%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL027-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:33:17 PM UTC 2026
% Result : Unsatisfiable 12.91s 2.14s
% Output : CNFRefutation 16.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 113
% Number of leaves : 15
% Syntax : Number of clauses : 708 ( 708 unt; 0 nHn; 121 RR)
% Number of literals : 708 ( 707 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 790 ( 62 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
meet(complement(composition(sk1,top)),one) != meet(complement(sk1),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
cnf(c2,axiom,
meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c3,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
join(A2,B2) = join(B2,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c5,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
complement(join(complement(X2),complement(X))) = meet(X2,X),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
complement(join(complement(X),complement(X2))) = meet(X2,X),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
meet(X,X2) = meet(X2,X),
inference(transitivity,[status(thm)],[c3,c10]) ).
cnf(c12,plain,
meet(one,complement(composition(sk1,top))) = meet(complement(composition(sk1,top)),one),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
meet(complement(composition(sk1,top)),one) = meet(one,complement(composition(sk1,top))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c15,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
complement(join(complement(X2),X)) = complement(join(X,complement(X2))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c18,plain,
join(X2,complement(X)) = join(complement(X),X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
complement(join(X2,complement(X))) = complement(join(complement(X),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c11]) ).
cnf(c21,axiom,
top = join(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
cnf(c22,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c27,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c23,c29]) ).
cnf(c31,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c37,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c11]) ).
cnf(c42,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c39]) ).
cnf(c43,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c45,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c47,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c51,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c54,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c52,c55]) ).
cnf(c57,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c59,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c49,c59]) ).
cnf(c61,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
composition(converse(one),one) = converse(one),
inference(substitution,[status(thm)],[c53]) ).
cnf(c65,plain,
converse(one) = composition(converse(one),one),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
composition(converse(one),one) = one,
inference(substitution,[status(thm)],[c60]) ).
cnf(c67,plain,
converse(one) = one,
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
composition(one,X) = composition(converse(one),X),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c69,c60]) ).
cnf(c71,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = join(complement(X2),composition(converse(X),complement(composition(X,X2)))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c76,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)],[c75]) ).
cnf(c77,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c78,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c76,c78]) ).
cnf(c80,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c74,c80]) ).
cnf(c82,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c63,c81]) ).
cnf(c83,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c87,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)],[c86]) ).
cnf(c88,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(c89,plain,
X2 = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))) = X2,
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
join(meet(X2,X),complement(join(complement(X2),X))) = X2,
inference(transitivity,[status(thm)],[c87,c90]) ).
cnf(c92,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c85,c92]) ).
cnf(c94,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c45,c93]) ).
cnf(c95,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c43,c95]) ).
cnf(c97,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c41,c96]) ).
cnf(c98,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c11]) ).
cnf(c101,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c103,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c105,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c107,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,axiom,
converse(join(A2,B2)) = join(converse(A2),converse(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(c110,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c113,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c111,c114]) ).
cnf(c116,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c108,c116]) ).
cnf(c118,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
converse(top) = join(complement(X),converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(complement(converse(complement(X)))))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c122,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
join(X2,join(complement(X2),X)) = join(X2,join(X,complement(X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c125,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c128,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c130,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c4]) ).
cnf(c133,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c128,c133]) ).
cnf(c135,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c126,c134]) ).
cnf(c136,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c137,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c135]) ).
cnf(c139,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c141,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c142,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c140,c142]) ).
cnf(c144,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c139,c143]) ).
cnf(c145,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c137,c144]) ).
cnf(c146,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c135]) ).
cnf(c149,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c135]) ).
cnf(c150,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c145]) ).
cnf(c152,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
join(X,join(top,complement(X))) = join(X2,top),
inference(transitivity,[status(thm)],[c148,c152]) ).
cnf(c154,plain,
join(X2,top) = join(X,top),
inference(transitivity,[status(thm)],[c147,c153]) ).
cnf(c155,plain,
join(X2,top) = join(X,top),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
join(X,top) = join(zero,top),
inference(substitution,[status(thm)],[c154]) ).
cnf(c157,plain,
join(top,zero) = join(zero,top),
inference(substitution,[status(thm)],[c4]) ).
cnf(c158,plain,
join(zero,top) = join(top,zero),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c160,plain,
join(top,zero) = join(top,complement(top)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
top = join(top,complement(top)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c162,plain,
join(top,complement(top)) = top,
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
join(top,zero) = top,
inference(transitivity,[status(thm)],[c160,c162]) ).
cnf(c164,plain,
join(zero,top) = top,
inference(transitivity,[status(thm)],[c158,c163]) ).
cnf(c165,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c156,c164]) ).
cnf(c166,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c155,c165]) ).
cnf(c167,plain,
join(X2,join(X,complement(X2))) = top,
inference(transitivity,[status(thm)],[c135,c166]) ).
cnf(c168,plain,
join(X2,join(complement(X2),X)) = top,
inference(transitivity,[status(thm)],[c123,c167]) ).
cnf(c169,plain,
join(X,join(complement(X),converse(complement(converse(complement(X)))))) = top,
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c120,c169]) ).
cnf(c171,plain,
top = join(X,converse(top)),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
converse(top) = converse(join(X,converse(top))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
converse(join(X,converse(top))) = join(converse(X),converse(converse(top))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c174,plain,
converse(converse(top)) = top,
inference(substitution,[status(thm)],[c46]) ).
cnf(c175,plain,
join(converse(X),converse(converse(top))) = join(converse(X),top),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
join(converse(X),top) = top,
inference(substitution,[status(thm)],[c165]) ).
cnf(c177,plain,
join(converse(X),converse(converse(top))) = top,
inference(transitivity,[status(thm)],[c175,c176]) ).
cnf(c178,plain,
converse(join(X,converse(top))) = top,
inference(transitivity,[status(thm)],[c173,c177]) ).
cnf(c179,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c172,c178]) ).
cnf(c180,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
meet(X,top) = meet(X,converse(top)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
join(meet(X,top),complement(top)) = join(meet(X,converse(top)),complement(top)),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
join(complement(X),converse(top)) = top,
inference(substitution,[status(thm)],[c170]) ).
cnf(c184,plain,
top = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
complement(top) = complement(join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
join(meet(X,converse(top)),complement(top)) = join(meet(X,converse(top)),complement(join(complement(X),converse(top)))),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
join(meet(X,converse(top)),complement(join(complement(X),converse(top)))) = X,
inference(substitution,[status(thm)],[c91]) ).
cnf(c188,plain,
join(meet(X,converse(top)),complement(top)) = X,
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c182,c188]) ).
cnf(c190,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c105,c189]) ).
cnf(c191,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c103,c190]) ).
cnf(c192,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c101,c191]) ).
cnf(c193,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c192]) ).
cnf(c194,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c99,c193]) ).
cnf(c195,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c198,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c197,c191]) ).
cnf(c199,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c196,c198]) ).
cnf(c200,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c40,c199]) ).
cnf(c201,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c20,c200]) ).
cnf(c202,plain,
X = meet(top,X),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
join(complement(X),X2) = join(complement(X),meet(top,X2)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
complement(join(complement(X),X2)) = complement(join(complement(X),meet(top,X2))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c206,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
meet(X3,join(complement(X2),complement(X))) = meet(X3,join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
meet(X3,join(complement(X),complement(X2))) = meet(join(complement(X),complement(X2)),X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c209,plain,
meet(join(complement(X),complement(X2)),X3) = complement(join(complement(join(complement(X),complement(X2))),complement(X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c210,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c211,plain,
complement(join(complement(X),complement(X2))) = meet(X,X2),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
join(complement(join(complement(X),complement(X2))),complement(X3)) = join(meet(X,X2),complement(X3)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = complement(join(meet(X,X2),complement(X3))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
join(meet(X,X2),complement(X3)) = join(complement(X3),meet(X,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c215,plain,
complement(join(meet(X,X2),complement(X3))) = complement(join(complement(X3),meet(X,X2))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c217,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
join(complement(X3),meet(X,X2)) = join(complement(X3),meet(X2,X)),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
complement(join(complement(X3),meet(X,X2))) = complement(join(complement(X3),meet(X2,X))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
complement(join(meet(X,X2),complement(X3))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c215,c219]) ).
cnf(c221,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c213,c220]) ).
cnf(c222,plain,
meet(join(complement(X),complement(X2)),X3) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c209,c221]) ).
cnf(c223,plain,
meet(X3,join(complement(X),complement(X2))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c208,c222]) ).
cnf(c224,plain,
meet(X3,join(complement(X2),complement(X))) = complement(join(complement(X3),meet(X2,X))),
inference(transitivity,[status(thm)],[c207,c223]) ).
cnf(c225,plain,
meet(X,join(complement(top),complement(X2))) = complement(join(complement(X),meet(top,X2))),
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
complement(join(complement(X),meet(top,X2))) = meet(X,join(complement(top),complement(X2))),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
join(complement(top),complement(X)) = join(zero,complement(X)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c228,plain,
meet(X,join(complement(top),complement(X2))) = meet(X,join(zero,complement(X2))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
meet(X,join(zero,complement(X2))) = meet(X,complement(X2)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c230,plain,
meet(X,join(complement(top),complement(X2))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c228,c229]) ).
cnf(c231,plain,
complement(join(complement(X),meet(top,X2))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c226,c230]) ).
cnf(c232,plain,
complement(join(complement(X),X2)) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c204,c231]) ).
cnf(c233,plain,
complement(join(X2,complement(X))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c19,c232]) ).
cnf(c234,plain,
complement(join(X,complement(X2))) = meet(X2,complement(X)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
complement(join(complement(X2),X)) = meet(X2,complement(X)),
inference(transitivity,[status(thm)],[c16,c234]) ).
cnf(c236,plain,
complement(join(complement(one),composition(sk1,top))) = meet(one,complement(composition(sk1,top))),
inference(substitution,[status(thm)],[c235]) ).
cnf(c237,plain,
meet(one,complement(composition(sk1,top))) = complement(join(complement(one),composition(sk1,top))),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
converse(converse(one)) = one,
inference(substitution,[status(thm)],[c46]) ).
cnf(c239,plain,
one = converse(converse(one)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
complement(one) = complement(converse(converse(one))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
composition(X,complement(one)) = composition(X,complement(converse(converse(one)))),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
join(X,composition(X,complement(one))) = join(X,composition(X,complement(converse(converse(one))))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
join(X,converse(zero)) = join(converse(zero),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c244,plain,
join(converse(zero),X) = join(X,converse(zero)),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c246,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
join(X,converse(zero)) = join(converse(converse(X)),converse(zero)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c194]) ).
cnf(c249,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c249,c94]) ).
cnf(c251,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
converse(X) = converse(complement(complement(X))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
join(converse(X),converse(zero)) = join(converse(complement(complement(X))),converse(zero)),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
join(converse(zero),converse(complement(complement(X)))) = join(converse(complement(complement(X))),converse(zero)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c255,plain,
join(converse(complement(complement(X))),converse(zero)) = join(converse(zero),converse(complement(complement(X)))),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c257,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c258,plain,
meet(X,X) = complement(complement(X)),
inference(transitivity,[status(thm)],[c256,c257]) ).
cnf(c259,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
converse(complement(complement(X))) = converse(meet(X,X)),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
join(converse(zero),converse(complement(complement(X)))) = join(converse(zero),converse(meet(X,X))),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
converse(join(zero,meet(X,X))) = join(converse(zero),converse(meet(X,X))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c263,plain,
join(converse(zero),converse(meet(X,X))) = converse(join(zero,meet(X,X))),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c265,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c267,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c91]) ).
cnf(c269,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c267,c268]) ).
cnf(c270,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c265,c269]) ).
cnf(c271,plain,
converse(join(zero,meet(X,X))) = converse(X),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
join(converse(zero),converse(meet(X,X))) = converse(X),
inference(transitivity,[status(thm)],[c263,c271]) ).
cnf(c273,plain,
join(converse(zero),converse(complement(complement(X)))) = converse(X),
inference(transitivity,[status(thm)],[c261,c272]) ).
cnf(c274,plain,
join(converse(complement(complement(X))),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c255,c273]) ).
cnf(c275,plain,
join(converse(X),converse(zero)) = converse(X),
inference(transitivity,[status(thm)],[c253,c274]) ).
cnf(c276,plain,
join(converse(converse(X)),converse(zero)) = converse(converse(X)),
inference(substitution,[status(thm)],[c275]) ).
cnf(c277,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c278,plain,
join(converse(converse(X)),converse(zero)) = X,
inference(transitivity,[status(thm)],[c276,c277]) ).
cnf(c279,plain,
join(X,converse(zero)) = X,
inference(transitivity,[status(thm)],[c247,c278]) ).
cnf(c280,plain,
join(converse(zero),X) = X,
inference(transitivity,[status(thm)],[c244,c279]) ).
cnf(c281,plain,
join(converse(zero),converse(complement(X))) = converse(complement(X)),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
converse(complement(X)) = join(converse(zero),converse(complement(X))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
converse(join(zero,complement(X))) = join(converse(zero),converse(complement(X))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c284,plain,
join(converse(zero),converse(complement(X))) = converse(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
converse(converse(complement(converse(complement(X))))) = complement(converse(complement(X))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c286,plain,
complement(converse(complement(X))) = converse(converse(complement(converse(complement(X))))),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
meet(complement(X2),X) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c288,plain,
join(meet(X2,X),meet(complement(X2),X)) = join(meet(X2,X),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c290,plain,
join(meet(X2,X),meet(X,complement(X2))) = join(meet(X,X2),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,X),meet(X2,complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c292,plain,
join(meet(X2,X),meet(X2,complement(X))) = join(meet(X2,complement(X)),meet(X2,X)),
inference(symmetry,[status(thm)],[c291]) ).
cnf(c293,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c294,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))) = X2,
inference(substitution,[status(thm)],[c91]) ).
cnf(c296,plain,
join(meet(X2,complement(X)),meet(X2,X)) = X2,
inference(transitivity,[status(thm)],[c294,c295]) ).
cnf(c297,plain,
join(meet(X2,X),meet(X2,complement(X))) = X2,
inference(transitivity,[status(thm)],[c292,c296]) ).
cnf(c298,plain,
join(meet(X,X2),meet(X,complement(X2))) = X,
inference(substitution,[status(thm)],[c297]) ).
cnf(c299,plain,
join(meet(X2,X),meet(X,complement(X2))) = X,
inference(transitivity,[status(thm)],[c290,c298]) ).
cnf(c300,plain,
join(meet(X2,X),meet(complement(X2),X)) = X,
inference(transitivity,[status(thm)],[c288,c299]) ).
cnf(c301,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)],[c300]) ).
cnf(c302,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)],[c301]) ).
cnf(c303,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c4]) ).
cnf(c304,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c303]) ).
cnf(c305,plain,
join(complement(complement(X)),X2) = join(X2,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c306,plain,
join(X2,complement(complement(X))) = join(complement(complement(X)),X2),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
join(zero,join(X2,complement(complement(X)))) = join(zero,join(complement(complement(X)),X2)),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
complement(complement(X)) = meet(X,X),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c309,plain,
join(complement(complement(X)),X2) = join(meet(X,X),X2),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
join(zero,join(complement(complement(X)),X2)) = join(zero,join(meet(X,X),X2)),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
join(zero,join(meet(X,X),X2)) = join(join(zero,meet(X,X)),X2),
inference(substitution,[status(thm)],[c127]) ).
cnf(c312,plain,
join(join(zero,meet(X,X)),X2) = join(X,X2),
inference(congruence,[status(thm)],[c270]) ).
cnf(c313,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c314,plain,
join(join(zero,meet(X,X)),X2) = join(X2,X),
inference(transitivity,[status(thm)],[c312,c313]) ).
cnf(c315,plain,
join(zero,join(meet(X,X),X2)) = join(X2,X),
inference(transitivity,[status(thm)],[c311,c314]) ).
cnf(c316,plain,
join(zero,join(complement(complement(X)),X2)) = join(X2,X),
inference(transitivity,[status(thm)],[c310,c315]) ).
cnf(c317,plain,
join(zero,join(X2,complement(complement(X)))) = join(X2,X),
inference(transitivity,[status(thm)],[c307,c316]) ).
cnf(c318,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,X),
inference(substitution,[status(thm)],[c317]) ).
cnf(c319,plain,
join(zero,X) = join(zero,join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c194]) ).
cnf(c321,plain,
join(zero,join(zero,complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
join(zero,join(zero,complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c321,c94]) ).
cnf(c323,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c319,c322]) ).
cnf(c324,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c304,c323]) ).
cnf(c325,plain,
join(meet(X,converse(complement(converse(X)))),zero) = meet(X,converse(complement(converse(X)))),
inference(substitution,[status(thm)],[c324]) ).
cnf(c326,plain,
meet(X,converse(complement(converse(X)))) = join(meet(X,converse(complement(converse(X)))),zero),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
meet(zero,X) = meet(X,zero),
inference(substitution,[status(thm)],[c11]) ).
cnf(c328,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c329,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c330,plain,
join(zero,meet(top,complement(zero))) = complement(zero),
inference(substitution,[status(thm)],[c192]) ).
cnf(c331,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c333,plain,
complement(zero) = complement(complement(top)),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
meet(top,complement(zero)) = meet(top,complement(complement(top))),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
join(zero,meet(top,complement(zero))) = join(zero,meet(top,complement(complement(top)))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c337,plain,
join(zero,meet(X,complement(complement(X)))) = join(meet(X,complement(X)),meet(X,complement(complement(X)))),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
join(meet(X,complement(X)),meet(X,complement(complement(X)))) = X,
inference(substitution,[status(thm)],[c297]) ).
cnf(c339,plain,
join(zero,meet(X,complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c337,c338]) ).
cnf(c340,plain,
join(zero,meet(top,complement(complement(top)))) = top,
inference(substitution,[status(thm)],[c339]) ).
cnf(c341,plain,
join(zero,meet(top,complement(zero))) = top,
inference(transitivity,[status(thm)],[c335,c340]) ).
cnf(c342,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c331,c341]) ).
cnf(c343,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c145]) ).
cnf(c346,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c345,c30]) ).
cnf(c347,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c344,c346]) ).
cnf(c348,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c329,c347]) ).
cnf(c349,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c328,c348]) ).
cnf(c350,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c327,c349]) ).
cnf(c351,plain,
meet(zero,converse(complement(converse(X)))) = zero,
inference(substitution,[status(thm)],[c350]) ).
cnf(c352,plain,
zero = meet(zero,converse(complement(converse(X)))),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,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)],[c352]) ).
cnf(c354,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c355,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
composition(zero,X) = composition(zero,converse(converse(X))),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
meet(converse(zero),top) = converse(zero),
inference(substitution,[status(thm)],[c200]) ).
cnf(c358,plain,
converse(zero) = meet(converse(zero),top),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
join(converse(zero),complement(converse(zero))) = complement(converse(zero)),
inference(substitution,[status(thm)],[c280]) ).
cnf(c360,plain,
complement(converse(zero)) = join(converse(zero),complement(converse(zero))),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
top = join(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c362,plain,
join(converse(zero),complement(converse(zero))) = top,
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
complement(converse(zero)) = top,
inference(transitivity,[status(thm)],[c360,c362]) ).
cnf(c364,plain,
top = complement(converse(zero)),
inference(symmetry,[status(thm)],[c363]) ).
cnf(c365,plain,
meet(converse(zero),top) = meet(converse(zero),complement(converse(zero))),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c367,plain,
meet(converse(zero),complement(converse(zero))) = zero,
inference(symmetry,[status(thm)],[c366]) ).
cnf(c368,plain,
meet(converse(zero),top) = zero,
inference(transitivity,[status(thm)],[c365,c367]) ).
cnf(c369,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c358,c368]) ).
cnf(c370,plain,
zero = converse(zero),
inference(symmetry,[status(thm)],[c369]) ).
cnf(c371,plain,
composition(zero,converse(X)) = composition(converse(zero),converse(X)),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
converse(composition(X,zero)) = composition(converse(zero),converse(X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c373,plain,
composition(converse(zero),converse(X)) = converse(composition(X,zero)),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c375,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c374]) ).
cnf(c376,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c375,c324]) ).
cnf(c377,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c376]) ).
cnf(c378,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c380,plain,
composition(top,zero) = composition(converse(top),zero),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
join(zero,composition(converse(top),zero)) = composition(converse(top),zero),
inference(substitution,[status(thm)],[c376]) ).
cnf(c382,plain,
composition(converse(top),zero) = join(zero,composition(converse(top),zero)),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c384,plain,
join(zero,composition(converse(top),zero)) = join(complement(top),composition(converse(top),zero)),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c386,plain,
composition(converse(top),zero) = composition(converse(top),complement(top)),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
join(complement(top),composition(converse(top),zero)) = join(complement(top),composition(converse(top),complement(top))),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
join(zero,composition(top,top)) = composition(top,top),
inference(substitution,[status(thm)],[c376]) ).
cnf(c389,plain,
composition(top,top) = join(zero,composition(top,top)),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c391,plain,
join(X,one) = join(one,X),
inference(symmetry,[status(thm)],[c390]) ).
cnf(c392,plain,
composition(join(X2,one),X) = composition(join(one,X2),X),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c394,plain,
join(one,X) = join(converse(one),X),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
composition(join(one,X2),X) = composition(join(converse(one),X2),X),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c397,plain,
composition(join(converse(one),X2),X) = join(composition(converse(one),X),composition(X2,X)),
inference(substitution,[status(thm)],[c396]) ).
cnf(c398,plain,
join(composition(converse(one),X),composition(X2,X)) = join(X,composition(X2,X)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c399,plain,
composition(join(converse(one),X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c397,c398]) ).
cnf(c400,plain,
composition(join(one,X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c395,c399]) ).
cnf(c401,plain,
composition(join(X2,one),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c392,c400]) ).
cnf(c402,plain,
composition(join(top,one),X) = join(X,composition(top,X)),
inference(substitution,[status(thm)],[c401]) ).
cnf(c403,plain,
join(X,composition(top,X)) = composition(join(top,one),X),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
join(complement(sk1),one) = join(one,complement(sk1)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c405,plain,
join(one,complement(sk1)) = join(complement(sk1),one),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c406,plain,
join(X,one) = join(one,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c407,plain,
join(one,X) = join(X,one),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
join(sk1,join(one,X)) = join(sk1,join(X,one)),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c410,plain,
join(X,one) = join(one,X),
inference(symmetry,[status(thm)],[c409]) ).
cnf(c411,plain,
join(sk1,join(X,one)) = join(sk1,join(one,X)),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,plain,
join(sk1,join(one,X)) = join(join(sk1,one),X),
inference(substitution,[status(thm)],[c127]) ).
cnf(c413,axiom,
join(sk1,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c414,plain,
join(join(sk1,one),X) = join(one,X),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c416,plain,
join(join(sk1,one),X) = join(X,one),
inference(transitivity,[status(thm)],[c414,c415]) ).
cnf(c417,plain,
join(sk1,join(one,X)) = join(X,one),
inference(transitivity,[status(thm)],[c412,c416]) ).
cnf(c418,plain,
join(sk1,join(X,one)) = join(X,one),
inference(transitivity,[status(thm)],[c411,c417]) ).
cnf(c419,plain,
join(sk1,join(one,X)) = join(X,one),
inference(transitivity,[status(thm)],[c408,c418]) ).
cnf(c420,plain,
join(sk1,join(one,complement(sk1))) = join(complement(sk1),one),
inference(substitution,[status(thm)],[c419]) ).
cnf(c421,plain,
join(complement(sk1),one) = join(sk1,join(one,complement(sk1))),
inference(symmetry,[status(thm)],[c420]) ).
cnf(c422,plain,
join(sk1,join(one,complement(sk1))) = join(one,top),
inference(substitution,[status(thm)],[c135]) ).
cnf(c423,plain,
join(one,top) = join(top,one),
inference(substitution,[status(thm)],[c4]) ).
cnf(c424,plain,
join(sk1,join(one,complement(sk1))) = join(top,one),
inference(transitivity,[status(thm)],[c422,c423]) ).
cnf(c425,plain,
join(complement(sk1),one) = join(top,one),
inference(transitivity,[status(thm)],[c421,c424]) ).
cnf(c426,plain,
join(one,complement(sk1)) = join(top,one),
inference(transitivity,[status(thm)],[c405,c425]) ).
cnf(c427,plain,
join(top,one) = join(one,complement(sk1)),
inference(symmetry,[status(thm)],[c426]) ).
cnf(c428,plain,
join(complement(sk1),one) = join(one,complement(sk1)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c429,plain,
join(one,complement(sk1)) = join(complement(sk1),one),
inference(symmetry,[status(thm)],[c428]) ).
cnf(c430,plain,
join(sk1,join(complement(sk1),one)) = join(complement(sk1),one),
inference(substitution,[status(thm)],[c418]) ).
cnf(c431,plain,
join(complement(sk1),one) = join(sk1,join(complement(sk1),one)),
inference(symmetry,[status(thm)],[c430]) ).
cnf(c432,plain,
join(sk1,join(complement(sk1),one)) = top,
inference(substitution,[status(thm)],[c168]) ).
cnf(c433,plain,
join(complement(sk1),one) = top,
inference(transitivity,[status(thm)],[c431,c432]) ).
cnf(c434,plain,
join(one,complement(sk1)) = top,
inference(transitivity,[status(thm)],[c429,c433]) ).
cnf(c435,plain,
join(top,one) = top,
inference(transitivity,[status(thm)],[c427,c434]) ).
cnf(c436,plain,
composition(join(top,one),X) = composition(top,X),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
join(X,composition(top,X)) = composition(top,X),
inference(transitivity,[status(thm)],[c403,c436]) ).
cnf(c438,plain,
join(top,composition(top,top)) = composition(top,top),
inference(substitution,[status(thm)],[c437]) ).
cnf(c439,plain,
composition(top,top) = join(top,composition(top,top)),
inference(symmetry,[status(thm)],[c438]) ).
cnf(c440,plain,
join(zero,composition(top,top)) = join(zero,join(top,composition(top,top))),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c442,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
join(zero,join(top,X)) = join(zero,join(X,top)),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
join(zero,join(X,top)) = join(X,top),
inference(substitution,[status(thm)],[c376]) ).
cnf(c445,plain,
join(X2,top) = join(X,top),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c446,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c445,c165]) ).
cnf(c447,plain,
join(zero,join(X,top)) = top,
inference(transitivity,[status(thm)],[c444,c446]) ).
cnf(c448,plain,
join(zero,join(top,X)) = top,
inference(transitivity,[status(thm)],[c443,c447]) ).
cnf(c449,plain,
join(zero,join(top,composition(top,top))) = top,
inference(substitution,[status(thm)],[c448]) ).
cnf(c450,plain,
join(zero,composition(top,top)) = top,
inference(transitivity,[status(thm)],[c440,c449]) ).
cnf(c451,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c389,c450]) ).
cnf(c452,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c451]) ).
cnf(c453,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c79]) ).
cnf(c457,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c456,c30]) ).
cnf(c458,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c455,c457]) ).
cnf(c459,plain,
join(complement(top),composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c387,c458]) ).
cnf(c460,plain,
join(zero,composition(converse(top),zero)) = zero,
inference(transitivity,[status(thm)],[c384,c459]) ).
cnf(c461,plain,
composition(converse(top),zero) = zero,
inference(transitivity,[status(thm)],[c382,c460]) ).
cnf(c462,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c380,c461]) ).
cnf(c463,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c462]) ).
cnf(c464,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c396]) ).
cnf(c466,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c465]) ).
cnf(c467,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c468,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c467]) ).
cnf(c469,plain,
join(X2,top) = join(X,top),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c470,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c469,c165]) ).
cnf(c471,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c468,c470]) ).
cnf(c472,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c472,c462]) ).
cnf(c474,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c466,c473]) ).
cnf(c475,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c464,c474]) ).
cnf(c476,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c378,c475]) ).
cnf(c477,plain,
converse(composition(X,zero)) = converse(zero),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
converse(composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c477,c369]) ).
cnf(c479,plain,
composition(converse(zero),converse(X)) = zero,
inference(transitivity,[status(thm)],[c373,c478]) ).
cnf(c480,plain,
composition(zero,converse(X)) = zero,
inference(transitivity,[status(thm)],[c371,c479]) ).
cnf(c481,plain,
composition(zero,converse(converse(X))) = zero,
inference(substitution,[status(thm)],[c480]) ).
cnf(c482,plain,
composition(zero,X) = zero,
inference(transitivity,[status(thm)],[c356,c481]) ).
cnf(c483,plain,
zero = composition(zero,X),
inference(symmetry,[status(thm)],[c482]) ).
cnf(c484,plain,
meet(zero,converse(complement(converse(X)))) = meet(composition(zero,X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,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)],[c484]) ).
cnf(c486,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c487,plain,
meet(X,converse(complement(converse(X)))) = meet(composition(one,X),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,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)],[c487]) ).
cnf(c489,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c490,plain,
composition(converse(complement(X)),X) = composition(converse(complement(X)),meet(X,top)),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
meet(one,composition(converse(complement(X)),X)) = meet(one,composition(converse(complement(X)),meet(X,top))),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
join(converse(zero),converse(complement(X))) = converse(complement(X)),
inference(substitution,[status(thm)],[c280]) ).
cnf(c493,plain,
converse(complement(X)) = join(converse(zero),converse(complement(X))),
inference(symmetry,[status(thm)],[c492]) ).
cnf(c494,plain,
composition(converse(complement(X)),meet(X,top)) = composition(join(converse(zero),converse(complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,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)],[c494]) ).
cnf(c496,plain,
converse(join(zero,complement(X))) = join(converse(zero),converse(complement(X))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c497,plain,
join(converse(zero),converse(complement(X))) = converse(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
composition(join(converse(zero),converse(complement(X))),meet(X,top)) = composition(converse(join(zero,complement(X))),meet(X,top)),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,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)],[c498]) ).
cnf(c500,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c501,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)],[c500]) ).
cnf(c502,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)],[c501]) ).
cnf(c503,plain,
meet(one,composition(converse(X),complement(X))) = meet(composition(converse(X),complement(X)),one),
inference(substitution,[status(thm)],[c11]) ).
cnf(c504,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = meet(one,complement(composition(converse(X),complement(X)))),
inference(substitution,[status(thm)],[c235]) ).
cnf(c505,plain,
meet(one,complement(composition(converse(X),complement(X)))) = complement(join(complement(one),composition(converse(X),complement(X)))),
inference(symmetry,[status(thm)],[c504]) ).
cnf(c506,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c507,plain,
X = composition(X,one),
inference(symmetry,[status(thm)],[c506]) ).
cnf(c508,plain,
complement(X) = complement(composition(X,one)),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
composition(converse(X),complement(X)) = composition(converse(X),complement(composition(X,one))),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
join(complement(one),composition(converse(X),complement(X))) = join(complement(one),composition(converse(X),complement(composition(X,one)))),
inference(congruence,[status(thm)],[c509]) ).
cnf(c511,plain,
join(complement(one),composition(converse(X),complement(composition(X,one)))) = complement(one),
inference(substitution,[status(thm)],[c79]) ).
cnf(c512,plain,
join(complement(one),composition(converse(X),complement(X))) = complement(one),
inference(transitivity,[status(thm)],[c510,c511]) ).
cnf(c513,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = complement(complement(one)),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
complement(complement(one)) = one,
inference(substitution,[status(thm)],[c250]) ).
cnf(c515,plain,
complement(join(complement(one),composition(converse(X),complement(X)))) = one,
inference(transitivity,[status(thm)],[c513,c514]) ).
cnf(c516,plain,
meet(one,complement(composition(converse(X),complement(X)))) = one,
inference(transitivity,[status(thm)],[c505,c515]) ).
cnf(c517,plain,
one = meet(one,complement(composition(converse(X),complement(X)))),
inference(symmetry,[status(thm)],[c516]) ).
cnf(c518,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)],[c517]) ).
cnf(c519,plain,
meet(X,complement(X2)) = meet(complement(X2),X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c520,plain,
meet(X2,meet(X,complement(X2))) = meet(X2,meet(complement(X2),X)),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
meet(X2,meet(complement(X2),X)) = complement(join(complement(X2),complement(meet(complement(X2),X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c522,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c523,plain,
complement(meet(X2,X)) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
join(X2,complement(meet(X2,X))) = join(X2,complement(meet(X,X2))),
inference(congruence,[status(thm)],[c523]) ).
cnf(c525,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c526,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c525]) ).
cnf(c527,plain,
join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c270]) ).
cnf(c528,plain,
join(complement(X),complement(X2)) = join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))),
inference(symmetry,[status(thm)],[c527]) ).
cnf(c529,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)],[c224]) ).
cnf(c530,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)],[c529]) ).
cnf(c531,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)],[c194]) ).
cnf(c532,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c533,plain,
complement(join(complement(X),complement(X2))) = meet(X,X2),
inference(symmetry,[status(thm)],[c532]) ).
cnf(c534,plain,
join(complement(join(complement(X),complement(X2))),meet(X,X2)) = join(meet(X,X2),meet(X,X2)),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))) = complement(join(meet(X,X2),meet(X,X2))),
inference(congruence,[status(thm)],[c534]) ).
cnf(c536,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c537,plain,
join(X,X) = join(X,complement(complement(X))),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
join(complement(complement(X)),X) = join(X,complement(complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c539,plain,
join(X,complement(complement(X))) = join(complement(complement(X)),X),
inference(symmetry,[status(thm)],[c538]) ).
cnf(c540,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(complement(complement(X)),X),
inference(substitution,[status(thm)],[c317]) ).
cnf(c541,plain,
join(complement(complement(X)),X) = join(zero,join(complement(complement(X)),complement(complement(X)))),
inference(symmetry,[status(thm)],[c540]) ).
cnf(c542,plain,
join(complement(complement(X)),complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c543,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c542]) ).
cnf(c544,plain,
join(zero,join(complement(complement(X)),complement(complement(X)))) = X,
inference(transitivity,[status(thm)],[c543,c94]) ).
cnf(c545,plain,
join(complement(complement(X)),X) = X,
inference(transitivity,[status(thm)],[c541,c544]) ).
cnf(c546,plain,
join(X,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c539,c545]) ).
cnf(c547,plain,
join(X,X) = X,
inference(transitivity,[status(thm)],[c537,c546]) ).
cnf(c548,plain,
join(meet(X,X2),meet(X,X2)) = meet(X,X2),
inference(substitution,[status(thm)],[c547]) ).
cnf(c549,plain,
complement(join(meet(X,X2),meet(X,X2))) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c551,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c550]) ).
cnf(c552,plain,
complement(meet(X,X2)) = complement(meet(X2,X)),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
complement(join(meet(X,X2),meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c549,c552]) ).
cnf(c554,plain,
complement(join(complement(join(complement(X),complement(X2))),meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c535,c553]) ).
cnf(c555,plain,
join(zero,complement(join(complement(join(complement(X),complement(X2))),meet(X,X2)))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c531,c554]) ).
cnf(c556,plain,
join(zero,meet(join(complement(X),complement(X2)),join(complement(X),complement(X2)))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c530,c555]) ).
cnf(c557,plain,
join(complement(X),complement(X2)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c528,c556]) ).
cnf(c558,plain,
join(complement(X2),complement(X)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c526,c557]) ).
cnf(c559,plain,
join(complement(X),complement(X2)) = complement(meet(X,X2)),
inference(substitution,[status(thm)],[c558]) ).
cnf(c560,plain,
complement(meet(X,X2)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c559]) ).
cnf(c561,plain,
join(X2,complement(meet(X,X2))) = join(X2,join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c560]) ).
cnf(c562,plain,
join(X2,join(complement(X),complement(X2))) = join(complement(X),top),
inference(substitution,[status(thm)],[c135]) ).
cnf(c563,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c165]) ).
cnf(c564,plain,
join(X2,join(complement(X),complement(X2))) = top,
inference(transitivity,[status(thm)],[c562,c563]) ).
cnf(c565,plain,
join(X2,complement(meet(X,X2))) = top,
inference(transitivity,[status(thm)],[c561,c564]) ).
cnf(c566,plain,
join(X2,complement(meet(X2,X))) = top,
inference(transitivity,[status(thm)],[c524,c565]) ).
cnf(c567,plain,
join(complement(X2),complement(meet(complement(X2),X))) = top,
inference(substitution,[status(thm)],[c566]) ).
cnf(c568,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = complement(top),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = zero,
inference(transitivity,[status(thm)],[c568,c30]) ).
cnf(c570,plain,
meet(X2,meet(complement(X2),X)) = zero,
inference(transitivity,[status(thm)],[c521,c569]) ).
cnf(c571,plain,
meet(X2,meet(X,complement(X2))) = zero,
inference(transitivity,[status(thm)],[c520,c570]) ).
cnf(c572,plain,
meet(composition(converse(X),complement(X)),meet(one,complement(composition(converse(X),complement(X))))) = zero,
inference(substitution,[status(thm)],[c571]) ).
cnf(c573,plain,
meet(composition(converse(X),complement(X)),one) = zero,
inference(transitivity,[status(thm)],[c518,c572]) ).
cnf(c574,plain,
meet(one,composition(converse(X),complement(X))) = zero,
inference(transitivity,[status(thm)],[c503,c573]) ).
cnf(c575,plain,
meet(one,composition(converse(join(zero,complement(X))),complement(join(zero,complement(X))))) = zero,
inference(substitution,[status(thm)],[c574]) ).
cnf(c576,plain,
meet(one,composition(converse(join(zero,complement(X))),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c502,c575]) ).
cnf(c577,plain,
meet(one,composition(join(converse(zero),converse(complement(X))),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c499,c576]) ).
cnf(c578,plain,
meet(one,composition(converse(complement(X)),meet(X,top))) = zero,
inference(transitivity,[status(thm)],[c495,c577]) ).
cnf(c579,plain,
meet(one,composition(converse(complement(X)),X)) = zero,
inference(transitivity,[status(thm)],[c491,c578]) ).
cnf(c580,plain,
meet(one,composition(converse(complement(converse(X))),converse(X))) = zero,
inference(substitution,[status(thm)],[c579]) ).
cnf(c581,plain,
zero = meet(one,composition(converse(complement(converse(X))),converse(X))),
inference(symmetry,[status(thm)],[c580]) ).
cnf(c582,plain,
composition(zero,X) = composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),
inference(congruence,[status(thm)],[c581]) ).
cnf(c583,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)],[c582]) ).
cnf(c584,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)],[c583]) ).
cnf(c585,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(c586,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)],[c585]) ).
cnf(c587,plain,
meet(one,composition(converse(complement(converse(X))),converse(X))) = zero,
inference(substitution,[status(thm)],[c579]) ).
cnf(c588,plain,
composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X) = composition(zero,X),
inference(congruence,[status(thm)],[c587]) ).
cnf(c589,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)],[c588]) ).
cnf(c590,plain,
meet(composition(zero,X),converse(complement(converse(X)))) = meet(zero,converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c482]) ).
cnf(c591,plain,
meet(zero,converse(complement(converse(X)))) = zero,
inference(substitution,[status(thm)],[c350]) ).
cnf(c592,plain,
meet(composition(zero,X),converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c590,c591]) ).
cnf(c593,plain,
meet(composition(meet(one,composition(converse(complement(converse(X))),converse(X))),X),converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c589,c592]) ).
cnf(c594,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)],[c586,c593]) ).
cnf(c595,plain,
join(meet(composition(one,X),converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c584,c594]) ).
cnf(c596,plain,
join(meet(X,converse(complement(converse(X)))),meet(composition(zero,X),converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c488,c595]) ).
cnf(c597,plain,
join(meet(X,converse(complement(converse(X)))),meet(zero,converse(complement(converse(X))))) = zero,
inference(transitivity,[status(thm)],[c485,c596]) ).
cnf(c598,plain,
join(meet(X,converse(complement(converse(X)))),zero) = zero,
inference(transitivity,[status(thm)],[c353,c597]) ).
cnf(c599,plain,
meet(X,converse(complement(converse(X)))) = zero,
inference(transitivity,[status(thm)],[c326,c598]) ).
cnf(c600,plain,
meet(complement(X),converse(complement(converse(complement(X))))) = zero,
inference(substitution,[status(thm)],[c599]) ).
cnf(c601,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)],[c600]) ).
cnf(c602,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = meet(X,converse(complement(converse(complement(X))))),
inference(substitution,[status(thm)],[c324]) ).
cnf(c603,plain,
meet(X,converse(complement(converse(complement(X))))) = complement(join(complement(X),complement(converse(complement(converse(complement(X))))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c604,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)],[c194]) ).
cnf(c605,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)],[c604]) ).
cnf(c606,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(substitution,[status(thm)],[c235]) ).
cnf(c607,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = complement(join(complement(X),converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c606]) ).
cnf(c608,plain,
join(complement(X),converse(complement(converse(complement(X))))) = converse(top),
inference(substitution,[status(thm)],[c117]) ).
cnf(c609,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = complement(converse(top)),
inference(congruence,[status(thm)],[c608]) ).
cnf(c610,plain,
complement(converse(top)) = complement(top),
inference(congruence,[status(thm)],[c179]) ).
cnf(c611,plain,
complement(converse(top)) = zero,
inference(transitivity,[status(thm)],[c610,c30]) ).
cnf(c612,plain,
complement(join(complement(X),converse(complement(converse(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c609,c611]) ).
cnf(c613,plain,
meet(X,complement(converse(complement(converse(complement(X)))))) = zero,
inference(transitivity,[status(thm)],[c607,c612]) ).
cnf(c614,plain,
zero = meet(X,complement(converse(complement(converse(complement(X)))))),
inference(symmetry,[status(thm)],[c613]) ).
cnf(c615,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)],[c614]) ).
cnf(c616,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)],[c91]) ).
cnf(c617,plain,
join(zero,complement(join(complement(X),complement(converse(complement(converse(complement(X)))))))) = X,
inference(transitivity,[status(thm)],[c615,c616]) ).
cnf(c618,plain,
complement(join(complement(X),complement(converse(complement(converse(complement(X))))))) = X,
inference(transitivity,[status(thm)],[c605,c617]) ).
cnf(c619,plain,
meet(X,converse(complement(converse(complement(X))))) = X,
inference(transitivity,[status(thm)],[c603,c618]) ).
cnf(c620,plain,
join(meet(X,converse(complement(converse(complement(X))))),zero) = X,
inference(transitivity,[status(thm)],[c602,c619]) ).
cnf(c621,plain,
join(meet(X,converse(complement(converse(complement(X))))),meet(complement(X),converse(complement(converse(complement(X)))))) = X,
inference(transitivity,[status(thm)],[c601,c620]) ).
cnf(c622,plain,
converse(complement(converse(complement(X)))) = X,
inference(transitivity,[status(thm)],[c302,c621]) ).
cnf(c623,plain,
converse(converse(complement(converse(complement(X))))) = converse(X),
inference(congruence,[status(thm)],[c622]) ).
cnf(c624,plain,
complement(converse(complement(X))) = converse(X),
inference(transitivity,[status(thm)],[c286,c623]) ).
cnf(c625,plain,
complement(converse(complement(join(zero,complement(X))))) = converse(join(zero,complement(X))),
inference(substitution,[status(thm)],[c624]) ).
cnf(c626,plain,
converse(join(zero,complement(X))) = complement(converse(complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c625]) ).
cnf(c627,plain,
converse(complement(join(zero,complement(X)))) = converse(meet(X,top)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c628,plain,
complement(converse(complement(join(zero,complement(X))))) = complement(converse(meet(X,top))),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
converse(meet(X,top)) = converse(X),
inference(congruence,[status(thm)],[c200]) ).
cnf(c630,plain,
complement(converse(meet(X,top))) = complement(converse(X)),
inference(congruence,[status(thm)],[c629]) ).
cnf(c631,plain,
complement(converse(complement(join(zero,complement(X))))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c628,c630]) ).
cnf(c632,plain,
converse(join(zero,complement(X))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c626,c631]) ).
cnf(c633,plain,
join(converse(zero),converse(complement(X))) = complement(converse(X)),
inference(transitivity,[status(thm)],[c284,c632]) ).
cnf(c634,plain,
converse(complement(X)) = complement(converse(X)),
inference(transitivity,[status(thm)],[c282,c633]) ).
cnf(c635,plain,
converse(complement(converse(one))) = complement(converse(converse(one))),
inference(substitution,[status(thm)],[c634]) ).
cnf(c636,plain,
complement(converse(converse(one))) = converse(complement(converse(one))),
inference(symmetry,[status(thm)],[c635]) ).
cnf(c637,plain,
composition(X,complement(converse(converse(one)))) = composition(X,converse(complement(converse(one)))),
inference(congruence,[status(thm)],[c636]) ).
cnf(c638,plain,
join(X,composition(X,complement(converse(converse(one))))) = join(X,composition(X,converse(complement(converse(one))))),
inference(congruence,[status(thm)],[c637]) ).
cnf(c639,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c640,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c639]) ).
cnf(c641,plain,
composition(X2,join(one,converse(X))) = composition(converse(converse(X2)),join(one,converse(X))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c642,plain,
join(converse(X),one) = join(one,converse(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c643,plain,
join(one,converse(X)) = join(converse(X),one),
inference(symmetry,[status(thm)],[c642]) ).
cnf(c644,plain,
composition(converse(X2),join(one,converse(X))) = composition(converse(X2),join(converse(X),one)),
inference(congruence,[status(thm)],[c643]) ).
cnf(c645,plain,
one = converse(one),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c646,plain,
join(converse(X),one) = join(converse(X),converse(one)),
inference(congruence,[status(thm)],[c645]) ).
cnf(c647,plain,
composition(converse(X2),join(converse(X),one)) = composition(converse(X2),join(converse(X),converse(one))),
inference(congruence,[status(thm)],[c646]) ).
cnf(c648,plain,
converse(join(X,one)) = join(converse(X),converse(one)),
inference(substitution,[status(thm)],[c109]) ).
cnf(c649,plain,
join(converse(X),converse(one)) = converse(join(X,one)),
inference(symmetry,[status(thm)],[c648]) ).
cnf(c650,plain,
composition(converse(X2),join(converse(X),converse(one))) = composition(converse(X2),converse(join(X,one))),
inference(congruence,[status(thm)],[c649]) ).
cnf(c651,plain,
converse(composition(join(X,one),X2)) = composition(converse(X2),converse(join(X,one))),
inference(substitution,[status(thm)],[c50]) ).
cnf(c652,plain,
composition(converse(X2),converse(join(X,one))) = converse(composition(join(X,one),X2)),
inference(symmetry,[status(thm)],[c651]) ).
cnf(c653,plain,
composition(join(X,one),X2) = join(X2,composition(X,X2)),
inference(substitution,[status(thm)],[c401]) ).
cnf(c654,plain,
converse(composition(join(X,one),X2)) = converse(join(X2,composition(X,X2))),
inference(congruence,[status(thm)],[c653]) ).
cnf(c655,plain,
converse(join(X2,composition(X,X2))) = join(converse(X2),converse(composition(X,X2))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c656,plain,
converse(composition(X,X2)) = composition(converse(X2),converse(X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c657,plain,
join(converse(X2),converse(composition(X,X2))) = join(converse(X2),composition(converse(X2),converse(X))),
inference(congruence,[status(thm)],[c656]) ).
cnf(c658,plain,
converse(join(X2,composition(X,X2))) = join(converse(X2),composition(converse(X2),converse(X))),
inference(transitivity,[status(thm)],[c655,c657]) ).
cnf(c659,plain,
converse(composition(join(X,one),X2)) = join(converse(X2),composition(converse(X2),converse(X))),
inference(transitivity,[status(thm)],[c654,c658]) ).
cnf(c660,plain,
composition(converse(X2),converse(join(X,one))) = join(converse(X2),composition(converse(X2),converse(X))),
inference(transitivity,[status(thm)],[c652,c659]) ).
cnf(c661,plain,
composition(converse(X2),join(converse(X),converse(one))) = join(converse(X2),composition(converse(X2),converse(X))),
inference(transitivity,[status(thm)],[c650,c660]) ).
cnf(c662,plain,
composition(converse(X2),join(converse(X),one)) = join(converse(X2),composition(converse(X2),converse(X))),
inference(transitivity,[status(thm)],[c647,c661]) ).
cnf(c663,plain,
composition(converse(X2),join(one,converse(X))) = join(converse(X2),composition(converse(X2),converse(X))),
inference(transitivity,[status(thm)],[c644,c662]) ).
cnf(c664,plain,
composition(converse(converse(X2)),join(one,converse(X))) = join(converse(converse(X2)),composition(converse(converse(X2)),converse(X))),
inference(substitution,[status(thm)],[c663]) ).
cnf(c665,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c666,plain,
join(converse(converse(X2)),composition(converse(converse(X2)),converse(X))) = join(X2,composition(converse(converse(X2)),converse(X))),
inference(congruence,[status(thm)],[c665]) ).
cnf(c667,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c668,plain,
composition(converse(converse(X2)),converse(X)) = composition(X2,converse(X)),
inference(congruence,[status(thm)],[c667]) ).
cnf(c669,plain,
join(X2,composition(converse(converse(X2)),converse(X))) = join(X2,composition(X2,converse(X))),
inference(congruence,[status(thm)],[c668]) ).
cnf(c670,plain,
join(converse(converse(X2)),composition(converse(converse(X2)),converse(X))) = join(X2,composition(X2,converse(X))),
inference(transitivity,[status(thm)],[c666,c669]) ).
cnf(c671,plain,
composition(converse(converse(X2)),join(one,converse(X))) = join(X2,composition(X2,converse(X))),
inference(transitivity,[status(thm)],[c664,c670]) ).
cnf(c672,plain,
composition(X2,join(one,converse(X))) = join(X2,composition(X2,converse(X))),
inference(transitivity,[status(thm)],[c641,c671]) ).
cnf(c673,plain,
composition(X,join(one,converse(complement(converse(one))))) = join(X,composition(X,converse(complement(converse(one))))),
inference(substitution,[status(thm)],[c672]) ).
cnf(c674,plain,
join(X,composition(X,converse(complement(converse(one))))) = composition(X,join(one,converse(complement(converse(one))))),
inference(symmetry,[status(thm)],[c673]) ).
cnf(c675,plain,
join(one,converse(complement(converse(one)))) = converse(top),
inference(substitution,[status(thm)],[c117]) ).
cnf(c676,plain,
composition(X,join(one,converse(complement(converse(one))))) = composition(X,converse(top)),
inference(congruence,[status(thm)],[c675]) ).
cnf(c677,plain,
composition(X,converse(top)) = composition(X,top),
inference(congruence,[status(thm)],[c179]) ).
cnf(c678,plain,
composition(X,join(one,converse(complement(converse(one))))) = composition(X,top),
inference(transitivity,[status(thm)],[c676,c677]) ).
cnf(c679,plain,
join(X,composition(X,converse(complement(converse(one))))) = composition(X,top),
inference(transitivity,[status(thm)],[c674,c678]) ).
cnf(c680,plain,
join(X,composition(X,complement(converse(converse(one))))) = composition(X,top),
inference(transitivity,[status(thm)],[c638,c679]) ).
cnf(c681,plain,
join(X,composition(X,complement(one))) = composition(X,top),
inference(transitivity,[status(thm)],[c242,c680]) ).
cnf(c682,plain,
join(sk1,composition(sk1,complement(one))) = composition(sk1,top),
inference(substitution,[status(thm)],[c681]) ).
cnf(c683,plain,
composition(sk1,top) = join(sk1,composition(sk1,complement(one))),
inference(symmetry,[status(thm)],[c682]) ).
cnf(c684,plain,
join(complement(one),composition(sk1,top)) = join(complement(one),join(sk1,composition(sk1,complement(one)))),
inference(congruence,[status(thm)],[c683]) ).
cnf(c685,plain,
join(composition(sk1,X2),X) = join(X,composition(sk1,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c686,plain,
join(X,composition(sk1,X2)) = join(composition(sk1,X2),X),
inference(symmetry,[status(thm)],[c685]) ).
cnf(c687,plain,
join(X2,join(X,composition(sk1,X2))) = join(X2,join(composition(sk1,X2),X)),
inference(congruence,[status(thm)],[c686]) ).
cnf(c688,plain,
join(X2,join(composition(sk1,X2),X)) = join(join(X2,composition(sk1,X2)),X),
inference(substitution,[status(thm)],[c127]) ).
cnf(c689,plain,
composition(join(sk1,one),X) = join(X,composition(sk1,X)),
inference(substitution,[status(thm)],[c401]) ).
cnf(c690,plain,
join(X,composition(sk1,X)) = composition(join(sk1,one),X),
inference(symmetry,[status(thm)],[c689]) ).
cnf(c691,plain,
composition(join(sk1,one),X) = composition(one,X),
inference(congruence,[status(thm)],[c413]) ).
cnf(c692,plain,
composition(join(sk1,one),X) = X,
inference(transitivity,[status(thm)],[c691,c70]) ).
cnf(c693,plain,
join(X,composition(sk1,X)) = X,
inference(transitivity,[status(thm)],[c690,c692]) ).
cnf(c694,plain,
join(join(X2,composition(sk1,X2)),X) = join(X2,X),
inference(congruence,[status(thm)],[c693]) ).
cnf(c695,plain,
join(X2,join(composition(sk1,X2),X)) = join(X2,X),
inference(transitivity,[status(thm)],[c688,c694]) ).
cnf(c696,plain,
join(X2,join(X,composition(sk1,X2))) = join(X2,X),
inference(transitivity,[status(thm)],[c687,c695]) ).
cnf(c697,plain,
join(complement(one),join(sk1,composition(sk1,complement(one)))) = join(complement(one),sk1),
inference(substitution,[status(thm)],[c696]) ).
cnf(c698,plain,
join(complement(one),sk1) = join(sk1,complement(one)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c699,plain,
join(complement(one),join(sk1,composition(sk1,complement(one)))) = join(sk1,complement(one)),
inference(transitivity,[status(thm)],[c697,c698]) ).
cnf(c700,plain,
join(complement(one),composition(sk1,top)) = join(sk1,complement(one)),
inference(transitivity,[status(thm)],[c684,c699]) ).
cnf(c701,plain,
complement(join(complement(one),composition(sk1,top))) = complement(join(sk1,complement(one))),
inference(congruence,[status(thm)],[c700]) ).
cnf(c702,plain,
complement(join(sk1,complement(one))) = meet(one,complement(sk1)),
inference(substitution,[status(thm)],[c233]) ).
cnf(c703,plain,
complement(join(complement(one),composition(sk1,top))) = meet(one,complement(sk1)),
inference(transitivity,[status(thm)],[c701,c702]) ).
cnf(c704,plain,
meet(one,complement(composition(sk1,top))) = meet(one,complement(sk1)),
inference(transitivity,[status(thm)],[c237,c703]) ).
cnf(c705,plain,
meet(one,complement(sk1)) = meet(complement(sk1),one),
inference(substitution,[status(thm)],[c11]) ).
cnf(c706,plain,
meet(one,complement(composition(sk1,top))) = meet(complement(sk1),one),
inference(transitivity,[status(thm)],[c704,c705]) ).
cnf(c707,plain,
meet(complement(composition(sk1,top)),one) = meet(complement(sk1),one),
inference(transitivity,[status(thm)],[c13,c706]) ).
cnf(c708,plain,
$false,
inference(resolution,[status(thm)],[c1,c707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL027-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 22:53:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.91/2.14 Command-line arguments: --no-flatten-goal
% 12.91/2.14
% 12.91/2.14 % SZS status Unsatisfiable
% 12.91/2.14
% 13.91/2.21 % SZS output start CNFRefutation
% See solution above
% 16.33/2.58
% 16.33/2.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------