ).
cnf(c462,plain,
join(complement(complement(X)),complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c463,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c463,c86]) ).
cnf(c465,plain,
join(complement(complement(X)),X) = X,
inference(transitivity,[status(thm)],[c461,c464]) ).
cnf(c466,plain,
join(X,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c459,c465]) ).
cnf(c467,plain,
join(X,X) = X,
inference(transitivity,[status(thm)],[c457,c466]) ).
cnf(c468,plain,
join(meet(X,X2),meet(X,X2)) = meet(X,X2),
inference(substitution,[status(thm)],[c467]) ).
cnf(c469,plain,
complement(join(meet(X,X2),meet(X,X2))) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c471,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c470]) ).
cnf(c472,plain,
complement(meet(X,X2)) = complement(meet(X2,X)),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
complement(join(meet(X,X2),meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c469,c472]) ).
cnf(c474,plain,
complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c455,c473]) ).
cnf(c475,plain,
join(zero,complement(join(complement(join(complement(X),complement(X2))),meet(X,X2)))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c451,c474]) ).
cnf(c476,plain,
join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c450,c475]) ).
cnf(c477,plain,
join(complement(X),complement(X2)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c448,c476]) ).
cnf(c478,plain,
join(complement(X2),complement(X)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c446,c477]) ).
cnf(c479,plain,
join(complement(X),complement(X2)) = complement(meet(X,X2)),
inference(substitution,[status(thm)],[c478]) ).
cnf(c480,plain,
complement(meet(X,X2)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c479]) ).
cnf(c481,plain,
join(X2,complement(meet(X,X2))) = join(X2,join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
join(X2,join(complement(X),complement(X2))) = join(complement(X),top),
inference(substitution,[status(thm)],[c127]) ).
cnf(c483,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c484,plain,
join(X2,join(complement(X),complement(X2))) = top,
inference(transitivity,[status(thm)],[c482,c483]) ).
cnf(c485,plain,
join(X2,complement(meet(X,X2))) = top,
inference(transitivity,[status(thm)],[c481,c484]) ).
cnf(c486,plain,
join(X2,complement(meet(X2,X))) = top,
inference(transitivity,[status(thm)],[c444,c485]) ).
cnf(c487,plain,
join(complement(X2),complement(meet(complement(X2),X))) = top,
inference(substitution,[status(thm)],[c486]) ).
cnf(c488,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = complement(top),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = zero,
inference(transitivity,[status(thm)],[c488,c24]) ).
cnf(c490,plain,
meet(X2,meet(complement(X2),X)) = zero,
inference(transitivity,[status(thm)],[c441,c489]) ).
cnf(c491,plain,
meet(X2,meet(X,complement(X2))) = zero,
inference(transitivity,[status(thm)],[c440,c490]) ).
cnf(c492,plain,
zero = meet(X2,meet(X,complement(X2))),
inference(symmetry,[status(thm)],[c491]) ).
cnf(c493,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)],[c492]) ).
cnf(c494,plain,
join(meet(X2,meet(X,complement(X2))),complement(join(complement(X2),meet(X,complement(X2))))) = X2,
inference(substitution,[status(thm)],[c83]) ).
cnf(c495,plain,
join(zero,complement(join(complement(X2),meet(X,complement(X2))))) = X2,
inference(transitivity,[status(thm)],[c493,c494]) ).
cnf(c496,plain,
complement(join(complement(X2),meet(X,complement(X2)))) = X2,
inference(transitivity,[status(thm)],[c438,c495]) ).
cnf(c497,plain,
meet(X2,complement(meet(X,complement(X2)))) = X2,
inference(transitivity,[status(thm)],[c436,c496]) ).
cnf(c498,plain,
meet(X2,join(X2,complement(X))) = X2,
inference(transitivity,[status(thm)],[c429,c497]) ).
cnf(c499,plain,
meet(X2,join(X2,complement(join(zero,complement(X))))) = X2,
inference(substitution,[status(thm)],[c498]) ).
cnf(c500,plain,
meet(X2,join(X2,meet(X,top))) = X2,
inference(transitivity,[status(thm)],[c426,c499]) ).
cnf(c501,plain,
meet(X2,join(X2,X)) = X2,
inference(transitivity,[status(thm)],[c423,c500]) ).
cnf(c502,plain,
meet(X2,join(X,X2)) = X2,
inference(transitivity,[status(thm)],[c420,c501]) ).
cnf(c503,plain,
meet(meet(join(X2,X),complement(X)),join(X2,meet(join(X2,X),complement(X)))) = meet(join(X2,X),complement(X)),
inference(substitution,[status(thm)],[c502]) ).
cnf(c504,plain,
meet(join(X2,X),complement(X)) = meet(meet(join(X2,X),complement(X)),join(X2,meet(join(X2,X),complement(X)))),
inference(symmetry,[status(thm)],[c503]) ).
cnf(c505,plain,
meet(join(X2,X),complement(X)) = meet(complement(X),join(X2,X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c506,plain,
join(X2,meet(join(X2,X),complement(X))) = join(X2,meet(complement(X),join(X2,X))),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c508,plain,
meet(complement(X),join(X2,X)) = meet(complement(X),join(X,X2)),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
join(X2,meet(complement(X),join(X2,X))) = join(X2,meet(complement(X),join(X,X2))),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
join(X2,meet(complement(X),join(X2,X))) = X2,
inference(transitivity,[status(thm)],[c509,c413]) ).
cnf(c511,plain,
join(X2,meet(join(X2,X),complement(X))) = X2,
inference(transitivity,[status(thm)],[c506,c510]) ).
cnf(c512,plain,
meet(meet(join(X2,X),complement(X)),join(X2,meet(join(X2,X),complement(X)))) = meet(meet(join(X2,X),complement(X)),X2),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
meet(meet(X3,X2),X) = meet(X,meet(X3,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c514,plain,
meet(X2,meet(X,X3)) = meet(X2,meet(X3,X)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c515,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c516,plain,
meet(X2,meet(X3,X)) = meet(meet(X2,top),meet(X3,X)),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c518,plain,
meet(meet(X2,top),meet(X3,X)) = meet(complement(join(zero,complement(X2))),meet(X3,X)),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
meet(complement(X),meet(X3,X2)) = meet(meet(X3,X2),complement(X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c520,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c521,plain,
meet(meet(X3,X2),complement(X)) = meet(complement(join(complement(X3),complement(X2))),complement(X)),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
meet(complement(join(complement(X3),complement(X2))),complement(X)) = complement(join(join(complement(X3),complement(X2)),X)),
inference(substitution,[status(thm)],[c313]) ).
cnf(c523,plain,
join(complement(X3),join(complement(X2),X)) = join(join(complement(X3),complement(X2)),X),
inference(substitution,[status(thm)],[c119]) ).
cnf(c524,plain,
join(join(complement(X3),complement(X2)),X) = join(complement(X3),join(complement(X2),X)),
inference(symmetry,[status(thm)],[c523]) ).
cnf(c525,plain,
complement(join(join(complement(X3),complement(X2)),X)) = complement(join(complement(X3),join(complement(X2),X))),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
complement(join(complement(X3),join(complement(X2),X))) = meet(X3,complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c434]) ).
cnf(c527,plain,
meet(X3,complement(join(complement(X2),X))) = meet(X3,meet(X2,complement(X))),
inference(congruence,[status(thm)],[c434]) ).
cnf(c528,plain,
complement(join(complement(X3),join(complement(X2),X))) = meet(X3,meet(X2,complement(X))),
inference(transitivity,[status(thm)],[c526,c527]) ).
cnf(c529,plain,
complement(join(join(complement(X3),complement(X2)),X)) = meet(X3,meet(X2,complement(X))),
inference(transitivity,[status(thm)],[c525,c528]) ).
cnf(c530,plain,
meet(complement(join(complement(X3),complement(X2))),complement(X)) = meet(X3,meet(X2,complement(X))),
inference(transitivity,[status(thm)],[c522,c529]) ).
cnf(c531,plain,
meet(meet(X3,X2),complement(X)) = meet(X3,meet(X2,complement(X))),
inference(transitivity,[status(thm)],[c521,c530]) ).
cnf(c532,plain,
meet(complement(X),meet(X3,X2)) = meet(X3,meet(X2,complement(X))),
inference(transitivity,[status(thm)],[c519,c531]) ).
cnf(c533,plain,
meet(complement(join(zero,complement(X2))),meet(X3,X)) = meet(X3,meet(X,complement(join(zero,complement(X2))))),
inference(substitution,[status(thm)],[c532]) ).
cnf(c534,plain,
meet(X,complement(join(zero,complement(X2)))) = meet(X,meet(X2,top)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c535,plain,
meet(X3,meet(X,complement(join(zero,complement(X2))))) = meet(X3,meet(X,meet(X2,top))),
inference(congruence,[status(thm)],[c534]) ).
cnf(c536,plain,
meet(X,meet(X2,top)) = meet(X,X2),
inference(congruence,[status(thm)],[c196]) ).
cnf(c537,plain,
meet(X3,meet(X,meet(X2,top))) = meet(X3,meet(X,X2)),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c539,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c538]) ).
cnf(c540,plain,
meet(X3,meet(X,X2)) = meet(X3,meet(X2,X)),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
meet(X3,meet(X,meet(X2,top))) = meet(X3,meet(X2,X)),
inference(transitivity,[status(thm)],[c537,c540]) ).
cnf(c542,plain,
meet(X3,meet(X,complement(join(zero,complement(X2))))) = meet(X3,meet(X2,X)),
inference(transitivity,[status(thm)],[c535,c541]) ).
cnf(c543,plain,
meet(complement(join(zero,complement(X2))),meet(X3,X)) = meet(X3,meet(X2,X)),
inference(transitivity,[status(thm)],[c533,c542]) ).
cnf(c544,plain,
meet(meet(X2,top),meet(X3,X)) = meet(X3,meet(X2,X)),
inference(transitivity,[status(thm)],[c518,c543]) ).
cnf(c545,plain,
meet(X2,meet(X3,X)) = meet(X3,meet(X2,X)),
inference(transitivity,[status(thm)],[c516,c544]) ).
cnf(c546,plain,
meet(X2,meet(X,X3)) = meet(X3,meet(X2,X)),
inference(transitivity,[status(thm)],[c514,c545]) ).
cnf(c547,plain,
meet(X3,meet(X2,X)) = meet(X,meet(X3,X2)),
inference(substitution,[status(thm)],[c546]) ).
cnf(c548,plain,
meet(X,meet(X3,X2)) = meet(X3,meet(X2,X)),
inference(symmetry,[status(thm)],[c547]) ).
cnf(c549,plain,
meet(meet(X3,X2),X) = meet(X3,meet(X2,X)),
inference(transitivity,[status(thm)],[c513,c548]) ).
cnf(c550,plain,
meet(meet(join(X2,X),complement(X)),X2) = meet(join(X2,X),meet(complement(X),X2)),
inference(substitution,[status(thm)],[c549]) ).
cnf(c551,plain,
meet(join(X3,X2),meet(X,X3)) = meet(meet(X,X3),join(X3,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c552,plain,
complement(complement(join(X2,X))) = join(X2,X),
inference(substitution,[status(thm)],[c407]) ).
cnf(c553,plain,
join(X2,X) = complement(complement(join(X2,X))),
inference(symmetry,[status(thm)],[c552]) ).
cnf(c554,plain,
meet(meet(X,X3),join(X3,X2)) = meet(meet(X,X3),complement(complement(join(X3,X2)))),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
join(zero,meet(meet(X,X3),complement(complement(join(X3,X2))))) = meet(meet(X,X3),complement(complement(join(X3,X2)))),
inference(substitution,[status(thm)],[c354]) ).
cnf(c556,plain,
meet(meet(X,X3),complement(complement(join(X3,X2)))) = join(zero,meet(meet(X,X3),complement(complement(join(X3,X2))))),
inference(symmetry,[status(thm)],[c555]) ).
cnf(c557,plain,
meet(complement(join(X3,X2)),meet(X,X3)) = meet(meet(X,X3),complement(join(X3,X2))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c558,plain,
complement(join(join(X3,X2),complement(meet(X,X3)))) = meet(meet(X,X3),complement(join(X3,X2))),
inference(substitution,[status(thm)],[c229]) ).
cnf(c559,plain,
meet(meet(X,X3),complement(join(X3,X2))) = complement(join(join(X3,X2),complement(meet(X,X3)))),
inference(symmetry,[status(thm)],[c558]) ).
cnf(c560,plain,
complement(meet(X,X2)) = complement(meet(X2,X)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c561,plain,
join(join(X3,X2),complement(meet(X,X3))) = join(join(X3,X2),complement(meet(X3,X))),
inference(congruence,[status(thm)],[c560]) ).
cnf(c562,plain,
join(complement(meet(X3,X)),join(X3,X2)) = join(join(X3,X2),complement(meet(X3,X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c563,plain,
join(join(X3,X2),complement(meet(X3,X))) = join(complement(meet(X3,X)),join(X3,X2)),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
join(complement(meet(X3,X)),join(X3,X2)) = join(X2,join(X3,complement(meet(X3,X)))),
inference(substitution,[status(thm)],[c248]) ).
cnf(c565,plain,
join(X2,join(X3,complement(meet(X3,X)))) = join(X2,top),
inference(congruence,[status(thm)],[c486]) ).
cnf(c566,plain,
join(X2,join(X3,complement(meet(X3,X)))) = top,
inference(transitivity,[status(thm)],[c565,c157]) ).
cnf(c567,plain,
join(complement(meet(X3,X)),join(X3,X2)) = top,
inference(transitivity,[status(thm)],[c564,c566]) ).
cnf(c568,plain,
join(join(X3,X2),complement(meet(X3,X))) = top,
inference(transitivity,[status(thm)],[c563,c567]) ).
cnf(c569,plain,
join(join(X3,X2),complement(meet(X,X3))) = top,
inference(transitivity,[status(thm)],[c561,c568]) ).
cnf(c570,plain,
complement(join(join(X3,X2),complement(meet(X,X3)))) = complement(top),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
complement(join(join(X3,X2),complement(meet(X,X3)))) = zero,
inference(transitivity,[status(thm)],[c570,c24]) ).
cnf(c572,plain,
meet(meet(X,X3),complement(join(X3,X2))) = zero,
inference(transitivity,[status(thm)],[c559,c571]) ).
cnf(c573,plain,
meet(complement(join(X3,X2)),meet(X,X3)) = zero,
inference(transitivity,[status(thm)],[c557,c572]) ).
cnf(c574,plain,
zero = meet(complement(join(X3,X2)),meet(X,X3)),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
join(zero,meet(meet(X,X3),complement(complement(join(X3,X2))))) = join(meet(complement(join(X3,X2)),meet(X,X3)),meet(meet(X,X3),complement(complement(join(X3,X2))))),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c577,plain,
join(meet(X2,X),meet(X,complement(X2))) = join(meet(X,X2),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c576]) ).
cnf(c578,plain,
join(meet(X,X2),meet(X,complement(X2))) = X,
inference(substitution,[status(thm)],[c287]) ).
cnf(c579,plain,
join(meet(X2,X),meet(X,complement(X2))) = X,
inference(transitivity,[status(thm)],[c577,c578]) ).
cnf(c580,plain,
join(meet(complement(join(X3,X2)),meet(X,X3)),meet(meet(X,X3),complement(complement(join(X3,X2))))) = meet(X,X3),
inference(substitution,[status(thm)],[c579]) ).
cnf(c581,plain,
join(zero,meet(meet(X,X3),complement(complement(join(X3,X2))))) = meet(X,X3),
inference(transitivity,[status(thm)],[c575,c580]) ).
cnf(c582,plain,
meet(meet(X,X3),complement(complement(join(X3,X2)))) = meet(X,X3),
inference(transitivity,[status(thm)],[c556,c581]) ).
cnf(c583,plain,
meet(meet(X,X3),join(X3,X2)) = meet(X,X3),
inference(transitivity,[status(thm)],[c554,c582]) ).
cnf(c584,plain,
meet(join(X3,X2),meet(X,X3)) = meet(X,X3),
inference(transitivity,[status(thm)],[c551,c583]) ).
cnf(c585,plain,
meet(join(X2,X),meet(complement(X),X2)) = meet(complement(X),X2),
inference(substitution,[status(thm)],[c584]) ).
cnf(c586,plain,
meet(X2,complement(X)) = meet(complement(X),X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c587,plain,
meet(complement(X),X2) = meet(X2,complement(X)),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
meet(join(X2,X),meet(complement(X),X2)) = meet(X2,complement(X)),
inference(transitivity,[status(thm)],[c585,c587]) ).
cnf(c589,plain,
meet(meet(join(X2,X),complement(X)),X2) = meet(X2,complement(X)),
inference(transitivity,[status(thm)],[c550,c588]) ).
cnf(c590,plain,
meet(meet(join(X2,X),complement(X)),join(X2,meet(join(X2,X),complement(X)))) = meet(X2,complement(X)),
inference(transitivity,[status(thm)],[c512,c589]) ).
cnf(c591,plain,
meet(join(X2,X),complement(X)) = meet(X2,complement(X)),
inference(transitivity,[status(thm)],[c504,c590]) ).
cnf(c592,plain,
meet(join(X,X2),complement(X2)) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c591]) ).
cnf(c593,plain,
complement(meet(join(X,X2),complement(X2))) = complement(meet(X,complement(X2))),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
complement(meet(X,complement(X2))) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c366]) ).
cnf(c595,plain,
complement(meet(join(X,X2),complement(X2))) = join(X2,complement(X)),
inference(transitivity,[status(thm)],[c593,c594]) ).
cnf(c596,plain,
join(X2,complement(join(X,X2))) = join(X2,complement(X)),
inference(transitivity,[status(thm)],[c417,c595]) ).
cnf(c597,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)],[c596]) ).
cnf(c598,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c599,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c598]) ).
cnf(c600,plain,
complement(X) = complement(converse(converse(X))),
inference(congruence,[status(thm)],[c599]) ).
cnf(c601,plain,
join(composition(composition(X,converse(X)),X),complement(X)) = join(composition(composition(X,converse(X)),X),complement(converse(converse(X)))),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
join(X,converse(zero)) = join(converse(zero),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c603,plain,
join(converse(zero),X) = join(X,converse(zero)),
inference(symmetry,[status(thm)],[c602]) ).
cnf(c604,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c605,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c604]) ).
cnf(c606,plain,
join(X,converse(zero)) = join(converse(converse(X)),converse(zero)),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c608,plain,
converse(X) = converse(complement(complement(X))),
inference(congruence,[status(thm)],[c607]) ).
cnf(c609,plain,
join(converse(X),converse(zero)) = join(converse(complement(complement(X))),converse(zero)),
inference(congruence,[status(thm)],[c608]) ).
cnf(c610,plain,
join(converse(zero),converse(complement(complement(X)))) = join(converse(complement(complement(X))),converse(zero)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c611,plain,
join(converse(complement(complement(X))),converse(zero)) = join(converse(zero),converse(complement(complement(X)))),
inference(symmetry,[status(thm)],[c610]) ).
cnf(c612,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c613,plain,
converse(complement(complement(X))) = converse(meet(X,X)),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
join(converse(zero),converse(complement(complement(X)))) = join(converse(zero),converse(meet(X,X))),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
converse(join(zero,meet(X,X))) = join(converse(zero),converse(meet(X,X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c616,plain,
join(converse(zero),converse(meet(X,X))) = converse(join(zero,meet(X,X))),
inference(symmetry,[status(thm)],[c615]) ).
cnf(c617,plain,
converse(join(zero,meet(X,X))) = converse(X),
inference(congruence,[status(thm)],[c340]) ).
cnf(c618,plain,
join(converse(zero),converse(meet(X,X))) = converse(X),
inference(transitivity,[status(thm)],[c616,c617]) ).
cnf(c619,plain,
join(converse(zero),converse(complement(complement(X)))) = converse(X),
inference(transitivity,[status(thm)],[c614,c618]) ).
cnf(c620,plain,
join(converse(complement(complement(X))),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c611,c619]) ).
cnf(c621,plain,
join(converse(X),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c609,c620]) ).
cnf(c622,plain,
join(converse(converse(X)),converse(zero)) = converse(converse(X)),
inference(substitution,[status(thm)],[c621]) ).
cnf(c623,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c624,plain,
join(converse(converse(X)),converse(zero)) = X,
inference(transitivity,[status(thm)],[c622,c623]) ).
cnf(c625,plain,
join(X,converse(zero)) = X,
inference(transitivity,[status(thm)],[c606,c624]) ).
cnf(c626,plain,
join(converse(zero),X) = X,
inference(transitivity,[status(thm)],[c603,c625]) ).
cnf(c627,plain,
join(converse(zero),converse(complement(X))) = converse(complement(X)),
inference(substitution,[status(thm)],[c626]) ).
cnf(c628,plain,
converse(complement(X)) = join(converse(zero),converse(complement(X))),
inference(symmetry,[status(thm)],[c627]) ).
cnf(c629,plain,
converse(join(zero,complement(X))) = join(converse(zero),converse(complement(X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c630,plain,
join(converse(zero),converse(complement(X))) = converse(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c629]) ).
cnf(c631,plain,
converse(converse(complement(converse(complement(X))))) = complement(converse(complement(X))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c632,plain,
complement(converse(complement(X))) = converse(converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c631]) ).
cnf(c633,plain,
meet(complement(X2),X) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c634,plain,
join(meet(X2,X),meet(complement(X2),X)) = join(meet(X2,X),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c633]) ).
cnf(c635,plain,
join(meet(X2,X),meet(complement(X2),X)) = X,
inference(transitivity,[status(thm)],[c634,c579]) ).
cnf(c636,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = converse(complement(converse(complement(X)))),
inference(substitution,[status(thm)],[c635]) ).
cnf(c637,plain,
converse(complement(converse(complement(X)))) = join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c636]) ).
cnf(c638,plain,
join(meet(X,converse(complement(converse(X)))),zero) = meet(X,converse(complement(converse(X)))),
inference(substitution,[status(thm)],[c353]) ).
cnf(c639,plain,
meet(X,converse(complement(converse(X)))) = join(meet(X,converse(complement(converse(X)))),zero),
inference(symmetry,[status(thm)],[c638]) ).
cnf(c640,plain,
meet(zero,X) = meet(X,zero),
inference(substitution,[status(thm)],[c11]) ).
cnf(c641,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c642,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c643,plain,
join(zero,meet(top,complement(zero))) = complement(zero),
inference(substitution,[status(thm)],[c181]) ).
cnf(c644,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(symmetry,[status(thm)],[c643]) ).
cnf(c645,plain,
meet(top,zero) = zero,
inference(substitution,[status(thm)],[c197]) ).
cnf(c646,plain,
zero = meet(top,zero),
inference(symmetry,[status(thm)],[c645]) ).
cnf(c647,plain,
join(zero,meet(top,complement(zero))) = join(meet(top,zero),meet(top,complement(zero))),
inference(congruence,[status(thm)],[c646]) ).
cnf(c648,plain,
join(meet(top,zero),meet(top,complement(zero))) = top,
inference(substitution,[status(thm)],[c287]) ).
cnf(c649,plain,
join(zero,meet(top,complement(zero))) = top,
inference(transitivity,[status(thm)],[c647,c648]) ).
cnf(c650,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c644,c649]) ).
cnf(c651,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c650]) ).
cnf(c652,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c651]) ).
cnf(c653,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c137]) ).
cnf(c654,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c653,c24]) ).
cnf(c655,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c652,c654]) ).
cnf(c656,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c642,c655]) ).
cnf(c657,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c641,c656]) ).
cnf(c658,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c640,c657]) ).
cnf(c659,plain,
meet(zero,converse(complement(converse(X)))) = zero,
inference(substitution,[status(thm)],[c658]) ).
cnf(c660,plain,
zero = meet(zero,converse(complement(converse(X)))),
inference(symmetry,[status(thm)],[c659]) ).
cnf(c661,plain,
join(meet(X,converse(complement(converse(X)))),zero) = join(meet(X,converse(complement(converse(X)))),meet(zero,converse(complement(converse(X))))),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
meet(composition(zero,X),top) = composition(zero,X),
inference(substitution,[status(thm)],[c196]) ).
cnf(c663,plain,
composition(zero,X) = meet(composition(zero,X),top),
inference(symmetry,[status(thm)],[c662]) ).
cnf(c664,plain,
top = complement(zero),
inference(symmetry,[status(thm)],[c650]) ).
cnf(c665,plain,
meet(composition(zero,X),top) = meet(composition(zero,X),complement(zero)),
inference(congruence,[status(thm)],[c664]) ).
cnf(c666,plain,
meet(converse(zero),top) = converse(zero),
inference(substitution,[status(thm)],[c196]) ).
cnf(c667,plain,
converse(zero) = meet(converse(zero),top),
inference(symmetry,[status(thm)],[c666]) ).
cnf(c668,plain,
join(converse(zero),complement(converse(zero))) = complement(converse(zero)),
inference(substitution,[status(thm)],[c626]) ).
cnf(c669,plain,
complement(converse(zero)) = join(converse(zero),complement(converse(zero))),
inference(symmetry,[status(thm)],[c668]) ).
cnf(c670,plain,
top = join(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c671,plain,
join(converse(zero),complement(converse(zero))) = top,
inference(symmetry,[status(thm)],[c670]) ).
cnf(c672,plain,
complement(converse(zero)) = top,
inference(transitivity,[status(thm)],[c669,c671]) ).
cnf(c673,plain,
top = complement(converse(zero)),
inference(symmetry,[status(thm)],[c672]) ).
cnf(c674,plain,
meet(converse(zero),top) = meet(converse(zero),complement(converse(zero))),
inference(congruence,[status(thm)],[c673]) ).
cnf(c675,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c676,plain,
meet(converse(zero),complement(converse(zero))) = zero,
inference(symmetry,[status(thm)],[c675]) ).
cnf(c677,plain,
meet(converse(zero),top) = zero,
inference(transitivity,[status(thm)],[c674,c676]) ).
cnf(c678,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c667,c677]) ).
cnf(c679,plain,
zero = converse(zero),
inference(symmetry,[status(thm)],[c678]) ).
cnf(c680,plain,
composition(zero,X) = composition(converse(zero),X),
inference(congruence,[status(thm)],[c679]) ).
cnf(c681,plain,
meet(composition(zero,X),complement(zero)) = meet(composition(converse(zero),X),complement(zero)),
inference(congruence,[status(thm)],[c680]) ).
cnf(c682,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c683,plain,
converse(zero) = converse(complement(top)),
inference(congruence,[status(thm)],[c682]) ).
cnf(c684,plain,
composition(converse(zero),X) = composition(converse(complement(top)),X),
inference(congruence,[status(thm)],[c683]) ).
cnf(c685,plain,
meet(composition(converse(zero),X),complement(zero)) = meet(composition(converse(complement(top)),X),complement(zero)),
inference(congruence,[status(thm)],[c684]) ).
cnf(c686,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c687,plain,
composition(top,X) = composition(converse(top),X),
inference(congruence,[status(thm)],[c686]) ).
cnf(c688,plain,
join(X,composition(top,X)) = join(X,composition(converse(top),X)),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
join(X,one) = join(one,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c690,plain,
join(one,X) = join(X,one),
inference(symmetry,[status(thm)],[c689]) ).
cnf(c691,plain,
composition(join(one,X),X2) = composition(join(X,one),X2),
inference(congruence,[status(thm)],[c690]) ).
cnf(c692,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c693,plain,
join(X,one) = join(one,X),
inference(symmetry,[status(thm)],[c692]) ).
cnf(c694,plain,
composition(join(X2,one),X) = composition(join(one,X2),X),
inference(congruence,[status(thm)],[c693]) ).
cnf(c695,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c696,plain,
join(one,X) = join(converse(one),X),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
composition(join(one,X2),X) = composition(join(converse(one),X2),X),
inference(congruence,[status(thm)],[c696]) ).
cnf(c698,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c699,plain,
composition(join(converse(one),X2),X) = join(composition(converse(one),X),composition(X2,X)),
inference(substitution,[status(thm)],[c698]) ).
cnf(c700,plain,
join(composition(converse(one),X),composition(X2,X)) = join(X,composition(X2,X)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c701,plain,
composition(join(converse(one),X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c699,c700]) ).
cnf(c702,plain,
composition(join(one,X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c697,c701]) ).
cnf(c703,plain,
composition(join(X2,one),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c694,c702]) ).
cnf(c704,plain,
composition(join(X,one),X2) = join(X2,composition(X,X2)),
inference(substitution,[status(thm)],[c703]) ).
cnf(c705,plain,
composition(join(one,X),X2) = join(X2,composition(X,X2)),
inference(transitivity,[status(thm)],[c691,c704]) ).
cnf(c706,plain,
composition(join(one,converse(top)),X) = join(X,composition(converse(top),X)),
inference(substitution,[status(thm)],[c705]) ).
cnf(c707,plain,
join(X,composition(converse(top),X)) = composition(join(one,converse(top)),X),
inference(symmetry,[status(thm)],[c706]) ).
cnf(c708,plain,
join(one,converse(top)) = top,
inference(substitution,[status(thm)],[c159]) ).
cnf(c709,plain,
composition(join(one,converse(top)),X) = composition(top,X),
inference(congruence,[status(thm)],[c708]) ).
cnf(c710,plain,
join(X,composition(converse(top),X)) = composition(top,X),
inference(transitivity,[status(thm)],[c707,c709]) ).
cnf(c711,plain,
join(X,composition(top,X)) = composition(top,X),
inference(transitivity,[status(thm)],[c688,c710]) ).
cnf(c712,plain,
join(top,composition(top,top)) = composition(top,top),
inference(substitution,[status(thm)],[c711]) ).
cnf(c713,plain,
composition(top,top) = join(top,composition(top,top)),
inference(symmetry,[status(thm)],[c712]) ).
cnf(c714,plain,
join(top,composition(top,top)) = top,
inference(substitution,[status(thm)],[c265]) ).
cnf(c715,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c713,c714]) ).
cnf(c716,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c715]) ).
cnf(c717,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
converse(complement(top)) = converse(complement(composition(top,top))),
inference(congruence,[status(thm)],[c717]) ).
cnf(c719,plain,
composition(converse(complement(top)),X) = composition(converse(complement(composition(top,top))),X),
inference(congruence,[status(thm)],[c718]) ).
cnf(c720,plain,
meet(composition(converse(complement(top)),X),complement(zero)) = meet(composition(converse(complement(composition(top,top))),X),complement(zero)),
inference(congruence,[status(thm)],[c719]) ).
cnf(c721,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c722,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c721]) ).
cnf(c723,plain,
composition(converse(complement(composition(X,top))),X) = composition(converse(complement(composition(X,top))),converse(converse(X))),
inference(congruence,[status(thm)],[c722]) ).
cnf(c724,plain,
converse(composition(converse(X),complement(composition(X,top)))) = composition(converse(complement(composition(X,top))),converse(converse(X))),
inference(substitution,[status(thm)],[c42]) ).
cnf(c725,plain,
composition(converse(complement(composition(X,top))),converse(converse(X))) = converse(composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c724]) ).
cnf(c726,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = composition(converse(X),complement(composition(X,top))),
inference(substitution,[status(thm)],[c354]) ).
cnf(c727,plain,
composition(converse(X),complement(composition(X,top))) = join(zero,composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c726]) ).
cnf(c728,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c729,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = join(complement(top),composition(converse(X),complement(composition(X,top)))),
inference(congruence,[status(thm)],[c728]) ).
cnf(c730,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = complement(top),
inference(substitution,[status(thm)],[c71]) ).
cnf(c731,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c730,c24]) ).
cnf(c732,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c729,c731]) ).
cnf(c733,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c727,c732]) ).
cnf(c734,plain,
converse(composition(converse(X),complement(composition(X,top)))) = converse(zero),
inference(congruence,[status(thm)],[c733]) ).
cnf(c735,plain,
converse(composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c734,c678]) ).
cnf(c736,plain,
composition(converse(complement(composition(X,top))),converse(converse(X))) = zero,
inference(transitivity,[status(thm)],[c725,c735]) ).
cnf(c737,plain,
composition(converse(complement(composition(X,top))),X) = zero,
inference(transitivity,[status(thm)],[c723,c736]) ).
cnf(c738,plain,
composition(converse(complement(composition(top,top))),top) = zero,
inference(substitution,[status(thm)],[c737]) ).
cnf(c739,plain,
zero = composition(converse(complement(composition(top,top))),top),
inference(symmetry,[status(thm)],[c738]) ).
cnf(c740,plain,
complement(zero) = complement(composition(converse(complement(composition(top,top))),top)),
inference(congruence,[status(thm)],[c739]) ).
cnf(c741,plain,
meet(composition(converse(complement(composition(top,top))),X),complement(zero)) = meet(composition(converse(complement(composition(top,top))),X),complement(composition(converse(complement(composition(top,top))),top))),
inference(congruence,[status(thm)],[c740]) ).
cnf(c742,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = meet(composition(X2,X),complement(composition(X2,top))),
inference(substitution,[status(thm)],[c353]) ).
cnf(c743,plain,
meet(composition(X2,X),complement(composition(X2,top))) = join(meet(composition(X2,X),complement(composition(X2,top))),zero),
inference(symmetry,[status(thm)],[c742]) ).
cnf(c744,plain,
meet(zero,complement(composition(X,top))) = zero,
inference(substitution,[status(thm)],[c658]) ).
cnf(c745,plain,
zero = meet(zero,complement(composition(X,top))),
inference(symmetry,[status(thm)],[c744]) ).
cnf(c746,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(zero,complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c745]) ).
cnf(c747,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c354]) ).
cnf(c748,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c747]) ).
cnf(c749,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c750,plain,
composition(top,zero) = composition(converse(top),zero),
inference(congruence,[status(thm)],[c749]) ).
cnf(c751,plain,
join(zero,composition(converse(top),zero)) = composition(converse(top),zero),
inference(substitution,[status(thm)],[c354]) ).
cnf(c752,plain,
composition(converse(top),zero) = join(zero,composition(converse(top),zero)),
inference(symmetry,[status(thm)],[c751]) ).
cnf(c753,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c754,plain,
join(zero,composition(converse(top),zero)) = join(complement(top),composition(converse(top),zero)),
inference(congruence,[status(thm)],[c753]) ).
cnf(c755,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c756,plain,
composition(converse(top),zero) = composition(converse(top),complement(top)),
inference(congruence,[status(thm)],[c755]) ).
cnf(c757,plain,
join(complement(top),composition(converse(top),zero)) = join(complement(top),composition(converse(top),complement(top))),
inference(congruence,[status(thm)],[c756]) ).
cnf(c758,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c715]) ).
cnf(c759,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c758]) ).
cnf(c760,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c759]) ).
cnf(c761,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c760]) ).
cnf(c762,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c71]) ).
cnf(c763,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c762,c24]) ).
cnf(c764,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c761,c763]) ).
cnf(c765,plain,
join(complement(top),composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c757,c764]) ).
cnf(c766,plain,
join(zero,composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c754,c765]) ).
cnf(c767,plain,
composition(converse(top),zero) = zero,
inference(transitivity,[status(thm)],[c752,c766]) ).
cnf(c768,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c750,c767]) ).
cnf(c769,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c768]) ).
cnf(c770,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c769]) ).
cnf(c771,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c698]) ).
cnf(c772,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c771]) ).
cnf(c773,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c265]) ).
cnf(c774,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c773,c768]) ).
cnf(c775,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c772,c774]) ).
cnf(c776,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c770,c775]) ).
cnf(c777,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c748,c776]) ).
cnf(c778,plain,
zero = composition(X,zero),
inference(symmetry,[status(thm)],[c777]) ).
cnf(c779,plain,
meet(zero,complement(composition(X,top))) = meet(composition(X,zero),complement(composition(X,top))),
inference(congruence,[status(thm)],[c778]) ).
cnf(c780,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(zero,complement(composition(X2,top)))) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,zero),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c779]) ).
cnf(c781,plain,
zero = meet(X,zero),
inference(symmetry,[status(thm)],[c657]) ).
cnf(c782,plain,
composition(X2,zero) = composition(X2,meet(X,zero)),
inference(congruence,[status(thm)],[c781]) ).
cnf(c783,plain,
meet(composition(X2,zero),complement(composition(X2,top))) = meet(composition(X2,meet(X,zero)),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c782]) ).
cnf(c784,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,zero),complement(composition(X2,top)))) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,zero)),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c783]) ).
cnf(c785,plain,
zero = composition(converse(X),complement(composition(X,top))),
inference(symmetry,[status(thm)],[c733]) ).
cnf(c786,plain,
meet(X,zero) = meet(X,composition(converse(X2),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c785]) ).
cnf(c787,plain,
composition(X2,meet(X,zero)) = composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),
inference(congruence,[status(thm)],[c786]) ).
cnf(c788,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c787]) ).
cnf(c789,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,zero)),complement(composition(X2,top)))) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c788]) ).
cnf(c790,axiom,
join(meet(composition(A2,B2),C2),meet(composition(A2,meet(B2,composition(converse(A2),C2))),C2)) = meet(composition(A2,meet(B2,composition(converse(A2),C2))),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1_15) ).
cnf(c791,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top)))) = meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))),
inference(substitution,[status(thm)],[c790]) ).
cnf(c792,plain,
meet(X,composition(converse(X2),complement(composition(X2,top)))) = meet(X,zero),
inference(congruence,[status(thm)],[c733]) ).
cnf(c793,plain,
composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))) = composition(X2,meet(X,zero)),
inference(congruence,[status(thm)],[c792]) ).
cnf(c794,plain,
meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))) = meet(composition(X2,meet(X,zero)),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c793]) ).
cnf(c795,plain,
composition(X2,meet(X,zero)) = composition(X2,zero),
inference(congruence,[status(thm)],[c657]) ).
cnf(c796,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = meet(composition(X2,zero),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
meet(composition(X,zero),complement(composition(X,top))) = meet(zero,complement(composition(X,top))),
inference(congruence,[status(thm)],[c777]) ).
cnf(c798,plain,
meet(zero,complement(composition(X,top))) = zero,
inference(substitution,[status(thm)],[c658]) ).
cnf(c799,plain,
meet(composition(X,zero),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c797,c798]) ).
cnf(c800,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c796,c799]) ).
cnf(c801,plain,
meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c794,c800]) ).
cnf(c802,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c791,c801]) ).
cnf(c803,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,zero)),complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c789,c802]) ).
cnf(c804,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,zero),complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c784,c803]) ).
cnf(c805,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(zero,complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c780,c804]) ).
cnf(c806,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = zero,
inference(transitivity,[status(thm)],[c746,c805]) ).
cnf(c807,plain,
meet(composition(X2,X),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c743,c806]) ).
cnf(c808,plain,
meet(composition(converse(complement(composition(top,top))),X),complement(composition(converse(complement(composition(top,top))),top))) = zero,
inference(substitution,[status(thm)],[c807]) ).
cnf(c809,plain,
meet(composition(converse(complement(composition(top,top))),X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c741,c808]) ).
cnf(c810,plain,
meet(composition(converse(complement(top)),X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c720,c809]) ).
cnf(c811,plain,
meet(composition(converse(zero),X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c685,c810]) ).
cnf(c812,plain,
meet(composition(zero,X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c681,c811]) ).
cnf(c813,plain,
meet(composition(zero,X),top) = zero,
inference(transitivity,[status(thm)],[c665,c812]) ).
cnf(c814,plain,
composition(zero,X) = zero,
inference(transitivity,[status(thm)],[c663,c813]) ).
cnf(c815,plain,
zero = composition(zero,X),
inference(symmetry,[status(thm)],[c814]) ).
cnf(c816,plain,
meet(zero,converse(complement(converse(X)))) = meet(composition(zero,X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c815]) ).
cnf(c817,plain,
join(meet(X,converse(complement(converse(X)))),meet(zero,converse(complement(converse(X))))) = join(meet(X,converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))),
inference(congruence,[status(thm)],[c816]) ).
cnf(c818,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c819,plain,
meet(X,converse(complement(converse(X)))) = meet(composition(one,X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c818]) ).
cnf(c820,plain,
join(meet(X,converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))),
inference(congruence,[status(thm)],[c819]) ).
cnf(c821,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c822,plain,
composition(converse(complement(X)),X) = composition(converse(complement(X)),meet(X,top)),
inference(congruence,[status(thm)],[c821]) ).
cnf(c823,plain,
meet(one,composition(converse(complement(X)),X)) = meet(one,composition(converse(complement(X)),meet(X,top))),
inference(congruence,[status(thm)],[c822]) ).
cnf(c824,plain,
join(converse(zero),converse(complement(X))) = converse(complement(X)),
inference(substitution,[status(thm)],[c626]) ).
cnf(c825,plain,
converse(complement(X)) = join(converse(zero),converse(complement(X))),
inference(symmetry,[status(thm)],[c824]) ).
cnf(c826,plain,
composition(converse(complement(X)),meet(X,top)) = composition(join(converse(zero),converse(complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c825]) ).
cnf(c827,plain,
meet(one,composition(converse(complement(X)),meet(X,top))) = meet(one,composition(join(converse(zero),converse(complement(X))),meet(X,top))),
inference(congruence,[status(thm)],[c826]) ).
cnf(c828,plain,
converse(join(zero,complement(X))) = join(converse(zero),converse(complement(X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c829,plain,
join(converse(zero),converse(complement(X))) = converse(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c828]) ).
cnf(c830,plain,
composition(join(converse(zero),converse(complement(X))),meet(X,top)) = composition(converse(join(zero,complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c829]) ).
cnf(c831,plain,
meet(one,composition(join(converse(zero),converse(complement(X))),meet(X,top))) = meet(one,composition(converse(join(zero,complement(X))),meet(X,top))),
inference(congruence,[status(thm)],[c830]) ).
cnf(c832,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c833,plain,
composition(converse(join(zero,complement(X))),meet(X,top)) = composition(converse(join(zero,complement(X))),complement(join(zero,complement(X)))),
inference(congruence,[status(thm)],[c832]) ).
cnf(c834,plain,
meet(one,composition(converse(join(zero,complement(X))),meet(X,top))) = meet(one,composition(converse(join(zero,complement(X))),complement(join(zero,complement(X))))),
inference(congruence,[status(thm)],[c833]) ).
cnf(c835,plain,
meet(one,composition(converse(X),complement(X))) = meet(composition(converse(X),complement(X)),one),
inference(substitution,[status(thm)],[c11]) ).
cnf(c836,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = meet(one,complement(composition(converse(X),complement(X)))),
inference(substitution,[status(thm)],[c434]) ).
cnf(c837,plain,
meet(one,complement(composition(converse(X),complement(X)))) = complement(join(complement(one),composition(converse(X),complement(X)))),
inference(symmetry,[status(thm)],[c836]) ).
cnf(c838,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c839,plain,
X = composition(X,one),
inference(symmetry,[status(thm)],[c838]) ).
cnf(c840,plain,
complement(X) = complement(composition(X,one)),
inference(congruence,[status(thm)],[c839]) ).
cnf(c841,plain,
composition(converse(X),complement(X)) = composition(converse(X),complement(composition(X,one))),
inference(congruence,[status(thm)],[c840]) ).
cnf(c842,plain,
join(complement(one),composition(converse(X),complement(X))) = join(complement(one),composition(converse(X),complement(composition(X,one)))),
inference(congruence,[status(thm)],[c841]) ).
cnf(c843,plain,
join(complement(one),composition(converse(X),complement(composition(X,one)))) = complement(one),
inference(substitution,[status(thm)],[c71]) ).
cnf(c844,plain,
join(complement(one),composition(converse(X),complement(X))) = complement(one),
inference(transitivity,[status(thm)],[c842,c843]) ).
cnf(c845,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = complement(complement(one)),
inference(congruence,[status(thm)],[c844]) ).
cnf(c846,plain,
complement(complement(one)) = one,
inference(substitution,[status(thm)],[c407]) ).
cnf(c847,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = one,
inference(transitivity,[status(thm)],[c845,c846]) ).
cnf(c848,plain,
meet(one,complement(composition(converse(X),complement(X)))) = one,
inference(transitivity,[status(thm)],[c837,c847]) ).
cnf(c849,plain,
one = meet(one,complement(composition(converse(X),complement(X)))),
inference(symmetry,[status(thm)],[c848]) ).
cnf(c850,plain,
meet(composition(converse(X),complement(X)),one) = meet(composition(converse(X),complement(X)),meet(one,complement(composition(converse(X),complement(X))))),
inference(congruence,[status(thm)],[c849]) ).
cnf(c851,plain,
meet(composition(converse(X),complement(X)),meet(one,complement(composition(converse(X),complement(X))))) = zero,
inference(substitution,[status(thm)],[c491]) ).
cnf(c852,plain,
meet(composition(converse(X),complement(X)),one) = zero,
inference(transitivity,[status(thm)],[c850,c851]) ).
cnf(c853,plain,
meet(one,composition(converse(X),complement(X))) = zero,
inference(transitivity,[status(thm)],[c835,c852]) ).
cnf(c854,plain,
meet(one,composition(converse(join(zero,complement(X))),complement(join(zero,complement(X))))) = zero,
inference(substitution,[status(thm)],[c853]) ).
cnf(c855,plain,
meet(one,composition(converse(join(zero,complement(X))),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c834,c854]) ).
cnf(c856,plain,
meet(one,composition(join(converse(zero),converse(complement(X))),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c831,c855]) ).
cnf(c857,plain,
meet(one,composition(converse(complement(X)),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c827,c856]) ).
cnf(c858,plain,
meet(one,composition(converse(complement(X)),X)) = zero,
inference(transitivity,[status(thm)],[c823,c857]) ).
cnf(c859,plain,
meet(one,composition(converse(complement(converse(X))),converse(X))) = zero,
inference(substitution,[status(thm)],[c858]) ).
cnf(c860,plain,
zero = meet(one,composition(converse(complement(converse(X))),converse(X))),
inference(symmetry,[status(thm)],[c859]) ).
cnf(c861,plain,
composition(zero,X) = composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),
inference(congruence,[status(thm)],[c860]) ).
cnf(c862,plain,
meet(composition(zero,X),converse(complement(converse(X)))) = meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c861]) ).
cnf(c863,plain,
join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X))))),
inference(congruence,[status(thm)],[c862]) ).
cnf(c864,axiom,
join(meet(composition(A2,B2),C2),meet(composition(meet(A2,composition(C2,converse(B2))),B2),C2)) = meet(composition(meet(A2,composition(C2,converse(B2))),B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_2_16) ).
cnf(c865,plain,
join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X))))) = meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X)))),
inference(substitution,[status(thm)],[c864]) ).
cnf(c866,plain,
meet(one,composition(converse(complement(converse(X))),converse(X))) = zero,
inference(substitution,[status(thm)],[c858]) ).
cnf(c867,plain,
composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X) = composition(zero,X),
inference(congruence,[status(thm)],[c866]) ).
cnf(c868,plain,
meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X)))) = meet(composition(zero,X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c867]) ).
cnf(c869,plain,
meet(composition(zero,X),converse(complement(converse(X)))) = meet(zero,converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c814]) ).
cnf(c870,plain,
meet(zero,converse(complement(converse(X)))) = zero,
inference(substitution,[status(thm)],[c658]) ).
cnf(c871,plain,
meet(composition(zero,X),converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c869,c870]) ).
cnf(c872,plain,
meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c868,c871]) ).
cnf(c873,plain,
join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c865,c872]) ).
cnf(c874,plain,
join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c863,c873]) ).
cnf(c875,plain,
join(meet(X,converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c820,c874]) ).
cnf(c876,plain,
join(meet(X,converse(complement(converse(X)))),meet(zero,converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c817,c875]) ).
cnf(c877,plain,
join(meet(X,converse(complement(converse(X)))),zero) = zero,
inference(transitivity,[status(thm)],[c661,c876]) ).
cnf(c878,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c639,c877]) ).
cnf(c879,plain,
meet(complement(X),converse(complement(converse(complement(X))))) = zero,
inference(substitution,[status(thm)],[c878]) ).
cnf(c880,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = join(meet(X,converse(complement(converse(complement(X))))),zero),
inference(congruence,[status(thm)],[c879]) ).
cnf(c881,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = meet(X,converse(complement(converse(complement(X))))),
inference(substitution,[status(thm)],[c353]) ).
cnf(c882,plain,
meet(X,converse(complement(converse(complement(X))))) = complement(join(complement(X),complement(converse(complement(converse(complement(X))))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c883,plain,
join(zero,complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))) = complement(join(complement(X),complement(converse(complement(converse(complement(X))))))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c884,plain,
complement(join(complement(X),complement(converse(complement(converse(complement(X))))))) = join(zero,complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))),
inference(symmetry,[status(thm)],[c883]) ).
cnf(c885,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(substitution,[status(thm)],[c434]) ).
cnf(c886,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = complement(join(complement(X),converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c885]) ).
cnf(c887,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c109]) ).
cnf(c888,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = complement(converse(top)),
inference(congruence,[status(thm)],[c887]) ).
cnf(c889,plain,
complement(converse(top)) = complement(top),
inference(congruence,[status(thm)],[c168]) ).
cnf(c890,plain,
complement(converse(top)) = zero,
inference(transitivity,[status(thm)],[c889,c24]) ).
cnf(c891,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c888,c890]) ).
cnf(c892,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c886,c891]) ).
cnf(c893,plain,
zero = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c892]) ).
cnf(c894,plain,
join(zero,complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))) = join(meet(X,complement(converse(complement(converse(complement(X)))))),complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))),
inference(congruence,[status(thm)],[c893]) ).
cnf(c895,plain,
join(meet(X,complement(converse(complement(converse(complement(X)))))),complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))) = X,
inference(substitution,[status(thm)],[c83]) ).
cnf(c896,plain,
join(zero,complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))) = X,
inference(transitivity,[status(thm)],[c894,c895]) ).
cnf(c897,plain,
complement(join(complement(X),complement(converse(complement(converse(complement(X))))))) = X,
inference(transitivity,[status(thm)],[c884,c896]) ).
cnf(c898,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(transitivity,[status(thm)],[c882,c897]) ).
cnf(c899,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = X,
inference(transitivity,[status(thm)],[c881,c898]) ).
cnf(c900,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = X,
inference(transitivity,[status(thm)],[c880,c899]) ).
cnf(c901,plain,
converse(complement(converse(complement(X)))) = X,
inference(transitivity,[status(thm)],[c637,c900]) ).
cnf(c902,plain,
converse(converse(complement(converse(complement(X))))) = converse(X),
inference(congruence,[status(thm)],[c901]) ).
cnf(c903,plain,
complement(converse(complement(X))) = converse(X),
inference(transitivity,[status(thm)],[c632,c902]) ).
cnf(c904,plain,
complement(converse(complement(join(zero,complement(X))))) = converse(join(zero,complement(X))),
inference(substitution,[status(thm)],[c903]) ).
cnf(c905,plain,
converse(join(zero,complement(X))) = complement(converse(complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c904]) ).
cnf(c906,plain,
converse(complement(join(zero,complement(X)))) = converse(meet(X,top)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c907,plain,
complement(converse(complement(join(zero,complement(X))))) = complement(converse(meet(X,top))),
inference(congruence,[status(thm)],[c906]) ).
cnf(c908,plain,
converse(meet(X,top)) = converse(X),
inference(congruence,[status(thm)],[c196]) ).
cnf(c909,plain,
complement(converse(meet(X,top))) = complement(converse(X)),
inference(congruence,[status(thm)],[c908]) ).
cnf(c910,plain,
complement(converse(complement(join(zero,complement(X))))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c907,c909]) ).
cnf(c911,plain,
converse(join(zero,complement(X))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c905,c910]) ).
cnf(c912,plain,
join(converse(zero),converse(complement(X))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c630,c911]) ).
cnf(c913,plain,
converse(complement(X)) = complement(converse(X)),
inference(transitivity,[status(thm)],[c628,c912]) ).
cnf(c914,plain,
converse(complement(converse(X))) = complement(converse(converse(X))),
inference(substitution,[status(thm)],[c913]) ).
cnf(c915,plain,
complement(converse(converse(X))) = converse(complement(converse(X))),
inference(symmetry,[status(thm)],[c914]) ).
cnf(c916,plain,
join(composition(composition(X,converse(X)),X),complement(converse(converse(X)))) = join(composition(composition(X,converse(X)),X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c915]) ).
cnf(c917,plain,
converse(converse(composition(composition(X,converse(X)),X))) = composition(composition(X,converse(X)),X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c918,plain,
composition(composition(X,converse(X)),X) = converse(converse(composition(composition(X,converse(X)),X))),
inference(symmetry,[status(thm)],[c917]) ).
cnf(c919,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)],[c918]) ).
cnf(c920,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)],[c101]) ).
cnf(c921,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)],[c920]) ).
cnf(c922,plain,
join(composition(converse(X),complement(composition(X,X3))),X2) = join(X2,composition(converse(X),complement(composition(X,X3)))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c923,plain,
join(X2,composition(converse(X),complement(composition(X,X3)))) = join(composition(converse(X),complement(composition(X,X3))),X2),
inference(symmetry,[status(thm)],[c922]) ).
cnf(c924,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)],[c923]) ).
cnf(c925,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)],[c119]) ).
cnf(c926,plain,
join(join(complement(X3),composition(converse(X),complement(composition(X,X3)))),X2) = join(complement(X3),X2),
inference(congruence,[status(thm)],[c71]) ).
cnf(c927,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c928,plain,
join(join(complement(X3),composition(converse(X),complement(composition(X,X3)))),X2) = join(X2,complement(X3)),
inference(transitivity,[status(thm)],[c926,c927]) ).
cnf(c929,plain,
join(complement(X3),join(composition(converse(X),complement(composition(X,X3))),X2)) = join(X2,complement(X3)),
inference(transitivity,[status(thm)],[c925,c928]) ).
cnf(c930,plain,
join(complement(X3),join(X2,composition(converse(X),complement(composition(X,X3))))) = join(X2,complement(X3)),
inference(transitivity,[status(thm)],[c924,c929]) ).
cnf(c931,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)],[c930]) ).
cnf(c932,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)],[c931]) ).
cnf(c933,plain,
converse(composition(X2,converse(X))) = composition(converse(converse(X)),converse(X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c934,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c38]) ).
cnf(c935,plain,
composition(converse(converse(X)),converse(X2)) = composition(X,converse(X2)),
inference(congruence,[status(thm)],[c934]) ).
cnf(c936,plain,
converse(composition(X2,converse(X))) = composition(X,converse(X2)),
inference(transitivity,[status(thm)],[c933,c935]) ).
cnf(c937,plain,
composition(X,converse(X2)) = converse(composition(X2,converse(X))),
inference(symmetry,[status(thm)],[c936]) ).
cnf(c938,plain,
complement(composition(X,converse(X2))) = complement(converse(composition(X2,converse(X)))),
inference(congruence,[status(thm)],[c937]) ).
cnf(c939,plain,
composition(converse(X),complement(composition(X2,converse(X3)))) = composition(converse(X),complement(converse(composition(X3,converse(X2))))),
inference(congruence,[status(thm)],[c938]) ).
cnf(c940,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),complement(converse(composition(X3,converse(X2)))))),
inference(congruence,[status(thm)],[c939]) ).
cnf(c941,plain,
converse(complement(composition(X2,converse(X)))) = complement(converse(composition(X2,converse(X)))),
inference(substitution,[status(thm)],[c913]) ).
cnf(c942,plain,
complement(converse(composition(X2,converse(X)))) = converse(complement(composition(X2,converse(X)))),
inference(symmetry,[status(thm)],[c941]) ).
cnf(c943,plain,
composition(converse(X),complement(converse(composition(X3,converse(X2))))) = composition(converse(X),converse(complement(composition(X3,converse(X2))))),
inference(congruence,[status(thm)],[c942]) ).
cnf(c944,plain,
join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),complement(converse(composition(X3,converse(X2)))))) = join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),converse(complement(composition(X3,converse(X2)))))),
inference(congruence,[status(thm)],[c943]) ).
cnf(c945,plain,
converse(composition(X2,X)) = composition(converse(X),converse(X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c946,plain,
composition(converse(X2),converse(X)) = converse(composition(X,X2)),
inference(symmetry,[status(thm)],[c945]) ).
cnf(c947,plain,
join(converse(composition(composition(X2,converse(X3)),X4)),composition(converse(X4),converse(X))) = join(converse(composition(composition(X2,converse(X3)),X4)),converse(composition(X,X4))),
inference(congruence,[status(thm)],[c946]) ).
cnf(c948,plain,
converse(join(composition(composition(X2,converse(X3)),X4),composition(X,X4))) = join(converse(composition(composition(X2,converse(X3)),X4)),converse(composition(X,X4))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c949,plain,
join(converse(composition(composition(X2,converse(X3)),X4)),converse(composition(X,X4))) = converse(join(composition(composition(X2,converse(X3)),X4),composition(X,X4))),
inference(symmetry,[status(thm)],[c948]) ).
cnf(c950,plain,
composition(join(X2,X3),X) = join(composition(X2,X),composition(X3,X)),
inference(substitution,[status(thm)],[c698]) ).
cnf(c951,plain,
join(composition(X2,X),composition(X3,X)) = composition(join(X2,X3),X),
inference(symmetry,[status(thm)],[c950]) ).
cnf(c952,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c953,plain,
composition(join(X2,X3),X) = composition(join(X3,X2),X),
inference(congruence,[status(thm)],[c952]) ).
cnf(c954,plain,
join(composition(X2,X),composition(X3,X)) = composition(join(X3,X2),X),
inference(transitivity,[status(thm)],[c951,c953]) ).
cnf(c955,plain,
join(composition(composition(X2,converse(X3)),X4),composition(X,X4)) = composition(join(X,composition(X2,converse(X3))),X4),
inference(substitution,[status(thm)],[c954]) ).
cnf(c956,plain,
converse(join(composition(composition(X2,converse(X3)),X4),composition(X,X4))) = converse(composition(join(X,composition(X2,converse(X3))),X4)),
inference(congruence,[status(thm)],[c955]) ).
cnf(c957,plain,
converse(composition(join(X,composition(X2,converse(X3))),X4)) = composition(converse(X4),converse(join(X,composition(X2,converse(X3))))),
inference(substitution,[status(thm)],[c42]) ).
cnf(c958,plain,
converse(join(X,composition(X2,converse(X3)))) = join(converse(X),converse(composition(X2,converse(X3)))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c959,plain,
composition(converse(X4),converse(join(X,composition(X2,converse(X3))))) = composition(converse(X4),join(converse(X),converse(composition(X2,converse(X3))))),
inference(congruence,[status(thm)],[c958]) ).
cnf(c960,plain,
converse(composition(X,converse(X2))) = composition(X2,converse(X)),
inference(substitution,[status(thm)],[c936]) ).
cnf(c961,plain,
join(converse(X),converse(composition(X2,converse(X3)))) = join(converse(X),composition(X3,converse(X2))),
inference(congruence,[status(thm)],[c960]) ).
cnf(c962,plain,
composition(converse(X4),join(converse(X),converse(composition(X2,converse(X3))))) = composition(converse(X4),join(converse(X),composition(X3,converse(X2)))),
inference(congruence,[status(thm)],[c961]) ).
cnf(c963,plain,
join(converse(X),composition(X3,converse(X2))) = join(composition(X3,converse(X2)),converse(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c964,plain,
composition(converse(X4),join(converse(X),composition(X3,converse(X2)))) = composition(converse(X4),join(composition(X3,converse(X2)),converse(X))),
inference(congruence,[status(thm)],[c963]) ).
cnf(c965,plain,
composition(converse(X4),join(converse(X),converse(composition(X2,converse(X3))))) = composition(converse(X4),join(composition(X3,converse(X2)),converse(X))),
inference(transitivity,[status(thm)],[c962,c964]) ).
cnf(c966,plain,
composition(converse(X4),converse(join(X,composition(X2,converse(X3))))) = composition(converse(X4),join(composition(X3,converse(X2)),converse(X))),
inference(transitivity,[status(thm)],[c959,c965]) ).
cnf(c967,plain,
converse(composition(join(X,composition(X2,converse(X3))),X4)) = composition(converse(X4),join(composition(X3,converse(X2)),converse(X))),
inference(transitivity,[status(thm)],[c957,c966]) ).
cnf(c968,plain,
converse(join(composition(composition(X2,converse(X3)),X4),composition(X,X4))) = composition(converse(X4),join(composition(X3,converse(X2)),converse(X))),
inference(transitivity,[status(thm)],[c956,c967]) ).
cnf(c969,plain,
join(converse(composition(composition(X2,converse(X3)),X4)),converse(composition(X,X4))) = composition(converse(X4),join(composition(X3,converse(X2)),converse(X))),
inference(transitivity,[status(thm)],[c949,c968]) ).
cnf(c970,plain,
join(converse(composition(composition(X2,converse(X3)),X4)),composition(converse(X4),converse(X))) = composition(converse(X4),join(composition(X3,converse(X2)),converse(X))),
inference(transitivity,[status(thm)],[c947,c969]) ).
cnf(c971,plain,
join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),converse(complement(composition(X3,converse(X2)))))) = composition(converse(X),join(composition(X2,converse(X3)),converse(complement(composition(X3,converse(X2)))))),
inference(substitution,[status(thm)],[c970]) ).
cnf(c972,plain,
converse(composition(X,converse(X2))) = composition(X2,converse(X)),
inference(substitution,[status(thm)],[c936]) ).
cnf(c973,plain,
composition(X2,converse(X)) = converse(composition(X,converse(X2))),
inference(symmetry,[status(thm)],[c972]) ).
cnf(c974,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)],[c973]) ).
cnf(c975,plain,
join(converse(composition(X,converse(X2))),converse(complement(composition(X,converse(X2))))) = converse(top),
inference(substitution,[status(thm)],[c107]) ).
cnf(c976,plain,
join(composition(X2,converse(X)),converse(complement(composition(X,converse(X2))))) = converse(top),
inference(transitivity,[status(thm)],[c974,c975]) ).
cnf(c977,plain,
join(composition(X,converse(X2)),converse(complement(composition(X2,converse(X))))) = converse(top),
inference(substitution,[status(thm)],[c976]) ).
cnf(c978,plain,
composition(converse(X),join(composition(X2,converse(X3)),converse(complement(composition(X3,converse(X2)))))) = composition(converse(X),converse(top)),
inference(congruence,[status(thm)],[c977]) ).
cnf(c979,plain,
composition(converse(X),converse(top)) = composition(converse(X),top),
inference(congruence,[status(thm)],[c168]) ).
cnf(c980,plain,
composition(converse(X),join(composition(X2,converse(X3)),converse(complement(composition(X3,converse(X2)))))) = composition(converse(X),top),
inference(transitivity,[status(thm)],[c978,c979]) ).
cnf(c981,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)],[c971,c980]) ).
cnf(c982,plain,
join(converse(composition(composition(X3,converse(X2)),X)),composition(converse(X),complement(converse(composition(X3,converse(X2)))))) = composition(converse(X),top),
inference(transitivity,[status(thm)],[c944,c981]) ).
cnf(c983,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)],[c940,c982]) ).
cnf(c984,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)],[c983]) ).
cnf(c985,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)],[c984]) ).
cnf(c986,plain,
join(composition(X,top),complement(X)) = join(complement(X),composition(X,top)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c987,plain,
join(complement(X),composition(X,top)) = join(composition(X,top),complement(X)),
inference(symmetry,[status(thm)],[c986]) ).
cnf(c988,plain,
complement(meet(X,complement(composition(X,top)))) = join(composition(X,top),complement(X)),
inference(substitution,[status(thm)],[c366]) ).
cnf(c989,plain,
join(composition(X,top),complement(X)) = complement(meet(X,complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c988]) ).
cnf(c990,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c991,plain,
X = composition(X,one),
inference(symmetry,[status(thm)],[c990]) ).
cnf(c992,plain,
meet(X,complement(composition(X,top))) = meet(composition(X,one),complement(composition(X,top))),
inference(congruence,[status(thm)],[c991]) ).
cnf(c993,plain,
meet(composition(X,one),complement(composition(X,top))) = zero,
inference(substitution,[status(thm)],[c807]) ).
cnf(c994,plain,
meet(X,complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c992,c993]) ).
cnf(c995,plain,
complement(meet(X,complement(composition(X,top)))) = complement(zero),
inference(congruence,[status(thm)],[c994]) ).
cnf(c996,plain,
complement(meet(X,complement(composition(X,top)))) = top,
inference(transitivity,[status(thm)],[c995,c650]) ).
cnf(c997,plain,
join(composition(X,top),complement(X)) = top,
inference(transitivity,[status(thm)],[c989,c996]) ).
cnf(c998,plain,
join(complement(X),composition(X,top)) = top,
inference(transitivity,[status(thm)],[c987,c997]) ).
cnf(c999,plain,
join(complement(converse(X)),composition(converse(X),top)) = top,
inference(substitution,[status(thm)],[c998]) ).
cnf(c1000,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)],[c985,c999]) ).
cnf(c1001,plain,
join(converse(composition(composition(X,converse(X)),X)),complement(converse(X))) = top,
inference(transitivity,[status(thm)],[c932,c1000]) ).
cnf(c1002,plain,
converse(join(converse(composition(composition(X,converse(X)),X)),complement(converse(X)))) = converse(top),
inference(congruence,[status(thm)],[c1001]) ).
cnf(c1003,plain,
converse(join(converse(composition(composition(X,converse(X)),X)),complement(converse(X)))) = top,
inference(transitivity,[status(thm)],[c1002,c168]) ).
cnf(c1004,plain,
join(converse(converse(composition(composition(X,converse(X)),X))),converse(complement(converse(X)))) = top,
inference(transitivity,[status(thm)],[c921,c1003]) ).
cnf(c1005,plain,
join(composition(composition(X,converse(X)),X),converse(complement(converse(X)))) = top,
inference(transitivity,[status(thm)],[c919,c1004]) ).
cnf(c1006,plain,
join(composition(composition(X,converse(X)),X),complement(converse(converse(X)))) = top,
inference(transitivity,[status(thm)],[c916,c1005]) ).
cnf(c1007,plain,
join(composition(composition(X,converse(X)),X),complement(X)) = top,
inference(transitivity,[status(thm)],[c601,c1006]) ).
cnf(c1008,plain,
join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))) = top,
inference(transitivity,[status(thm)],[c597,c1007]) ).
cnf(c1009,plain,
meet(complement(composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X))))) = meet(complement(composition(composition(X,converse(X)),X)),top),
inference(congruence,[status(thm)],[c1008]) ).
cnf(c1010,plain,
join(complement(join(X,composition(composition(X,converse(X)),X))),meet(complement(composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))))) = join(complement(join(X,composition(composition(X,converse(X)),X))),meet(complement(composition(composition(X,converse(X)),X)),top)),
inference(congruence,[status(thm)],[c1009]) ).
cnf(c1011,plain,
meet(complement(X2),X) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c1012,plain,
join(complement(X3),meet(complement(X2),X)) = join(complement(X3),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c1011]) ).
cnf(c1013,plain,
join(meet(X2,complement(X)),complement(X3)) = join(complement(X3),meet(X2,complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c1014,plain,
join(complement(X3),meet(X2,complement(X))) = join(meet(X2,complement(X)),complement(X3)),
inference(symmetry,[status(thm)],[c1013]) ).
cnf(c1015,plain,
complement(join(X,complement(X2))) = meet(X2,complement(X)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c1016,plain,
meet(X2,complement(X)) = complement(join(X,complement(X2))),
inference(symmetry,[status(thm)],[c1015]) ).
cnf(c1017,plain,
join(meet(X2,complement(X)),complement(X3)) = join(complement(join(X,complement(X2))),complement(X3)),
inference(congruence,[status(thm)],[c1016]) ).
cnf(c1018,plain,
join(complement(join(X,complement(X2))),complement(X3)) = complement(meet(join(X,complement(X2)),X3)),
inference(substitution,[status(thm)],[c478]) ).
cnf(c1019,plain,
meet(X3,join(X,complement(X2))) = meet(join(X,complement(X2)),X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c1020,plain,
meet(join(X,complement(X2)),X3) = meet(X3,join(X,complement(X2))),
inference(symmetry,[status(thm)],[c1019]) ).
cnf(c1021,plain,
complement(meet(join(X,complement(X2)),X3)) = complement(meet(X3,join(X,complement(X2)))),
inference(congruence,[status(thm)],[c1020]) ).
cnf(c1022,plain,
join(complement(join(X,complement(X2))),complement(X3)) = complement(meet(X3,join(X,complement(X2)))),
inference(transitivity,[status(thm)],[c1018,c1021]) ).
cnf(c1023,plain,
join(meet(X2,complement(X)),complement(X3)) = complement(meet(X3,join(X,complement(X2)))),
inference(transitivity,[status(thm)],[c1017,c1022]) ).
cnf(c1024,plain,
join(complement(X3),meet(X2,complement(X))) = complement(meet(X3,join(X,complement(X2)))),
inference(transitivity,[status(thm)],[c1014,c1023]) ).
cnf(c1025,plain,
join(complement(X3),meet(X,complement(X2))) = complement(meet(X3,join(X2,complement(X)))),
inference(substitution,[status(thm)],[c1024]) ).
cnf(c1026,plain,
join(complement(X3),meet(complement(X2),X)) = complement(meet(X3,join(X2,complement(X)))),
inference(transitivity,[status(thm)],[c1012,c1025]) ).
cnf(c1027,plain,
join(complement(join(X,composition(composition(X,converse(X)),X))),meet(complement(composition(composition(X,converse(X)),X)),top)) = complement(meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(top)))),
inference(substitution,[status(thm)],[c1026]) ).
cnf(c1028,plain,
join(composition(composition(X,converse(X)),X),complement(top)) = join(composition(composition(X,converse(X)),X),zero),
inference(congruence,[status(thm)],[c24]) ).
cnf(c1029,plain,
meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(top))) = meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),zero)),
inference(congruence,[status(thm)],[c1028]) ).
cnf(c1030,plain,
complement(meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(top)))) = complement(meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),zero))),
inference(congruence,[status(thm)],[c1029]) ).
cnf(c1031,plain,
join(composition(composition(X,converse(X)),X),zero) = composition(composition(X,converse(X)),X),
inference(substitution,[status(thm)],[c353]) ).
cnf(c1032,plain,
meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),zero)) = meet(join(X,composition(composition(X,converse(X)),X)),composition(composition(X,converse(X)),X)),
inference(congruence,[status(thm)],[c1031]) ).
cnf(c1033,plain,
complement(meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),zero))) = complement(meet(join(X,composition(composition(X,converse(X)),X)),composition(composition(X,converse(X)),X))),
inference(congruence,[status(thm)],[c1032]) ).
cnf(c1034,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)],[c277]) ).
cnf(c1035,plain,
complement(meet(join(X,composition(composition(X,converse(X)),X)),composition(composition(X,converse(X)),X))) = complement(composition(composition(X,converse(X)),X)),
inference(congruence,[status(thm)],[c1034]) ).
cnf(c1036,plain,
complement(meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),zero))) = complement(composition(composition(X,converse(X)),X)),
inference(transitivity,[status(thm)],[c1033,c1035]) ).
cnf(c1037,plain,
complement(meet(join(X,composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(top)))) = complement(composition(composition(X,converse(X)),X)),
inference(transitivity,[status(thm)],[c1030,c1036]) ).
cnf(c1038,plain,
join(complement(join(X,composition(composition(X,converse(X)),X))),meet(complement(composition(composition(X,converse(X)),X)),top)) = complement(composition(composition(X,converse(X)),X)),
inference(transitivity,[status(thm)],[c1027,c1037]) ).
cnf(c1039,plain,
join(complement(join(X,composition(composition(X,converse(X)),X))),meet(complement(composition(composition(X,converse(X)),X)),join(composition(composition(X,converse(X)),X),complement(join(X,composition(composition(X,converse(X)),X)))))) = complement(composition(composition(X,converse(X)),X)),
inference(transitivity,[status(thm)],[c1010,c1038]) ).
cnf(c1040,plain,
complement(join(X,composition(composition(X,converse(X)),X))) = complement(composition(composition(X,converse(X)),X)),
inference(transitivity,[status(thm)],[c415,c1039]) ).
cnf(c1041,plain,
complement(composition(composition(X,converse(X)),X)) = complement(join(X,composition(composition(X,converse(X)),X))),
inference(symmetry,[status(thm)],[c1040]) ).
cnf(c1042,plain,
meet(join(X,composition(composition(X,converse(X)),X)),complement(composition(composition(X,converse(X)),X))) = meet(join(X,composition(composition(X,converse(X)),X)),complement(join(X,composition(composition(X,converse(X)),X)))),
inference(congruence,[status(thm)],[c1041]) ).
cnf(c1043,plain,
join(composition(composition(X,converse(X)),X),meet(join(X,composition(composition(X,converse(X)),X)),complement(composition(composition(X,converse(X)),X)))) = join(composition(composition(X,converse(X)),X),meet(join(X,composition(composition(X,converse(X)),X)),complement(join(X,composition(composition(X,converse(X)),X))))),
inference(congruence,[status(thm)],[c1042]) ).
cnf(c1044,plain,
zero = meet(join(X,composition(composition(X,converse(X)),X)),complement(join(X,composition(composition(X,converse(X)),X)))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c1045,plain,
meet(join(X,composition(composition(X,converse(X)),X)),complement(join(X,composition(composition(X,converse(X)),X)))) = zero,
inference(symmetry,[status(thm)],[c1044]) ).
cnf(c1046,plain,
join(composition(composition(X,converse(X)),X),meet(join(X,composition(composition(X,converse(X)),X)),complement(join(X,composition(composition(X,converse(X)),X))))) = join(composition(composition(X,converse(X)),X),zero),
inference(congruence,[status(thm)],[c1045]) ).
cnf(c1047,plain,
join(composition(composition(X,converse(X)),X),zero) = composition(composition(X,converse(X)),X),
inference(substitution,[status(thm)],[c353]) ).
cnf(c1048,plain,
join(composition(composition(X,converse(X)),X),meet(join(X,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)],[c1046,c1047]) ).
cnf(c1049,plain,
join(composition(composition(X,converse(X)),X),meet(join(X,composition(composition(X,converse(X)),X)),complement(composition(composition(X,converse(X)),X)))) = composition(composition(X,converse(X)),X),
inference(transitivity,[status(thm)],[c1043,c1048]) ).
cnf(c1050,plain,
join(X,composition(composition(X,converse(X)),X)) = composition(composition(X,converse(X)),X),
inference(transitivity,[status(thm)],[c291,c1049]) ).
cnf(c1051,plain,
join(sk1,composition(composition(sk1,converse(sk1)),sk1)) = composition(composition(sk1,converse(sk1)),sk1),
inference(substitution,[status(thm)],[c1050]) ).
cnf(c1052,plain,
$false,
inference(resolution,[status(thm)],[c1,c1051]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL045-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 23:02:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.15/2.68 Command-line arguments: --flatten --complete-subsets
% 17.15/2.68
% 17.15/2.68 % SZS status Unsatisfiable
% 17.15/2.68
% 17.93/2.77 % SZS output start CNFRefutation
% See solution above
% 22.87/3.33
% 22.87/3.33 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------