%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL012-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:33:05 PM UTC 2026
% Result : Unsatisfiable 13.08s 17.31s
% Output : CNFRefutation 15.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 114
% Number of leaves : 15
% Syntax : Number of clauses : 709 ( 709 unt; 0 nHn; 83 RR)
% Number of literals : 709 ( 708 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 876 ( 76 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(c2,axiom,
join(A,B) = join(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c3,plain,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) = join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c5,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
composition(X2,X) = composition(X2,converse(converse(X))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
complement(composition(X2,X)) = complement(composition(X2,converse(converse(X)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
composition(complement(composition(X2,X)),converse(X)) = composition(complement(composition(X2,converse(converse(X)))),converse(X)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
join(complement(X2),composition(complement(composition(X2,X)),converse(X))) = join(complement(X2),composition(complement(composition(X2,converse(converse(X)))),converse(X))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c12,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
composition(X2,converse(X)) = composition(converse(converse(X2)),converse(X)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
complement(composition(X2,converse(X))) = complement(composition(converse(converse(X2)),converse(X))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
composition(complement(composition(X2,converse(X))),X) = composition(complement(composition(converse(converse(X2)),converse(X))),X),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
join(complement(X2),composition(complement(composition(X2,converse(X))),X)) = join(complement(X2),composition(complement(composition(converse(converse(X2)),converse(X))),X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c18,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
complement(X) = complement(converse(converse(X))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
join(complement(X2),composition(complement(composition(converse(converse(X2)),converse(X))),X)) = join(complement(converse(converse(X2))),composition(complement(composition(converse(converse(X2)),converse(X))),X)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c22,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
composition(complement(composition(converse(X2),converse(X))),X) = composition(complement(composition(converse(X2),converse(X))),converse(converse(X))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
join(complement(converse(X2)),composition(complement(composition(converse(X2),converse(X))),X)) = join(complement(converse(X2)),composition(complement(composition(converse(X2),converse(X))),converse(converse(X)))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c26,plain,
converse(composition(X,X2)) = composition(converse(X2),converse(X)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
composition(converse(X2),converse(X)) = converse(composition(X,X2)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
complement(composition(converse(X2),converse(X))) = complement(converse(composition(X,X2))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
composition(complement(composition(converse(X2),converse(X))),converse(converse(X))) = composition(complement(converse(composition(X,X2))),converse(converse(X))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
join(complement(converse(X2)),composition(complement(composition(converse(X2),converse(X))),converse(converse(X)))) = join(complement(converse(X2)),composition(complement(converse(composition(X,X2))),converse(converse(X)))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
join(X,converse(zero)) = join(converse(zero),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
join(converse(zero),X) = join(X,converse(zero)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c34,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
join(X,converse(zero)) = join(converse(converse(X)),converse(zero)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
meet(A2,B2) = complement(join(complement(A2),complement(B2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c37,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c42,plain,
complement(join(complement(X2),complement(X))) = meet(X2,X),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
complement(join(complement(X),complement(X2))) = meet(X2,X),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
meet(X,X2) = meet(X2,X),
inference(transitivity,[status(thm)],[c37,c43]) ).
cnf(c45,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,axiom,
top = join(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
cnf(c47,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c50,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c52,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c50,c53]) ).
cnf(c55,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c48,c54]) ).
cnf(c56,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c60,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c62,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c58,c63]) ).
cnf(c65,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c68,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c70,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c73,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c75,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c73,c76]) ).
cnf(c78,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c80,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c71,c80]) ).
cnf(c82,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
composition(converse(one),one) = converse(one),
inference(substitution,[status(thm)],[c74]) ).
cnf(c86,plain,
converse(one) = composition(converse(one),one),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
composition(converse(one),one) = one,
inference(substitution,[status(thm)],[c81]) ).
cnf(c88,plain,
converse(one) = one,
inference(transitivity,[status(thm)],[c86,c87]) ).
cnf(c89,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
composition(one,X) = composition(converse(one),X),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c90,c81]) ).
cnf(c92,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,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)],[c2]) ).
cnf(c97,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)],[c96]) ).
cnf(c98,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c99,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c97,c99]) ).
cnf(c101,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c95,c101]) ).
cnf(c103,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c84,c102]) ).
cnf(c104,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c108,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)],[c107]) ).
cnf(c109,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(c110,plain,
X2 = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))) = X2,
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
join(meet(X2,X),complement(join(complement(X2),X))) = X2,
inference(transitivity,[status(thm)],[c108,c111]) ).
cnf(c113,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c106,c113]) ).
cnf(c115,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c68,c114]) ).
cnf(c116,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c66,c116]) ).
cnf(c118,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c45,c117]) ).
cnf(c119,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c44]) ).
cnf(c122,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c124,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c126,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c128,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,axiom,
converse(join(A2,B2)) = join(converse(A2),converse(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(c131,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c134,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c132,c135]) ).
cnf(c137,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c129,c137]) ).
cnf(c139,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
converse(top) = join(complement(X),converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(complement(converse(complement(X)))))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c143,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
join(X2,join(complement(X2),X)) = join(X2,join(X,complement(X2))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c146,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c149,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c151,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c2]) ).
cnf(c154,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c149,c154]) ).
cnf(c156,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c147,c155]) ).
cnf(c157,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c158,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c156]) ).
cnf(c160,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c162,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c163,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c161,c163]) ).
cnf(c165,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c160,c164]) ).
cnf(c166,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c158,c165]) ).
cnf(c167,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c156]) ).
cnf(c170,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c156]) ).
cnf(c171,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c166]) ).
cnf(c173,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c171,c172]) ).
cnf(c174,plain,
join(X,join(top,complement(X))) = join(X2,top),
inference(transitivity,[status(thm)],[c169,c173]) ).
cnf(c175,plain,
join(X2,top) = join(X,top),
inference(transitivity,[status(thm)],[c168,c174]) ).
cnf(c176,plain,
join(X2,top) = join(X,top),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
join(X3,join(X2,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c156,c176]) ).
cnf(c178,plain,
join(X3,join(complement(X3),X2)) = join(X,top),
inference(transitivity,[status(thm)],[c144,c177]) ).
cnf(c179,plain,
join(X2,join(complement(X2),converse(complement(converse(complement(X2)))))) = join(X,top),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = join(X3,top),
inference(substitution,[status(thm)],[c178]) ).
cnf(c181,plain,
join(X3,top) = join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = join(X2,complement(X2)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c183,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c184,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
join(X2,join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = top,
inference(transitivity,[status(thm)],[c182,c184]) ).
cnf(c186,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c181,c185]) ).
cnf(c187,plain,
join(X,join(complement(X),converse(complement(converse(complement(X)))))) = top,
inference(transitivity,[status(thm)],[c179,c186]) ).
cnf(c188,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c141,c187]) ).
cnf(c189,plain,
top = join(X,converse(top)),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
converse(top) = converse(join(X,converse(top))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
converse(join(X,converse(top))) = join(converse(X),converse(converse(top))),
inference(substitution,[status(thm)],[c130]) ).
cnf(c192,plain,
converse(converse(top)) = top,
inference(substitution,[status(thm)],[c4]) ).
cnf(c193,plain,
join(converse(X),converse(converse(top))) = join(converse(X),top),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
join(converse(X),top) = top,
inference(substitution,[status(thm)],[c186]) ).
cnf(c195,plain,
join(converse(X),converse(converse(top))) = top,
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
converse(join(X,converse(top))) = top,
inference(transitivity,[status(thm)],[c191,c195]) ).
cnf(c197,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c190,c196]) ).
cnf(c198,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
meet(X,top) = meet(X,converse(top)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
join(meet(X,top),complement(top)) = join(meet(X,converse(top)),complement(top)),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
join(complement(X),converse(top)) = top,
inference(substitution,[status(thm)],[c188]) ).
cnf(c202,plain,
top = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
complement(top) = complement(join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
join(meet(X,converse(top)),complement(top)) = join(meet(X,converse(top)),complement(join(complement(X),converse(top)))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
join(meet(X,converse(top)),complement(join(complement(X),converse(top)))) = X,
inference(substitution,[status(thm)],[c112]) ).
cnf(c206,plain,
join(meet(X,converse(top)),complement(top)) = X,
inference(transitivity,[status(thm)],[c204,c205]) ).
cnf(c207,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c200,c206]) ).
cnf(c208,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c126,c207]) ).
cnf(c209,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c124,c208]) ).
cnf(c210,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c122,c209]) ).
cnf(c211,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c210]) ).
cnf(c212,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c120,c211]) ).
cnf(c213,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c214,c115]) ).
cnf(c216,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
converse(X) = converse(complement(complement(X))),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
join(converse(X),converse(zero)) = join(converse(complement(complement(X))),converse(zero)),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
join(converse(zero),converse(complement(complement(X)))) = join(converse(complement(complement(X))),converse(zero)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c220,plain,
join(converse(complement(complement(X))),converse(zero)) = join(converse(zero),converse(complement(complement(X)))),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c222,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c223,plain,
meet(X,X) = complement(complement(X)),
inference(transitivity,[status(thm)],[c221,c222]) ).
cnf(c224,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
converse(complement(complement(X))) = converse(meet(X,X)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
join(converse(zero),converse(complement(complement(X)))) = join(converse(zero),converse(meet(X,X))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
converse(join(zero,meet(X,X))) = join(converse(zero),converse(meet(X,X))),
inference(substitution,[status(thm)],[c130]) ).
cnf(c228,plain,
join(converse(zero),converse(meet(X,X))) = converse(join(zero,meet(X,X))),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c230,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c232,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c112]) ).
cnf(c234,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c232,c233]) ).
cnf(c235,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c230,c234]) ).
cnf(c236,plain,
converse(join(zero,meet(X,X))) = converse(X),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
join(converse(zero),converse(meet(X,X))) = converse(X),
inference(transitivity,[status(thm)],[c228,c236]) ).
cnf(c238,plain,
join(converse(zero),converse(complement(complement(X)))) = converse(X),
inference(transitivity,[status(thm)],[c226,c237]) ).
cnf(c239,plain,
join(converse(complement(complement(X))),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c220,c238]) ).
cnf(c240,plain,
join(converse(X),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c218,c239]) ).
cnf(c241,plain,
join(converse(converse(X)),converse(zero)) = converse(converse(X)),
inference(substitution,[status(thm)],[c240]) ).
cnf(c242,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c243,plain,
join(converse(converse(X)),converse(zero)) = X,
inference(transitivity,[status(thm)],[c241,c242]) ).
cnf(c244,plain,
join(X,converse(zero)) = X,
inference(transitivity,[status(thm)],[c35,c243]) ).
cnf(c245,plain,
join(converse(zero),X) = X,
inference(transitivity,[status(thm)],[c32,c244]) ).
cnf(c246,plain,
join(converse(zero),converse(complement(X))) = converse(complement(X)),
inference(substitution,[status(thm)],[c245]) ).
cnf(c247,plain,
converse(complement(X)) = join(converse(zero),converse(complement(X))),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
converse(join(zero,complement(X))) = join(converse(zero),converse(complement(X))),
inference(substitution,[status(thm)],[c130]) ).
cnf(c249,plain,
join(converse(zero),converse(complement(X))) = converse(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
converse(converse(complement(converse(complement(X))))) = complement(converse(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c251,plain,
complement(converse(complement(X))) = converse(converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
meet(complement(X2),X) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c253,plain,
join(meet(X2,X),meet(complement(X2),X)) = join(meet(X2,X),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c255,plain,
join(meet(X2,X),meet(X,complement(X2))) = join(meet(X,X2),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,X),meet(X2,complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c257,plain,
join(meet(X2,X),meet(X2,complement(X))) = join(meet(X2,complement(X)),meet(X2,X)),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c259,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))) = X2,
inference(substitution,[status(thm)],[c112]) ).
cnf(c261,plain,
join(meet(X2,complement(X)),meet(X2,X)) = X2,
inference(transitivity,[status(thm)],[c259,c260]) ).
cnf(c262,plain,
join(meet(X2,X),meet(X2,complement(X))) = X2,
inference(transitivity,[status(thm)],[c257,c261]) ).
cnf(c263,plain,
join(meet(X,X2),meet(X,complement(X2))) = X,
inference(substitution,[status(thm)],[c262]) ).
cnf(c264,plain,
join(meet(X2,X),meet(X,complement(X2))) = X,
inference(transitivity,[status(thm)],[c255,c263]) ).
cnf(c265,plain,
join(meet(X2,X),meet(complement(X2),X)) = X,
inference(transitivity,[status(thm)],[c253,c264]) ).
cnf(c266,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)],[c265]) ).
cnf(c267,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)],[c266]) ).
cnf(c268,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c2]) ).
cnf(c269,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
join(complement(complement(X)),X2) = join(X2,complement(complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c271,plain,
join(X2,complement(complement(X))) = join(complement(complement(X)),X2),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
join(zero,join(X2,complement(complement(X)))) = join(zero,join(complement(complement(X)),X2)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c274,plain,
join(complement(complement(X)),X2) = join(meet(X,X),X2),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
join(zero,join(complement(complement(X)),X2)) = join(zero,join(meet(X,X),X2)),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
join(zero,join(meet(X,X),X2)) = join(join(zero,meet(X,X)),X2),
inference(substitution,[status(thm)],[c148]) ).
cnf(c277,plain,
join(join(zero,meet(X,X)),X2) = join(X,X2),
inference(congruence,[status(thm)],[c235]) ).
cnf(c278,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c279,plain,
join(join(zero,meet(X,X)),X2) = join(X2,X),
inference(transitivity,[status(thm)],[c277,c278]) ).
cnf(c280,plain,
join(zero,join(meet(X,X),X2)) = join(X2,X),
inference(transitivity,[status(thm)],[c276,c279]) ).
cnf(c281,plain,
join(zero,join(complement(complement(X)),X2)) = join(X2,X),
inference(transitivity,[status(thm)],[c275,c280]) ).
cnf(c282,plain,
join(zero,join(X2,complement(complement(X)))) = join(X2,X),
inference(transitivity,[status(thm)],[c272,c281]) ).
cnf(c283,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,X),
inference(substitution,[status(thm)],[c282]) ).
cnf(c284,plain,
join(zero,X) = join(zero,join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c286,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
join(zero,join(zero,complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c286,c115]) ).
cnf(c288,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c284,c287]) ).
cnf(c289,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c269,c288]) ).
cnf(c290,plain,
join(meet(X,converse(complement(converse(X)))),zero) = meet(X,converse(complement(converse(X)))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
meet(X,converse(complement(converse(X)))) = join(meet(X,converse(complement(converse(X)))),zero),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
meet(zero,X) = meet(X,zero),
inference(substitution,[status(thm)],[c44]) ).
cnf(c293,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c294,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c295,plain,
join(zero,meet(top,complement(zero))) = complement(zero),
inference(substitution,[status(thm)],[c210]) ).
cnf(c296,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c298,plain,
meet(top,zero) = meet(top,complement(top)),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
zero = meet(top,complement(top)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c300,plain,
meet(top,complement(top)) = zero,
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
meet(top,zero) = zero,
inference(transitivity,[status(thm)],[c298,c300]) ).
cnf(c302,plain,
zero = meet(top,zero),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c303,plain,
join(zero,meet(top,complement(zero))) = join(meet(top,zero),meet(top,complement(zero))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
join(meet(top,zero),meet(top,complement(zero))) = top,
inference(substitution,[status(thm)],[c262]) ).
cnf(c305,plain,
join(zero,meet(top,complement(zero))) = top,
inference(transitivity,[status(thm)],[c303,c304]) ).
cnf(c306,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c296,c305]) ).
cnf(c307,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c166]) ).
cnf(c310,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c309,c55]) ).
cnf(c311,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c308,c310]) ).
cnf(c312,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c294,c311]) ).
cnf(c313,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c293,c312]) ).
cnf(c314,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c292,c313]) ).
cnf(c315,plain,
meet(zero,converse(complement(converse(X)))) = zero,
inference(substitution,[status(thm)],[c314]) ).
cnf(c316,plain,
zero = meet(zero,converse(complement(converse(X)))),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,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)],[c316]) ).
cnf(c318,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c319,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c212]) ).
cnf(c320,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c321,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c322,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c321,c209]) ).
cnf(c323,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c320,c322]) ).
cnf(c324,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c318,c323]) ).
cnf(c325,plain,
meet(composition(zero,X),top) = composition(zero,X),
inference(substitution,[status(thm)],[c324]) ).
cnf(c326,plain,
composition(zero,X) = meet(composition(zero,X),top),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
top = complement(zero),
inference(symmetry,[status(thm)],[c306]) ).
cnf(c328,plain,
meet(composition(zero,X),top) = meet(composition(zero,X),complement(zero)),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
meet(converse(zero),top) = converse(zero),
inference(substitution,[status(thm)],[c324]) ).
cnf(c330,plain,
converse(zero) = meet(converse(zero),top),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
join(converse(zero),complement(converse(zero))) = complement(converse(zero)),
inference(substitution,[status(thm)],[c245]) ).
cnf(c332,plain,
complement(converse(zero)) = join(converse(zero),complement(converse(zero))),
inference(symmetry,[status(thm)],[c331]) ).
cnf(c333,plain,
top = join(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c334,plain,
join(converse(zero),complement(converse(zero))) = top,
inference(symmetry,[status(thm)],[c333]) ).
cnf(c335,plain,
complement(converse(zero)) = top,
inference(transitivity,[status(thm)],[c332,c334]) ).
cnf(c336,plain,
top = complement(converse(zero)),
inference(symmetry,[status(thm)],[c335]) ).
cnf(c337,plain,
meet(converse(zero),top) = meet(converse(zero),complement(converse(zero))),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c339,plain,
meet(converse(zero),complement(converse(zero))) = zero,
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
meet(converse(zero),top) = zero,
inference(transitivity,[status(thm)],[c337,c339]) ).
cnf(c341,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c330,c340]) ).
cnf(c342,plain,
zero = converse(zero),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
composition(zero,X) = composition(converse(zero),X),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
meet(composition(zero,X),complement(zero)) = meet(composition(converse(zero),X),complement(zero)),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c346,plain,
converse(zero) = converse(complement(top)),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
composition(converse(zero),X) = composition(converse(complement(top)),X),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
meet(composition(converse(zero),X),complement(zero)) = meet(composition(converse(complement(top)),X),complement(zero)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c350,plain,
composition(top,X) = composition(converse(top),X),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
join(X,composition(top,X)) = join(X,composition(converse(top),X)),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
join(X,one) = join(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c353,plain,
join(one,X) = join(X,one),
inference(symmetry,[status(thm)],[c352]) ).
cnf(c354,plain,
composition(join(one,X),X2) = composition(join(X,one),X2),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c356,plain,
join(X,one) = join(one,X),
inference(symmetry,[status(thm)],[c355]) ).
cnf(c357,plain,
composition(join(X2,one),X) = composition(join(one,X2),X),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c359,plain,
join(one,X) = join(converse(one),X),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
composition(join(one,X2),X) = composition(join(converse(one),X2),X),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c362,plain,
composition(join(converse(one),X2),X) = join(composition(converse(one),X),composition(X2,X)),
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
join(composition(converse(one),X),composition(X2,X)) = join(X,composition(X2,X)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c364,plain,
composition(join(converse(one),X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c362,c363]) ).
cnf(c365,plain,
composition(join(one,X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c360,c364]) ).
cnf(c366,plain,
composition(join(X2,one),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c357,c365]) ).
cnf(c367,plain,
composition(join(X,one),X2) = join(X2,composition(X,X2)),
inference(substitution,[status(thm)],[c366]) ).
cnf(c368,plain,
composition(join(one,X),X2) = join(X2,composition(X,X2)),
inference(transitivity,[status(thm)],[c354,c367]) ).
cnf(c369,plain,
composition(join(one,converse(top)),X) = join(X,composition(converse(top),X)),
inference(substitution,[status(thm)],[c368]) ).
cnf(c370,plain,
join(X,composition(converse(top),X)) = composition(join(one,converse(top)),X),
inference(symmetry,[status(thm)],[c369]) ).
cnf(c371,plain,
join(one,converse(top)) = top,
inference(substitution,[status(thm)],[c188]) ).
cnf(c372,plain,
composition(join(one,converse(top)),X) = composition(top,X),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
join(X,composition(converse(top),X)) = composition(top,X),
inference(transitivity,[status(thm)],[c370,c372]) ).
cnf(c374,plain,
join(X,composition(top,X)) = composition(top,X),
inference(transitivity,[status(thm)],[c351,c373]) ).
cnf(c375,plain,
join(top,composition(top,top)) = composition(top,top),
inference(substitution,[status(thm)],[c374]) ).
cnf(c376,plain,
composition(top,top) = join(top,composition(top,top)),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c378,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
join(X2,top) = join(X,top),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c380,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c379,c186]) ).
cnf(c381,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c378,c380]) ).
cnf(c382,plain,
join(top,composition(top,top)) = top,
inference(substitution,[status(thm)],[c381]) ).
cnf(c383,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c376,c382]) ).
cnf(c384,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
converse(complement(top)) = converse(complement(composition(top,top))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
composition(converse(complement(top)),X) = composition(converse(complement(composition(top,top))),X),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
meet(composition(converse(complement(top)),X),complement(zero)) = meet(composition(converse(complement(composition(top,top))),X),complement(zero)),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c390,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c389]) ).
cnf(c391,plain,
composition(converse(complement(composition(X,top))),X) = composition(converse(complement(composition(X,top))),converse(converse(X))),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
converse(composition(converse(X),complement(composition(X,top)))) = composition(converse(complement(composition(X,top))),converse(converse(X))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c393,plain,
composition(converse(complement(composition(X,top))),converse(converse(X))) = converse(composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c395,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c394]) ).
cnf(c396,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c395,c289]) ).
cnf(c397,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = composition(converse(X),complement(composition(X,top))),
inference(substitution,[status(thm)],[c396]) ).
cnf(c398,plain,
composition(converse(X),complement(composition(X,top))) = join(zero,composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c400,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = join(complement(top),composition(converse(X),complement(composition(X,top)))),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = complement(top),
inference(substitution,[status(thm)],[c100]) ).
cnf(c402,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c401,c55]) ).
cnf(c403,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c400,c402]) ).
cnf(c404,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c398,c403]) ).
cnf(c405,plain,
converse(composition(converse(X),complement(composition(X,top)))) = converse(zero),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
converse(composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c405,c341]) ).
cnf(c407,plain,
composition(converse(complement(composition(X,top))),converse(converse(X))) = zero,
inference(transitivity,[status(thm)],[c393,c406]) ).
cnf(c408,plain,
composition(converse(complement(composition(X,top))),X) = zero,
inference(transitivity,[status(thm)],[c391,c407]) ).
cnf(c409,plain,
composition(converse(complement(composition(top,top))),top) = zero,
inference(substitution,[status(thm)],[c408]) ).
cnf(c410,plain,
zero = composition(converse(complement(composition(top,top))),top),
inference(symmetry,[status(thm)],[c409]) ).
cnf(c411,plain,
complement(zero) = complement(composition(converse(complement(composition(top,top))),top)),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,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)],[c411]) ).
cnf(c413,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = meet(composition(X2,X),complement(composition(X2,top))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c414,plain,
meet(composition(X2,X),complement(composition(X2,top))) = join(meet(composition(X2,X),complement(composition(X2,top))),zero),
inference(symmetry,[status(thm)],[c413]) ).
cnf(c415,plain,
meet(zero,complement(composition(X,top))) = zero,
inference(substitution,[status(thm)],[c314]) ).
cnf(c416,plain,
zero = meet(zero,complement(composition(X,top))),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,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)],[c416]) ).
cnf(c418,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c396]) ).
cnf(c419,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c421,plain,
composition(top,zero) = composition(converse(top),zero),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
join(zero,composition(converse(top),zero)) = composition(converse(top),zero),
inference(substitution,[status(thm)],[c396]) ).
cnf(c423,plain,
composition(converse(top),zero) = join(zero,composition(converse(top),zero)),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c424,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c425,plain,
join(zero,composition(converse(top),zero)) = join(complement(top),composition(converse(top),zero)),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c427,plain,
composition(converse(top),zero) = composition(converse(top),complement(top)),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
join(complement(top),composition(converse(top),zero)) = join(complement(top),composition(converse(top),complement(top))),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c430,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c100]) ).
cnf(c434,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c433,c55]) ).
cnf(c435,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c432,c434]) ).
cnf(c436,plain,
join(complement(top),composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c428,c435]) ).
cnf(c437,plain,
join(zero,composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c425,c436]) ).
cnf(c438,plain,
composition(converse(top),zero) = zero,
inference(transitivity,[status(thm)],[c423,c437]) ).
cnf(c439,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c421,c438]) ).
cnf(c440,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c361]) ).
cnf(c443,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c442]) ).
cnf(c444,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c381]) ).
cnf(c445,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c444,c439]) ).
cnf(c446,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c443,c445]) ).
cnf(c447,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c441,c446]) ).
cnf(c448,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c419,c447]) ).
cnf(c449,plain,
zero = composition(X,zero),
inference(symmetry,[status(thm)],[c448]) ).
cnf(c450,plain,
meet(zero,complement(composition(X,top))) = meet(composition(X,zero),complement(composition(X,top))),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,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)],[c450]) ).
cnf(c452,plain,
zero = meet(X,zero),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c453,plain,
composition(X2,zero) = composition(X2,meet(X,zero)),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
meet(composition(X2,zero),complement(composition(X2,top))) = meet(composition(X2,meet(X,zero)),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,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)],[c454]) ).
cnf(c456,plain,
zero = composition(converse(X),complement(composition(X,top))),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c457,plain,
meet(X,zero) = meet(X,composition(converse(X2),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
composition(X2,meet(X,zero)) = composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,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)],[c458]) ).
cnf(c460,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)],[c459]) ).
cnf(c461,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(c462,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)],[c461]) ).
cnf(c463,plain,
meet(X,composition(converse(X2),complement(composition(X2,top)))) = meet(X,zero),
inference(congruence,[status(thm)],[c404]) ).
cnf(c464,plain,
composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))) = composition(X2,meet(X,zero)),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,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)],[c464]) ).
cnf(c466,plain,
composition(X2,meet(X,zero)) = composition(X2,zero),
inference(congruence,[status(thm)],[c313]) ).
cnf(c467,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = meet(composition(X2,zero),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
meet(composition(X,zero),complement(composition(X,top))) = meet(zero,complement(composition(X,top))),
inference(congruence,[status(thm)],[c448]) ).
cnf(c469,plain,
meet(zero,complement(composition(X,top))) = zero,
inference(substitution,[status(thm)],[c314]) ).
cnf(c470,plain,
meet(composition(X,zero),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c468,c469]) ).
cnf(c471,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c467,c470]) ).
cnf(c472,plain,
meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c465,c471]) ).
cnf(c473,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)],[c462,c472]) ).
cnf(c474,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)],[c460,c473]) ).
cnf(c475,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,zero),complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c455,c474]) ).
cnf(c476,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(zero,complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c451,c475]) ).
cnf(c477,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = zero,
inference(transitivity,[status(thm)],[c417,c476]) ).
cnf(c478,plain,
meet(composition(X2,X),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c414,c477]) ).
cnf(c479,plain,
meet(composition(converse(complement(composition(top,top))),X),complement(composition(converse(complement(composition(top,top))),top))) = zero,
inference(substitution,[status(thm)],[c478]) ).
cnf(c480,plain,
meet(composition(converse(complement(composition(top,top))),X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c412,c479]) ).
cnf(c481,plain,
meet(composition(converse(complement(top)),X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c388,c480]) ).
cnf(c482,plain,
meet(composition(converse(zero),X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c348,c481]) ).
cnf(c483,plain,
meet(composition(zero,X),complement(zero)) = zero,
inference(transitivity,[status(thm)],[c344,c482]) ).
cnf(c484,plain,
meet(composition(zero,X),top) = zero,
inference(transitivity,[status(thm)],[c328,c483]) ).
cnf(c485,plain,
composition(zero,X) = zero,
inference(transitivity,[status(thm)],[c326,c484]) ).
cnf(c486,plain,
zero = composition(zero,X),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
meet(zero,converse(complement(converse(X)))) = meet(composition(zero,X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,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)],[c487]) ).
cnf(c489,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c490,plain,
meet(X,converse(complement(converse(X)))) = meet(composition(one,X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,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)],[c490]) ).
cnf(c492,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c493,plain,
composition(converse(complement(X)),X) = composition(converse(complement(X)),meet(X,top)),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
meet(one,composition(converse(complement(X)),X)) = meet(one,composition(converse(complement(X)),meet(X,top))),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
join(converse(zero),converse(complement(X))) = converse(complement(X)),
inference(substitution,[status(thm)],[c245]) ).
cnf(c496,plain,
converse(complement(X)) = join(converse(zero),converse(complement(X))),
inference(symmetry,[status(thm)],[c495]) ).
cnf(c497,plain,
composition(converse(complement(X)),meet(X,top)) = composition(join(converse(zero),converse(complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c496]) ).
cnf(c498,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)],[c497]) ).
cnf(c499,plain,
converse(join(zero,complement(X))) = join(converse(zero),converse(complement(X))),
inference(substitution,[status(thm)],[c130]) ).
cnf(c500,plain,
join(converse(zero),converse(complement(X))) = converse(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c499]) ).
cnf(c501,plain,
composition(join(converse(zero),converse(complement(X))),meet(X,top)) = composition(converse(join(zero,complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c500]) ).
cnf(c502,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)],[c501]) ).
cnf(c503,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c504,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)],[c503]) ).
cnf(c505,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)],[c504]) ).
cnf(c506,plain,
meet(one,composition(converse(X),complement(X))) = meet(composition(converse(X),complement(X)),one),
inference(substitution,[status(thm)],[c44]) ).
cnf(c507,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c508,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
complement(join(complement(X2),X)) = complement(join(X,complement(X2))),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c511,plain,
join(X2,complement(X)) = join(complement(X),X2),
inference(symmetry,[status(thm)],[c510]) ).
cnf(c512,plain,
complement(join(X2,complement(X))) = complement(join(complement(X),X2)),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c44]) ).
cnf(c514,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c513,c324]) ).
cnf(c515,plain,
X = meet(top,X),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
join(complement(X),X2) = join(complement(X),meet(top,X2)),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
complement(join(complement(X),X2)) = complement(join(complement(X),meet(top,X2))),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c519,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c518]) ).
cnf(c520,plain,
meet(X3,join(complement(X2),complement(X))) = meet(X3,join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
meet(X3,join(complement(X),complement(X2))) = meet(join(complement(X),complement(X2)),X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c522,plain,
meet(join(complement(X),complement(X2)),X3) = complement(join(complement(join(complement(X),complement(X2))),complement(X3))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c523,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c524,plain,
complement(join(complement(X),complement(X2))) = meet(X,X2),
inference(symmetry,[status(thm)],[c523]) ).
cnf(c525,plain,
join(complement(join(complement(X),complement(X2))),complement(X3)) = join(meet(X,X2),complement(X3)),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = complement(join(meet(X,X2),complement(X3))),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
join(meet(X,X2),complement(X3)) = join(complement(X3),meet(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c528,plain,
complement(join(meet(X,X2),complement(X3))) = complement(join(complement(X3),meet(X,X2))),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c530,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
join(complement(X3),meet(X,X2)) = join(complement(X3),meet(X2,X)),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
complement(join(complement(X3),meet(X,X2))) = complement(join(complement(X3),meet(X2,X))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
complement(join(meet(X,X2),complement(X3))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c528,c532]) ).
cnf(c534,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c526,c533]) ).
cnf(c535,plain,
meet(join(complement(X),complement(X2)),X3) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c522,c534]) ).
cnf(c536,plain,
meet(X3,join(complement(X),complement(X2))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c521,c535]) ).
cnf(c537,plain,
meet(X3,join(complement(X2),complement(X))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c520,c536]) ).
cnf(c538,plain,
meet(X,join(complement(top),complement(X2))) = complement(join(complement(X),meet(top,X2))),
inference(substitution,[status(thm)],[c537]) ).
cnf(c539,plain,
complement(join(complement(X),meet(top,X2))) = meet(X,join(complement(top),complement(X2))),
inference(symmetry,[status(thm)],[c538]) ).
cnf(c540,plain,
join(complement(top),complement(X)) = join(zero,complement(X)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c541,plain,
meet(X,join(complement(top),complement(X2))) = meet(X,join(zero,complement(X2))),
inference(congruence,[status(thm)],[c540]) ).
cnf(c542,plain,
meet(X,join(zero,complement(X2))) = meet(X,complement(X2)),
inference(congruence,[status(thm)],[c212]) ).
cnf(c543,plain,
meet(X,join(complement(top),complement(X2))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c541,c542]) ).
cnf(c544,plain,
complement(join(complement(X),meet(top,X2))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c539,c543]) ).
cnf(c545,plain,
complement(join(complement(X),X2)) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c517,c544]) ).
cnf(c546,plain,
complement(join(X2,complement(X))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c512,c545]) ).
cnf(c547,plain,
complement(join(X,complement(X2))) = meet(X2,complement(X)),
inference(substitution,[status(thm)],[c546]) ).
cnf(c548,plain,
complement(join(complement(X2),X)) = meet(X2,complement(X)),
inference(transitivity,[status(thm)],[c509,c547]) ).
cnf(c549,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = meet(one,complement(composition(converse(X),complement(X)))),
inference(substitution,[status(thm)],[c548]) ).
cnf(c550,plain,
meet(one,complement(composition(converse(X),complement(X)))) = complement(join(complement(one),composition(converse(X),complement(X)))),
inference(symmetry,[status(thm)],[c549]) ).
cnf(c551,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c552,plain,
X = composition(X,one),
inference(symmetry,[status(thm)],[c551]) ).
cnf(c553,plain,
complement(X) = complement(composition(X,one)),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
composition(converse(X),complement(X)) = composition(converse(X),complement(composition(X,one))),
inference(congruence,[status(thm)],[c553]) ).
cnf(c555,plain,
join(complement(one),composition(converse(X),complement(X))) = join(complement(one),composition(converse(X),complement(composition(X,one)))),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
join(complement(one),composition(converse(X),complement(composition(X,one)))) = complement(one),
inference(substitution,[status(thm)],[c100]) ).
cnf(c557,plain,
join(complement(one),composition(converse(X),complement(X))) = complement(one),
inference(transitivity,[status(thm)],[c555,c556]) ).
cnf(c558,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = complement(complement(one)),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
complement(complement(one)) = one,
inference(substitution,[status(thm)],[c215]) ).
cnf(c560,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = one,
inference(transitivity,[status(thm)],[c558,c559]) ).
cnf(c561,plain,
meet(one,complement(composition(converse(X),complement(X)))) = one,
inference(transitivity,[status(thm)],[c550,c560]) ).
cnf(c562,plain,
one = meet(one,complement(composition(converse(X),complement(X)))),
inference(symmetry,[status(thm)],[c561]) ).
cnf(c563,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)],[c562]) ).
cnf(c564,plain,
meet(X,complement(X2)) = meet(complement(X2),X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c565,plain,
meet(X2,meet(X,complement(X2))) = meet(X2,meet(complement(X2),X)),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
meet(X2,meet(complement(X2),X)) = complement(join(complement(X2),complement(meet(complement(X2),X)))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c567,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c568,plain,
complement(meet(X2,X)) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
join(X2,complement(meet(X2,X))) = join(X2,complement(meet(X,X2))),
inference(congruence,[status(thm)],[c568]) ).
cnf(c570,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c571,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c570]) ).
cnf(c572,plain,
join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c235]) ).
cnf(c573,plain,
join(complement(X),complement(X2)) = join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))),
inference(symmetry,[status(thm)],[c572]) ).
cnf(c574,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)],[c537]) ).
cnf(c575,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)],[c574]) ).
cnf(c576,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)],[c212]) ).
cnf(c577,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c578,plain,
complement(join(complement(X),complement(X2))) = meet(X,X2),
inference(symmetry,[status(thm)],[c577]) ).
cnf(c579,plain,
join(complement(join(complement(X),complement(X2))),meet(X,X2)) = join(meet(X,X2),meet(X,X2)),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))) = complement(join(meet(X,X2),meet(X,X2))),
inference(congruence,[status(thm)],[c579]) ).
cnf(c581,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c582,plain,
join(X,X) = join(X,complement(complement(X))),
inference(congruence,[status(thm)],[c581]) ).
cnf(c583,plain,
join(complement(complement(X)),X) = join(X,complement(complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c584,plain,
join(X,complement(complement(X))) = join(complement(complement(X)),X),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c585,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(complement(complement(X)),X),
inference(substitution,[status(thm)],[c282]) ).
cnf(c586,plain,
join(complement(complement(X)),X) = join(zero,join(complement(complement(X)),complement(complement(X)))),
inference(symmetry,[status(thm)],[c585]) ).
cnf(c587,plain,
join(complement(complement(X)),complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c588,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c587]) ).
cnf(c589,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c588,c115]) ).
cnf(c590,plain,
join(complement(complement(X)),X) = X,
inference(transitivity,[status(thm)],[c586,c589]) ).
cnf(c591,plain,
join(X,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c584,c590]) ).
cnf(c592,plain,
join(X,X) = X,
inference(transitivity,[status(thm)],[c582,c591]) ).
cnf(c593,plain,
join(meet(X,X2),meet(X,X2)) = meet(X,X2),
inference(substitution,[status(thm)],[c592]) ).
cnf(c594,plain,
complement(join(meet(X,X2),meet(X,X2))) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c596,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c595]) ).
cnf(c597,plain,
complement(meet(X,X2)) = complement(meet(X2,X)),
inference(congruence,[status(thm)],[c596]) ).
cnf(c598,plain,
complement(join(meet(X,X2),meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c594,c597]) ).
cnf(c599,plain,
complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c580,c598]) ).
cnf(c600,plain,
join(zero,complement(join(complement(join(complement(X),complement(X2))),meet(X,X2)))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c576,c599]) ).
cnf(c601,plain,
join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c575,c600]) ).
cnf(c602,plain,
join(complement(X),complement(X2)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c573,c601]) ).
cnf(c603,plain,
join(complement(X2),complement(X)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c571,c602]) ).
cnf(c604,plain,
join(complement(X),complement(X2)) = complement(meet(X,X2)),
inference(substitution,[status(thm)],[c603]) ).
cnf(c605,plain,
complement(meet(X,X2)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c604]) ).
cnf(c606,plain,
join(X2,complement(meet(X,X2))) = join(X2,join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
join(X2,join(complement(X),complement(X2))) = join(complement(X),top),
inference(substitution,[status(thm)],[c156]) ).
cnf(c608,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c186]) ).
cnf(c609,plain,
join(X2,join(complement(X),complement(X2))) = top,
inference(transitivity,[status(thm)],[c607,c608]) ).
cnf(c610,plain,
join(X2,complement(meet(X,X2))) = top,
inference(transitivity,[status(thm)],[c606,c609]) ).
cnf(c611,plain,
join(X2,complement(meet(X2,X))) = top,
inference(transitivity,[status(thm)],[c569,c610]) ).
cnf(c612,plain,
join(complement(X2),complement(meet(complement(X2),X))) = top,
inference(substitution,[status(thm)],[c611]) ).
cnf(c613,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = complement(top),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = zero,
inference(transitivity,[status(thm)],[c613,c55]) ).
cnf(c615,plain,
meet(X2,meet(complement(X2),X)) = zero,
inference(transitivity,[status(thm)],[c566,c614]) ).
cnf(c616,plain,
meet(X2,meet(X,complement(X2))) = zero,
inference(transitivity,[status(thm)],[c565,c615]) ).
cnf(c617,plain,
meet(composition(converse(X),complement(X)),meet(one,complement(composition(converse(X),complement(X))))) = zero,
inference(substitution,[status(thm)],[c616]) ).
cnf(c618,plain,
meet(composition(converse(X),complement(X)),one) = zero,
inference(transitivity,[status(thm)],[c563,c617]) ).
cnf(c619,plain,
meet(one,composition(converse(X),complement(X))) = zero,
inference(transitivity,[status(thm)],[c506,c618]) ).
cnf(c620,plain,
meet(one,composition(converse(join(zero,complement(X))),complement(join(zero,complement(X))))) = zero,
inference(substitution,[status(thm)],[c619]) ).
cnf(c621,plain,
meet(one,composition(converse(join(zero,complement(X))),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c505,c620]) ).
cnf(c622,plain,
meet(one,composition(join(converse(zero),converse(complement(X))),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c502,c621]) ).
cnf(c623,plain,
meet(one,composition(converse(complement(X)),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c498,c622]) ).
cnf(c624,plain,
meet(one,composition(converse(complement(X)),X)) = zero,
inference(transitivity,[status(thm)],[c494,c623]) ).
cnf(c625,plain,
meet(one,composition(converse(complement(converse(X))),converse(X))) = zero,
inference(substitution,[status(thm)],[c624]) ).
cnf(c626,plain,
zero = meet(one,composition(converse(complement(converse(X))),converse(X))),
inference(symmetry,[status(thm)],[c625]) ).
cnf(c627,plain,
composition(zero,X) = composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),
inference(congruence,[status(thm)],[c626]) ).
cnf(c628,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)],[c627]) ).
cnf(c629,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)],[c628]) ).
cnf(c630,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(c631,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)],[c630]) ).
cnf(c632,plain,
meet(one,composition(converse(complement(converse(X))),converse(X))) = zero,
inference(substitution,[status(thm)],[c624]) ).
cnf(c633,plain,
composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X) = composition(zero,X),
inference(congruence,[status(thm)],[c632]) ).
cnf(c634,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)],[c633]) ).
cnf(c635,plain,
meet(composition(zero,X),converse(complement(converse(X)))) = meet(zero,converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c485]) ).
cnf(c636,plain,
meet(zero,converse(complement(converse(X)))) = zero,
inference(substitution,[status(thm)],[c314]) ).
cnf(c637,plain,
meet(composition(zero,X),converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c635,c636]) ).
cnf(c638,plain,
meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c634,c637]) ).
cnf(c639,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)],[c631,c638]) ).
cnf(c640,plain,
join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c629,c639]) ).
cnf(c641,plain,
join(meet(X,converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c491,c640]) ).
cnf(c642,plain,
join(meet(X,converse(complement(converse(X)))),meet(zero,converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c488,c641]) ).
cnf(c643,plain,
join(meet(X,converse(complement(converse(X)))),zero) = zero,
inference(transitivity,[status(thm)],[c317,c642]) ).
cnf(c644,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c291,c643]) ).
cnf(c645,plain,
meet(complement(X),converse(complement(converse(complement(X))))) = zero,
inference(substitution,[status(thm)],[c644]) ).
cnf(c646,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)],[c645]) ).
cnf(c647,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = meet(X,converse(complement(converse(complement(X))))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c648,plain,
meet(X,converse(complement(converse(complement(X))))) = complement(join(complement(X),complement(converse(complement(converse(complement(X))))))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c649,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)],[c212]) ).
cnf(c650,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)],[c649]) ).
cnf(c651,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(substitution,[status(thm)],[c548]) ).
cnf(c652,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = complement(join(complement(X),converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c651]) ).
cnf(c653,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c138]) ).
cnf(c654,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = complement(converse(top)),
inference(congruence,[status(thm)],[c653]) ).
cnf(c655,plain,
complement(converse(top)) = complement(top),
inference(congruence,[status(thm)],[c197]) ).
cnf(c656,plain,
complement(converse(top)) = zero,
inference(transitivity,[status(thm)],[c655,c55]) ).
cnf(c657,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c654,c656]) ).
cnf(c658,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c652,c657]) ).
cnf(c659,plain,
zero = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c660,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)],[c659]) ).
cnf(c661,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)],[c112]) ).
cnf(c662,plain,
join(zero,complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))) = X,
inference(transitivity,[status(thm)],[c660,c661]) ).
cnf(c663,plain,
complement(join(complement(X),complement(converse(complement(converse(complement(X))))))) = X,
inference(transitivity,[status(thm)],[c650,c662]) ).
cnf(c664,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(transitivity,[status(thm)],[c648,c663]) ).
cnf(c665,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = X,
inference(transitivity,[status(thm)],[c647,c664]) ).
cnf(c666,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = X,
inference(transitivity,[status(thm)],[c646,c665]) ).
cnf(c667,plain,
converse(complement(converse(complement(X)))) = X,
inference(transitivity,[status(thm)],[c267,c666]) ).
cnf(c668,plain,
converse(converse(complement(converse(complement(X))))) = converse(X),
inference(congruence,[status(thm)],[c667]) ).
cnf(c669,plain,
complement(converse(complement(X))) = converse(X),
inference(transitivity,[status(thm)],[c251,c668]) ).
cnf(c670,plain,
complement(converse(complement(join(zero,complement(X))))) = converse(join(zero,complement(X))),
inference(substitution,[status(thm)],[c669]) ).
cnf(c671,plain,
converse(join(zero,complement(X))) = complement(converse(complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c670]) ).
cnf(c672,plain,
converse(complement(join(zero,complement(X)))) = converse(meet(X,top)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c673,plain,
complement(converse(complement(join(zero,complement(X))))) = complement(converse(meet(X,top))),
inference(congruence,[status(thm)],[c672]) ).
cnf(c674,plain,
converse(meet(X,top)) = converse(X),
inference(congruence,[status(thm)],[c324]) ).
cnf(c675,plain,
complement(converse(meet(X,top))) = complement(converse(X)),
inference(congruence,[status(thm)],[c674]) ).
cnf(c676,plain,
complement(converse(complement(join(zero,complement(X))))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c673,c675]) ).
cnf(c677,plain,
converse(join(zero,complement(X))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c671,c676]) ).
cnf(c678,plain,
join(converse(zero),converse(complement(X))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c249,c677]) ).
cnf(c679,plain,
converse(complement(X)) = complement(converse(X)),
inference(transitivity,[status(thm)],[c247,c678]) ).
cnf(c680,plain,
converse(complement(composition(X,X2))) = complement(converse(composition(X,X2))),
inference(substitution,[status(thm)],[c679]) ).
cnf(c681,plain,
complement(converse(composition(X,X2))) = converse(complement(composition(X,X2))),
inference(symmetry,[status(thm)],[c680]) ).
cnf(c682,plain,
composition(complement(converse(composition(X,X2))),converse(converse(X))) = composition(converse(complement(composition(X,X2))),converse(converse(X))),
inference(congruence,[status(thm)],[c681]) ).
cnf(c683,plain,
join(complement(converse(X2)),composition(complement(converse(composition(X,X2))),converse(converse(X)))) = join(complement(converse(X2)),composition(converse(complement(composition(X,X2))),converse(converse(X)))),
inference(congruence,[status(thm)],[c682]) ).
cnf(c684,plain,
converse(composition(converse(X),complement(composition(X,X2)))) = composition(converse(complement(composition(X,X2))),converse(converse(X))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c685,plain,
composition(converse(complement(composition(X,X2))),converse(converse(X))) = converse(composition(converse(X),complement(composition(X,X2)))),
inference(symmetry,[status(thm)],[c684]) ).
cnf(c686,plain,
join(complement(converse(X2)),composition(converse(complement(composition(X,X2))),converse(converse(X)))) = join(complement(converse(X2)),converse(composition(converse(X),complement(composition(X,X2))))),
inference(congruence,[status(thm)],[c685]) ).
cnf(c687,plain,
complement(converse(X)) = converse(complement(X)),
inference(symmetry,[status(thm)],[c679]) ).
cnf(c688,plain,
join(complement(converse(X2)),converse(composition(converse(X),complement(composition(X,X2))))) = join(converse(complement(X2)),converse(composition(converse(X),complement(composition(X,X2))))),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
converse(join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = join(converse(complement(X2)),converse(composition(converse(X),complement(composition(X,X2))))),
inference(substitution,[status(thm)],[c130]) ).
cnf(c690,plain,
join(converse(complement(X2)),converse(composition(converse(X),complement(composition(X,X2))))) = converse(join(complement(X2),composition(converse(X),complement(composition(X,X2))))),
inference(symmetry,[status(thm)],[c689]) ).
cnf(c691,plain,
converse(join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = converse(complement(X2)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c692,plain,
converse(join(complement(X2),composition(converse(X),complement(composition(X,X2))))) = complement(converse(X2)),
inference(transitivity,[status(thm)],[c691,c679]) ).
cnf(c693,plain,
join(converse(complement(X2)),converse(composition(converse(X),complement(composition(X,X2))))) = complement(converse(X2)),
inference(transitivity,[status(thm)],[c690,c692]) ).
cnf(c694,plain,
join(complement(converse(X2)),converse(composition(converse(X),complement(composition(X,X2))))) = complement(converse(X2)),
inference(transitivity,[status(thm)],[c688,c693]) ).
cnf(c695,plain,
join(complement(converse(X2)),composition(converse(complement(composition(X,X2))),converse(converse(X)))) = complement(converse(X2)),
inference(transitivity,[status(thm)],[c686,c694]) ).
cnf(c696,plain,
join(complement(converse(X2)),composition(complement(converse(composition(X,X2))),converse(converse(X)))) = complement(converse(X2)),
inference(transitivity,[status(thm)],[c683,c695]) ).
cnf(c697,plain,
join(complement(converse(X2)),composition(complement(composition(converse(X2),converse(X))),converse(converse(X)))) = complement(converse(X2)),
inference(transitivity,[status(thm)],[c30,c696]) ).
cnf(c698,plain,
join(complement(converse(X2)),composition(complement(composition(converse(X2),converse(X))),X)) = complement(converse(X2)),
inference(transitivity,[status(thm)],[c24,c697]) ).
cnf(c699,plain,
join(complement(converse(converse(X2))),composition(complement(composition(converse(converse(X2)),converse(X))),X)) = complement(converse(converse(X2))),
inference(substitution,[status(thm)],[c698]) ).
cnf(c700,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c701,plain,
complement(converse(converse(X))) = complement(X),
inference(congruence,[status(thm)],[c700]) ).
cnf(c702,plain,
join(complement(converse(converse(X2))),composition(complement(composition(converse(converse(X2)),converse(X))),X)) = complement(X2),
inference(transitivity,[status(thm)],[c699,c701]) ).
cnf(c703,plain,
join(complement(X2),composition(complement(composition(converse(converse(X2)),converse(X))),X)) = complement(X2),
inference(transitivity,[status(thm)],[c20,c702]) ).
cnf(c704,plain,
join(complement(X2),composition(complement(composition(X2,converse(X))),X)) = complement(X2),
inference(transitivity,[status(thm)],[c16,c703]) ).
cnf(c705,plain,
join(complement(X2),composition(complement(composition(X2,converse(converse(X)))),converse(X))) = complement(X2),
inference(substitution,[status(thm)],[c704]) ).
cnf(c706,plain,
join(complement(X2),composition(complement(composition(X2,X)),converse(X))) = complement(X2),
inference(transitivity,[status(thm)],[c10,c705]) ).
cnf(c707,plain,
join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) = complement(sk1),
inference(substitution,[status(thm)],[c706]) ).
cnf(c708,plain,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) = complement(sk1),
inference(transitivity,[status(thm)],[c3,c707]) ).
cnf(c709,plain,
$false,
inference(resolution,[status(thm)],[c1,c708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL012-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.56 % Computer : n008.cluster.edu
% 0.10/15.56 % Model : x86_64 x86_64
% 0.10/15.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.56 % Memory : 8046.5625MB
% 0.10/15.56 % OS : Linux 6.8.0-71-generic
% 0.10/15.56 % CPULimit : 300
% 0.10/15.56 % WCLimit : 300
% 0.10/15.56 % DateTime : Sun Sep 27 22:51:55 UTC 2026
% 0.10/15.56 % CPUTime :
% 0.10/15.56 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.08/17.31 Command-line arguments: --no-flatten-goal
% 13.08/17.31
% 13.08/17.31 % SZS status Unsatisfiable
% 13.08/17.31
% 13.08/17.35 % SZS output start CNFRefutation
% See solution above
% 15.56/17.70
% 15.56/17.70 RESULT: Unsatisfiable (the axioms are contradictory).
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