%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL017-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:33:08 PM UTC 2026
% Result : Unsatisfiable 29.85s 4.21s
% Output : CNFRefutation 32.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 15
% Syntax : Number of clauses : 591 ( 591 unt; 0 nHn; 22 RR)
% Number of literals : 591 ( 590 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 1139 ( 53 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(complement(composition(sk1,sk2)),composition(sk1,sk3)) != join(complement(composition(sk1,meet(sk2,complement(sk3)))),composition(sk1,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
cnf(c2,axiom,
top = join(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
cnf(c3,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
meet(A2,B) = complement(join(complement(A2),complement(B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c6,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c9,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c4,c11]) ).
cnf(c13,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c17,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c19,axiom,
join(A2,B2) = join(B2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c20,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c24,plain,
complement(join(complement(X2),complement(X))) = meet(X2,X),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
complement(join(complement(X),complement(X2))) = meet(X2,X),
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
meet(X,X2) = meet(X2,X),
inference(transitivity,[status(thm)],[c18,c25]) ).
cnf(c27,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c17,c28]) ).
cnf(c30,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c15,c29]) ).
cnf(c31,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
join(complement(X),zero) = join(zero,complement(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c33,plain,
join(zero,complement(X)) = join(complement(X),zero),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c26]) ).
cnf(c35,plain,
join(meet(X2,X),complement(join(complement(X),X2))) = join(meet(X,X2),complement(join(complement(X),X2))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c37,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)],[c36]) ).
cnf(c38,axiom,
A2 = join(complement(join(complement(A2),complement(B2))),complement(join(complement(A2),B2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c39,plain,
X2 = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))) = X2,
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
join(meet(X2,X),complement(join(complement(X2),X))) = X2,
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
join(meet(X,X2),complement(join(complement(X),X2))) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
join(meet(X2,X),complement(join(complement(X),X2))) = X,
inference(transitivity,[status(thm)],[c35,c42]) ).
cnf(c44,plain,
join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))) = meet(X,zero),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
meet(X,zero) = join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c47,plain,
meet(top,meet(X,zero)) = meet(top,meet(zero,X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
meet(top,meet(zero,X)) = meet(meet(zero,X),top),
inference(substitution,[status(thm)],[c26]) ).
cnf(c49,plain,
complement(join(zero,complement(meet(zero,X)))) = meet(meet(zero,X),top),
inference(substitution,[status(thm)],[c30]) ).
cnf(c50,plain,
meet(meet(zero,X),top) = complement(join(zero,complement(meet(zero,X)))),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
join(complement(join(complement(X2),X)),X3) = join(X3,complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c52,plain,
join(X,complement(join(complement(X3),X2))) = join(complement(join(complement(X3),X2)),X),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
join(meet(X3,X2),join(X,complement(join(complement(X3),X2)))) = join(meet(X3,X2),join(complement(join(complement(X3),X2)),X)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c55,plain,
join(meet(X3,X2),join(complement(join(complement(X3),X2)),X)) = join(join(meet(X3,X2),complement(join(complement(X3),X2))),X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
join(join(meet(X3,X2),complement(join(complement(X3),X2))),X) = join(X3,X),
inference(congruence,[status(thm)],[c41]) ).
cnf(c57,plain,
join(meet(X3,X2),join(complement(join(complement(X3),X2)),X)) = join(X3,X),
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
join(meet(X3,X2),join(X,complement(join(complement(X3),X2)))) = join(X3,X),
inference(transitivity,[status(thm)],[c53,c57]) ).
cnf(c59,plain,
join(meet(X2,X),join(complement(meet(X2,X)),complement(join(complement(X2),X)))) = join(X2,complement(meet(X2,X))),
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
join(X2,complement(meet(X2,X))) = join(meet(X2,X),join(complement(meet(X2,X)),complement(join(complement(X2),X)))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c62,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
join(X2,join(complement(X2),X)) = join(X2,join(X,complement(X2))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c65,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c68,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c19]) ).
cnf(c72,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c67,c72]) ).
cnf(c74,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c66,c73]) ).
cnf(c75,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c63,c74]) ).
cnf(c76,plain,
join(meet(X2,X),join(complement(meet(X2,X)),complement(join(complement(X2),X)))) = join(complement(join(complement(X2),X)),top),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
join(X2,top) = join(X2,join(X,complement(X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
join(complement(X),X) = join(X,complement(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c80,plain,
join(X,complement(X)) = join(complement(X),X),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
join(X2,join(X,complement(X))) = join(X2,join(complement(X),X)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
join(join(X2,X),X3) = join(X3,join(X2,X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c83,plain,
join(X3,join(X2,X)) = join(join(X2,X),X3),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
join(X2,join(X,X3)) = join(join(X2,X),X3),
inference(substitution,[status(thm)],[c54]) ).
cnf(c85,plain,
join(join(X2,X),X3) = join(X2,join(X,X3)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c87,plain,
join(X2,join(X,X3)) = join(X2,join(X3,X)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
join(join(X2,X),X3) = join(X2,join(X3,X)),
inference(transitivity,[status(thm)],[c85,c87]) ).
cnf(c89,plain,
join(X3,join(X2,X)) = join(X2,join(X3,X)),
inference(transitivity,[status(thm)],[c83,c88]) ).
cnf(c90,plain,
join(complement(X),join(X2,X)) = join(X2,join(complement(X),X)),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
join(X2,join(complement(X),X)) = join(complement(X),join(X2,X)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
join(complement(X),join(X2,X)) = join(join(complement(X),X2),X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c93,plain,
join(meet(X,X2),complement(join(complement(X),X2))) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c94,plain,
X = join(meet(X,X2),complement(join(complement(X),X2))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
join(join(complement(X),X2),X) = join(join(complement(X),X2),join(meet(X,X2),complement(join(complement(X),X2)))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
join(join(complement(X),X2),join(meet(X,X2),complement(join(complement(X),X2)))) = join(meet(X,X2),top),
inference(substitution,[status(thm)],[c74]) ).
cnf(c97,plain,
join(meet(X,X2),top) = join(top,meet(X,X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c98,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c99,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
X = composition(X,one),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
meet(X2,X) = meet(X2,composition(X,one)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
join(top,meet(X2,X)) = join(top,meet(X2,composition(X,one))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(X3,composition(X2,X)) = meet(composition(X2,X),X3),
inference(substitution,[status(thm)],[c26]) ).
cnf(c104,plain,
join(top,meet(X3,composition(X2,X))) = join(top,meet(composition(X2,X),X3)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
join(meet(composition(X2,X),X3),top) = join(top,meet(composition(X2,X),X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c106,plain,
join(top,meet(composition(X2,X),X3)) = join(meet(composition(X2,X),X3),top),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
top = join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c108,plain,
join(meet(composition(X2,X),X3),top) = join(meet(composition(X2,X),X3),join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3)))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,axiom,
join(meet(composition(A2,B2),C2),meet(composition(A2,meet(B2,composition(converse(A2),C2))),C2)) = meet(composition(A2,meet(B2,composition(converse(A2),C2))),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular_law_1_15) ).
cnf(c110,plain,
join(meet(composition(X2,X),X3),meet(composition(X2,meet(X,composition(converse(X2),X3))),X3)) = meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
meet(composition(X2,meet(X,composition(converse(X2),X3))),X3) = join(meet(composition(X2,X),X3),meet(composition(X2,meet(X,composition(converse(X2),X3))),X3)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
complement(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3)) = complement(join(meet(composition(X2,X),X3),meet(composition(X2,meet(X,composition(converse(X2),X3))),X3))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3))) = join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(join(meet(composition(X2,X),X3),meet(composition(X2,meet(X,composition(converse(X2),X3))),X3)))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
join(meet(composition(X2,X),X3),join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3)))) = join(meet(composition(X2,X),X3),join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(join(meet(composition(X2,X),X3),meet(composition(X2,meet(X,composition(converse(X2),X3))),X3))))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
join(X2,join(X,complement(join(X2,X)))) = join(join(X2,X),complement(join(X2,X))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c116,plain,
top = join(join(X2,X),complement(join(X2,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c117,plain,
join(join(X2,X),complement(join(X2,X))) = top,
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
join(X2,join(X,complement(join(X2,X)))) = top,
inference(transitivity,[status(thm)],[c115,c117]) ).
cnf(c119,plain,
join(meet(composition(X2,X),X3),join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(join(meet(composition(X2,X),X3),meet(composition(X2,meet(X,composition(converse(X2),X3))),X3))))) = top,
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
join(meet(composition(X2,X),X3),join(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3),complement(meet(composition(X2,meet(X,composition(converse(X2),X3))),X3)))) = top,
inference(transitivity,[status(thm)],[c114,c119]) ).
cnf(c121,plain,
join(meet(composition(X2,X),X3),top) = top,
inference(transitivity,[status(thm)],[c108,c120]) ).
cnf(c122,plain,
join(top,meet(composition(X2,X),X3)) = top,
inference(transitivity,[status(thm)],[c106,c121]) ).
cnf(c123,plain,
join(top,meet(X3,composition(X2,X))) = top,
inference(transitivity,[status(thm)],[c104,c122]) ).
cnf(c124,plain,
join(top,meet(X2,composition(X,one))) = top,
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
join(top,meet(X2,X)) = top,
inference(transitivity,[status(thm)],[c102,c124]) ).
cnf(c126,plain,
join(top,meet(X,X2)) = top,
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
join(meet(X,X2),top) = top,
inference(transitivity,[status(thm)],[c97,c126]) ).
cnf(c128,plain,
join(join(complement(X),X2),join(meet(X,X2),complement(join(complement(X),X2)))) = top,
inference(transitivity,[status(thm)],[c96,c127]) ).
cnf(c129,plain,
join(join(complement(X),X2),X) = top,
inference(transitivity,[status(thm)],[c95,c128]) ).
cnf(c130,plain,
join(complement(X),join(X2,X)) = top,
inference(transitivity,[status(thm)],[c92,c129]) ).
cnf(c131,plain,
join(X2,join(complement(X),X)) = top,
inference(transitivity,[status(thm)],[c91,c130]) ).
cnf(c132,plain,
join(X2,join(X,complement(X))) = top,
inference(transitivity,[status(thm)],[c81,c131]) ).
cnf(c133,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c78,c132]) ).
cnf(c134,plain,
join(complement(join(complement(X2),X)),top) = top,
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
join(meet(X2,X),join(complement(meet(X2,X)),complement(join(complement(X2),X)))) = top,
inference(transitivity,[status(thm)],[c76,c134]) ).
cnf(c136,plain,
join(X2,complement(meet(X2,X))) = top,
inference(transitivity,[status(thm)],[c60,c135]) ).
cnf(c137,plain,
join(zero,complement(meet(zero,X))) = top,
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
complement(join(zero,complement(meet(zero,X)))) = complement(top),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
complement(join(zero,complement(meet(zero,X)))) = zero,
inference(transitivity,[status(thm)],[c138,c12]) ).
cnf(c140,plain,
meet(meet(zero,X),top) = zero,
inference(transitivity,[status(thm)],[c50,c139]) ).
cnf(c141,plain,
meet(top,meet(zero,X)) = zero,
inference(transitivity,[status(thm)],[c48,c140]) ).
cnf(c142,plain,
meet(top,meet(X,zero)) = zero,
inference(transitivity,[status(thm)],[c47,c141]) ).
cnf(c143,plain,
join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))) = join(zero,complement(join(complement(meet(X,zero)),top))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
join(complement(meet(X,zero)),top) = top,
inference(substitution,[status(thm)],[c133]) ).
cnf(c145,plain,
complement(join(complement(meet(X,zero)),top)) = complement(top),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
join(zero,complement(join(complement(meet(X,zero)),top))) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
join(zero,complement(top)) = join(zero,zero),
inference(congruence,[status(thm)],[c12]) ).
cnf(c148,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c149,plain,
join(zero,zero) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c151,plain,
join(zero,complement(top)) = join(complement(top),complement(top)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c153,plain,
converse(composition(converse(X2),X)) = composition(converse(X),converse(converse(X2))),
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c155,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
composition(converse(X),converse(converse(X2))) = composition(converse(X),X2),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
converse(composition(converse(X2),X)) = composition(converse(X),X2),
inference(transitivity,[status(thm)],[c153,c156]) ).
cnf(c158,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c98]) ).
cnf(c161,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c154]) ).
cnf(c163,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c161,c162]) ).
cnf(c164,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c159,c163]) ).
cnf(c165,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,axiom,
composition(A2,composition(B2,C2)) = composition(composition(A2,B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
cnf(c168,plain,
composition(X2,composition(one,X)) = composition(composition(X2,one),X),
inference(substitution,[status(thm)],[c167]) ).
cnf(c169,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c98]) ).
cnf(c170,plain,
composition(composition(X2,one),X) = composition(X2,X),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
composition(X2,composition(one,X)) = composition(X2,X),
inference(transitivity,[status(thm)],[c168,c170]) ).
cnf(c172,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c172,c164]) ).
cnf(c174,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c166,c173]) ).
cnf(c175,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
join(complement(X),complement(X)) = join(complement(X),complement(composition(one,X))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
converse(converse(one)) = one,
inference(substitution,[status(thm)],[c154]) ).
cnf(c179,plain,
one = converse(converse(one)),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
composition(one,X) = composition(converse(converse(one)),X),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
complement(composition(one,X)) = complement(composition(converse(converse(one)),X)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
join(complement(X),complement(composition(one,X))) = join(complement(X),complement(composition(converse(converse(one)),X))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
composition(converse(one),complement(composition(converse(converse(one)),X))) = complement(composition(converse(converse(one)),X)),
inference(substitution,[status(thm)],[c164]) ).
cnf(c184,plain,
complement(composition(converse(converse(one)),X)) = composition(converse(one),complement(composition(converse(converse(one)),X))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
join(complement(X),complement(composition(converse(converse(one)),X))) = join(complement(X),composition(converse(one),complement(composition(converse(converse(one)),X)))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c154]) ).
cnf(c187,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
composition(X,complement(composition(converse(X),X2))) = composition(converse(converse(X)),complement(composition(converse(X),X2))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
join(complement(X2),composition(X,complement(composition(converse(X),X2)))) = join(complement(X2),composition(converse(converse(X)),complement(composition(converse(X),X2)))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = join(complement(X2),composition(converse(X),complement(composition(X,X2)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c191,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)],[c190]) ).
cnf(c192,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c193,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c192]) ).
cnf(c194,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c191,c193]) ).
cnf(c195,plain,
join(complement(X2),composition(converse(converse(X)),complement(composition(converse(X),X2)))) = complement(X2),
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
join(complement(X2),composition(X,complement(composition(converse(X),X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c189,c195]) ).
cnf(c197,plain,
join(complement(X),composition(converse(one),complement(composition(converse(converse(one)),X)))) = complement(X),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
join(complement(X),complement(composition(converse(converse(one)),X))) = complement(X),
inference(transitivity,[status(thm)],[c185,c197]) ).
cnf(c199,plain,
join(complement(X),complement(composition(one,X))) = complement(X),
inference(transitivity,[status(thm)],[c182,c198]) ).
cnf(c200,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c177,c199]) ).
cnf(c201,plain,
join(complement(top),complement(top)) = complement(top),
inference(substitution,[status(thm)],[c200]) ).
cnf(c202,plain,
join(complement(top),complement(top)) = zero,
inference(transitivity,[status(thm)],[c201,c12]) ).
cnf(c203,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c151,c202]) ).
cnf(c204,plain,
join(zero,zero) = zero,
inference(transitivity,[status(thm)],[c149,c203]) ).
cnf(c205,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c147,c204]) ).
cnf(c206,plain,
join(zero,complement(join(complement(meet(X,zero)),top))) = zero,
inference(transitivity,[status(thm)],[c146,c205]) ).
cnf(c207,plain,
join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))) = zero,
inference(transitivity,[status(thm)],[c143,c206]) ).
cnf(c208,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c45,c207]) ).
cnf(c209,plain,
meet(complement(X),zero) = zero,
inference(substitution,[status(thm)],[c208]) ).
cnf(c210,plain,
zero = meet(complement(X),zero),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
join(complement(X),zero) = join(complement(X),meet(complement(X),zero)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c213,plain,
meet(complement(X),zero) = meet(complement(X),complement(top)),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
join(complement(X),meet(complement(X),zero)) = join(complement(X),meet(complement(X),complement(top))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c216,plain,
meet(top,complement(X)) = meet(top,join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c218,plain,
meet(top,join(complement(X),complement(X))) = meet(join(X,complement(X)),join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c220,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
meet(join(X2,complement(X)),join(complement(X2),complement(X))) = meet(join(X2,complement(X)),join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c223,plain,
join(X2,complement(X)) = join(complement(X),X2),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
meet(join(X2,complement(X)),join(complement(X),complement(X2))) = meet(join(complement(X),X2),join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c226,plain,
join(meet(X3,X2),complement(X)) = join(complement(join(complement(X3),complement(X2))),complement(X)),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
complement(join(meet(X3,X2),complement(X))) = complement(join(complement(join(complement(X3),complement(X2))),complement(X))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
meet(join(complement(X3),complement(X2)),X) = complement(join(complement(join(complement(X3),complement(X2))),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c229,plain,
complement(join(complement(join(complement(X3),complement(X2))),complement(X))) = meet(join(complement(X3),complement(X2)),X),
inference(symmetry,[status(thm)],[c228]) ).
cnf(c230,plain,
meet(X,join(complement(X3),complement(X2))) = meet(join(complement(X3),complement(X2)),X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c231,plain,
meet(join(complement(X3),complement(X2)),X) = meet(X,join(complement(X3),complement(X2))),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
complement(join(complement(join(complement(X3),complement(X2))),complement(X))) = meet(X,join(complement(X3),complement(X2))),
inference(transitivity,[status(thm)],[c229,c231]) ).
cnf(c233,plain,
complement(join(meet(X3,X2),complement(X))) = meet(X,join(complement(X3),complement(X2))),
inference(transitivity,[status(thm)],[c227,c232]) ).
cnf(c234,plain,
complement(join(meet(X,X2),complement(join(complement(X),X2)))) = meet(join(complement(X),X2),join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
meet(join(complement(X),X2),join(complement(X),complement(X2))) = complement(join(meet(X,X2),complement(join(complement(X),X2)))),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
join(meet(X,X2),complement(join(complement(X),X2))) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c237,plain,
complement(join(meet(X,X2),complement(join(complement(X),X2)))) = complement(X),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
meet(join(complement(X),X2),join(complement(X),complement(X2))) = complement(X),
inference(transitivity,[status(thm)],[c235,c237]) ).
cnf(c239,plain,
meet(join(X2,complement(X)),join(complement(X),complement(X2))) = complement(X),
inference(transitivity,[status(thm)],[c224,c238]) ).
cnf(c240,plain,
meet(join(X2,complement(X)),join(complement(X2),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c221,c239]) ).
cnf(c241,plain,
meet(join(X,complement(X)),join(complement(X),complement(X))) = complement(X),
inference(substitution,[status(thm)],[c240]) ).
cnf(c242,plain,
meet(top,join(complement(X),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c218,c241]) ).
cnf(c243,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c216,c242]) ).
cnf(c244,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
join(complement(X),meet(complement(X),complement(top))) = join(meet(top,complement(X)),meet(complement(X),complement(top))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c26]) ).
cnf(c247,plain,
join(meet(X2,X),meet(X,complement(X2))) = join(meet(X,X2),meet(X,complement(X2))),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,X),meet(X2,complement(X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c249,plain,
join(meet(X2,X),meet(X2,complement(X))) = join(meet(X2,complement(X)),meet(X2,X)),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c251,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))) = X2,
inference(substitution,[status(thm)],[c41]) ).
cnf(c253,plain,
join(meet(X2,complement(X)),meet(X2,X)) = X2,
inference(transitivity,[status(thm)],[c251,c252]) ).
cnf(c254,plain,
join(meet(X2,X),meet(X2,complement(X))) = X2,
inference(transitivity,[status(thm)],[c249,c253]) ).
cnf(c255,plain,
join(meet(X,X2),meet(X,complement(X2))) = X,
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
join(meet(X2,X),meet(X,complement(X2))) = X,
inference(transitivity,[status(thm)],[c247,c255]) ).
cnf(c257,plain,
join(meet(top,complement(X)),meet(complement(X),complement(top))) = complement(X),
inference(substitution,[status(thm)],[c256]) ).
cnf(c258,plain,
join(complement(X),meet(complement(X),complement(top))) = complement(X),
inference(transitivity,[status(thm)],[c245,c257]) ).
cnf(c259,plain,
join(complement(X),meet(complement(X),zero)) = complement(X),
inference(transitivity,[status(thm)],[c214,c258]) ).
cnf(c260,plain,
join(complement(X),zero) = complement(X),
inference(transitivity,[status(thm)],[c211,c259]) ).
cnf(c261,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c33,c260]) ).
cnf(c262,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c263,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c265,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c266,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c268,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c133]) ).
cnf(c270,plain,
top = join(complement(X),top),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
complement(top) = complement(join(complement(X),top)),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
join(meet(X,top),complement(top)) = join(meet(X,top),complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
join(meet(X,top),complement(join(complement(X),top))) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c274,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c272,c273]) ).
cnf(c275,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c268,c274]) ).
cnf(c276,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c266,c275]) ).
cnf(c277,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c264,c276]) ).
cnf(c278,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c263,c277]) ).
cnf(c279,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c31,c278]) ).
cnf(c280,plain,
meet(join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),top) = join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),
inference(substitution,[status(thm)],[c279]) ).
cnf(c281,plain,
join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))) = meet(join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),top),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
join(composition(X3,X2),join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X))) = join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),composition(X3,X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c283,plain,
join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),composition(X3,X2)) = join(composition(X3,X2),join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X))),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
join(complement(composition(X3,meet(X2,complement(X)))),join(composition(X3,X2),composition(X3,X))) = join(composition(X3,X2),join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c285,plain,
join(composition(X3,X2),join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X))) = join(complement(composition(X3,meet(X2,complement(X)))),join(composition(X3,X2),composition(X3,X))),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
join(composition(X3,X),composition(X3,meet(X2,complement(X)))) = join(composition(X3,meet(X2,complement(X))),composition(X3,X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c287,plain,
join(composition(X3,meet(X2,complement(X))),composition(X3,X)) = join(composition(X3,X),composition(X3,meet(X2,complement(X)))),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c154]) ).
cnf(c289,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
composition(X2,X) = composition(converse(converse(X2)),X),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
join(composition(X3,X2),composition(X3,X)) = join(composition(X3,X2),composition(converse(converse(X3)),X)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
converse(converse(composition(X2,X))) = composition(X2,X),
inference(substitution,[status(thm)],[c154]) ).
cnf(c293,plain,
composition(X2,X) = converse(converse(composition(X2,X))),
inference(symmetry,[status(thm)],[c292]) ).
cnf(c294,plain,
join(composition(X3,X2),composition(converse(converse(X3)),X)) = join(converse(converse(composition(X3,X2))),composition(converse(converse(X3)),X)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
join(composition(converse(X2),X),X3) = join(X3,composition(converse(X2),X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c296,plain,
join(X3,composition(converse(X2),X)) = join(composition(converse(X2),X),X3),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
converse(join(X3,composition(converse(X2),X))) = converse(join(composition(converse(X2),X),X3)),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,axiom,
converse(join(A2,B2)) = join(converse(A2),converse(B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(c299,plain,
converse(join(composition(converse(X2),X),X3)) = join(converse(composition(converse(X2),X)),converse(X3)),
inference(substitution,[status(thm)],[c298]) ).
cnf(c300,plain,
join(converse(composition(converse(X2),X)),converse(X3)) = join(composition(converse(X),X2),converse(X3)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c301,plain,
join(composition(converse(X),X2),converse(X3)) = join(converse(X3),composition(converse(X),X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c302,plain,
join(converse(composition(converse(X2),X)),converse(X3)) = join(converse(X3),composition(converse(X),X2)),
inference(transitivity,[status(thm)],[c300,c301]) ).
cnf(c303,plain,
converse(join(composition(converse(X2),X),X3)) = join(converse(X3),composition(converse(X),X2)),
inference(transitivity,[status(thm)],[c299,c302]) ).
cnf(c304,plain,
converse(join(X3,composition(converse(X2),X))) = join(converse(X3),composition(converse(X),X2)),
inference(transitivity,[status(thm)],[c297,c303]) ).
cnf(c305,plain,
converse(join(converse(composition(X3,X2)),composition(converse(X),converse(X3)))) = join(converse(converse(composition(X3,X2))),composition(converse(converse(X3)),X)),
inference(substitution,[status(thm)],[c304]) ).
cnf(c306,plain,
join(converse(converse(composition(X3,X2))),composition(converse(converse(X3)),X)) = converse(join(converse(composition(X3,X2)),composition(converse(X),converse(X3)))),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
join(composition(X,converse(X3)),converse(composition(X3,X2))) = join(converse(composition(X3,X2)),composition(X,converse(X3))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c308,plain,
join(converse(composition(X3,X2)),composition(X,converse(X3))) = join(composition(X,converse(X3)),converse(composition(X3,X2))),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
join(converse(composition(X2,X)),composition(X3,converse(X2))) = join(composition(X3,converse(X2)),converse(composition(X2,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c310,plain,
join(composition(X3,converse(X2)),converse(composition(X2,X))) = join(converse(composition(X2,X)),composition(X3,converse(X2))),
inference(symmetry,[status(thm)],[c309]) ).
cnf(c311,plain,
converse(composition(X2,X)) = composition(converse(X),converse(X2)),
inference(substitution,[status(thm)],[c152]) ).
cnf(c312,plain,
join(converse(composition(X2,X)),composition(X3,converse(X2))) = join(composition(converse(X),converse(X2)),composition(X3,converse(X2))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c314,plain,
composition(join(converse(X),X3),converse(X2)) = join(composition(converse(X),converse(X2)),composition(X3,converse(X2))),
inference(substitution,[status(thm)],[c313]) ).
cnf(c315,plain,
join(composition(converse(X),converse(X2)),composition(X3,converse(X2))) = composition(join(converse(X),X3),converse(X2)),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
join(converse(X),X2) = join(X2,converse(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c317,plain,
composition(join(converse(X),X3),converse(X2)) = composition(join(X3,converse(X)),converse(X2)),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
join(composition(converse(X),converse(X2)),composition(X3,converse(X2))) = composition(join(X3,converse(X)),converse(X2)),
inference(transitivity,[status(thm)],[c315,c317]) ).
cnf(c319,plain,
join(converse(composition(X2,X)),composition(X3,converse(X2))) = composition(join(X3,converse(X)),converse(X2)),
inference(transitivity,[status(thm)],[c312,c318]) ).
cnf(c320,plain,
join(composition(X3,converse(X2)),converse(composition(X2,X))) = composition(join(X3,converse(X)),converse(X2)),
inference(transitivity,[status(thm)],[c310,c319]) ).
cnf(c321,plain,
join(composition(X,converse(X3)),converse(composition(X3,X2))) = composition(join(X,converse(X2)),converse(X3)),
inference(substitution,[status(thm)],[c320]) ).
cnf(c322,plain,
join(converse(composition(X3,X2)),composition(X,converse(X3))) = composition(join(X,converse(X2)),converse(X3)),
inference(transitivity,[status(thm)],[c308,c321]) ).
cnf(c323,plain,
join(converse(composition(X3,X2)),composition(converse(X),converse(X3))) = composition(join(converse(X),converse(X2)),converse(X3)),
inference(substitution,[status(thm)],[c322]) ).
cnf(c324,plain,
converse(join(converse(composition(X3,X2)),composition(converse(X),converse(X3)))) = converse(composition(join(converse(X),converse(X2)),converse(X3))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
converse(composition(join(X3,converse(X2)),X)) = composition(converse(X),converse(join(X3,converse(X2)))),
inference(substitution,[status(thm)],[c152]) ).
cnf(c326,plain,
join(converse(X),X2) = join(X2,converse(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c327,plain,
join(X2,converse(X)) = join(converse(X),X2),
inference(symmetry,[status(thm)],[c326]) ).
cnf(c328,plain,
converse(join(X2,converse(X))) = converse(join(converse(X),X2)),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
converse(join(converse(X),X2)) = join(converse(converse(X)),converse(X2)),
inference(substitution,[status(thm)],[c298]) ).
cnf(c330,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c154]) ).
cnf(c331,plain,
join(converse(converse(X)),converse(X2)) = join(X,converse(X2)),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
converse(join(converse(X),X2)) = join(X,converse(X2)),
inference(transitivity,[status(thm)],[c329,c331]) ).
cnf(c333,plain,
converse(join(X2,converse(X))) = join(X,converse(X2)),
inference(transitivity,[status(thm)],[c328,c332]) ).
cnf(c334,plain,
composition(converse(X),converse(join(X3,converse(X2)))) = composition(converse(X),join(X2,converse(X3))),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
converse(composition(join(X3,converse(X2)),X)) = composition(converse(X),join(X2,converse(X3))),
inference(transitivity,[status(thm)],[c325,c334]) ).
cnf(c336,plain,
converse(composition(join(converse(X),converse(X2)),converse(X3))) = composition(converse(converse(X3)),join(X2,converse(converse(X)))),
inference(substitution,[status(thm)],[c335]) ).
cnf(c337,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c154]) ).
cnf(c338,plain,
composition(converse(converse(X3)),join(X2,converse(converse(X)))) = composition(X3,join(X2,converse(converse(X)))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c154]) ).
cnf(c340,plain,
join(X2,converse(converse(X))) = join(X2,X),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
composition(X3,join(X2,converse(converse(X)))) = composition(X3,join(X2,X)),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c343,plain,
composition(X3,join(X2,X)) = composition(X3,join(X,X2)),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
composition(X3,join(X2,converse(converse(X)))) = composition(X3,join(X,X2)),
inference(transitivity,[status(thm)],[c341,c343]) ).
cnf(c345,plain,
composition(converse(converse(X3)),join(X2,converse(converse(X)))) = composition(X3,join(X,X2)),
inference(transitivity,[status(thm)],[c338,c344]) ).
cnf(c346,plain,
converse(composition(join(converse(X),converse(X2)),converse(X3))) = composition(X3,join(X,X2)),
inference(transitivity,[status(thm)],[c336,c345]) ).
cnf(c347,plain,
converse(join(converse(composition(X3,X2)),composition(converse(X),converse(X3)))) = composition(X3,join(X,X2)),
inference(transitivity,[status(thm)],[c324,c346]) ).
cnf(c348,plain,
join(converse(converse(composition(X3,X2))),composition(converse(converse(X3)),X)) = composition(X3,join(X,X2)),
inference(transitivity,[status(thm)],[c306,c347]) ).
cnf(c349,plain,
join(composition(X3,X2),composition(converse(converse(X3)),X)) = composition(X3,join(X,X2)),
inference(transitivity,[status(thm)],[c294,c348]) ).
cnf(c350,plain,
join(composition(X3,X2),composition(X3,X)) = composition(X3,join(X,X2)),
inference(transitivity,[status(thm)],[c291,c349]) ).
cnf(c351,plain,
join(composition(X3,X),composition(X3,meet(X2,complement(X)))) = composition(X3,join(meet(X2,complement(X)),X)),
inference(substitution,[status(thm)],[c350]) ).
cnf(c352,plain,
join(meet(X2,complement(X)),X) = join(X,meet(X2,complement(X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c353,plain,
composition(X3,join(meet(X2,complement(X)),X)) = composition(X3,join(X,meet(X2,complement(X)))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
join(meet(X,complement(X2)),X2) = join(X2,meet(X,complement(X2))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c355,plain,
join(X2,meet(X,complement(X2))) = join(meet(X,complement(X2)),X2),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c357,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
join(zero,complement(join(complement(X),complement(X)))) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c261]) ).
cnf(c359,plain,
complement(join(complement(X),complement(X))) = join(zero,complement(join(complement(X),complement(X)))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c361,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c363,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c361,c362]) ).
cnf(c364,plain,
complement(join(complement(X),complement(X))) = X,
inference(transitivity,[status(thm)],[c359,c363]) ).
cnf(c365,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c357,c364]) ).
cnf(c366,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
join(meet(X,complement(X2)),X2) = join(meet(X,complement(X2)),complement(complement(X2))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
join(meet(X2,X3),X) = join(X,meet(X2,X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c369,plain,
join(X,meet(X2,X3)) = join(meet(X2,X3),X),
inference(symmetry,[status(thm)],[c368]) ).
cnf(c370,plain,
join(meet(X3,complement(X2)),join(X,meet(X2,X3))) = join(meet(X3,complement(X2)),join(meet(X2,X3),X)),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
join(meet(X3,complement(X2)),join(meet(X2,X3),X)) = join(join(meet(X3,complement(X2)),meet(X2,X3)),X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c372,plain,
join(meet(X2,complement(X)),meet(X,X2)) = join(meet(X2,complement(X)),meet(X2,X)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c373,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c374,plain,
complement(join(complement(X2),complement(X))) = meet(X2,X),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
meet(X2,X) = meet(X,X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c376,plain,
complement(join(complement(X2),complement(X))) = meet(X,X2),
inference(transitivity,[status(thm)],[c374,c375]) ).
cnf(c377,plain,
complement(join(complement(X),complement(X2))) = meet(X2,X),
inference(substitution,[status(thm)],[c376]) ).
cnf(c378,plain,
meet(X2,X) = complement(join(complement(X),complement(X2))),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
join(meet(X2,complement(X)),meet(X2,X)) = join(meet(X2,complement(X)),complement(join(complement(X),complement(X2)))),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c381,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c380]) ).
cnf(c382,plain,
complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
join(meet(X2,complement(X)),complement(join(complement(X),complement(X2)))) = join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
join(meet(X2,complement(X)),complement(join(complement(X2),complement(X)))) = X2,
inference(substitution,[status(thm)],[c41]) ).
cnf(c385,plain,
join(meet(X2,complement(X)),complement(join(complement(X),complement(X2)))) = X2,
inference(transitivity,[status(thm)],[c383,c384]) ).
cnf(c386,plain,
join(meet(X2,complement(X)),meet(X2,X)) = X2,
inference(transitivity,[status(thm)],[c379,c385]) ).
cnf(c387,plain,
join(meet(X2,complement(X)),meet(X,X2)) = X2,
inference(transitivity,[status(thm)],[c372,c386]) ).
cnf(c388,plain,
join(join(meet(X3,complement(X2)),meet(X2,X3)),X) = join(X3,X),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c390,plain,
join(join(meet(X3,complement(X2)),meet(X2,X3)),X) = join(X,X3),
inference(transitivity,[status(thm)],[c388,c389]) ).
cnf(c391,plain,
join(meet(X3,complement(X2)),join(meet(X2,X3),X)) = join(X,X3),
inference(transitivity,[status(thm)],[c371,c390]) ).
cnf(c392,plain,
join(meet(X3,complement(X2)),join(X,meet(X2,X3))) = join(X,X3),
inference(transitivity,[status(thm)],[c370,c391]) ).
cnf(c393,plain,
join(X,X3) = join(meet(X3,complement(X2)),join(X,meet(X2,X3))),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
meet(meet(X3,complement(X2)),join(X,X3)) = meet(meet(X3,complement(X2)),join(meet(X3,complement(X2)),join(X,meet(X2,X3)))),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c396,plain,
join(X2,X) = join(X,X2),
inference(symmetry,[status(thm)],[c395]) ).
cnf(c397,plain,
meet(X2,join(X2,X)) = meet(X2,join(X,X2)),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
join(meet(X2,X),join(zero,complement(join(complement(X2),X)))) = join(X2,zero),
inference(substitution,[status(thm)],[c58]) ).
cnf(c399,plain,
join(X2,zero) = join(meet(X2,X),join(zero,complement(join(complement(X2),X)))),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
join(zero,complement(join(complement(X2),X))) = complement(join(complement(X2),X)),
inference(substitution,[status(thm)],[c261]) ).
cnf(c401,plain,
join(meet(X2,X),join(zero,complement(join(complement(X2),X)))) = join(meet(X2,X),complement(join(complement(X2),X))),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
join(meet(X2,X),join(zero,complement(join(complement(X2),X)))) = X2,
inference(transitivity,[status(thm)],[c401,c41]) ).
cnf(c403,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c399,c402]) ).
cnf(c404,plain,
X = join(X,zero),
inference(symmetry,[status(thm)],[c403]) ).
cnf(c405,plain,
join(X,X2) = join(X,join(X2,zero)),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
meet(X2,join(X,X2)) = meet(X2,join(X,join(X2,zero))),
inference(congruence,[status(thm)],[c405]) ).
cnf(c407,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c408,plain,
join(X,zero) = join(X,complement(top)),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
join(X,join(X2,zero)) = join(X,join(X2,complement(top))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
meet(X2,join(X,join(X2,zero))) = meet(X2,join(X,join(X2,complement(top)))),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
top = join(X,top),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c412,plain,
complement(top) = complement(join(X,top)),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
join(X2,complement(top)) = join(X2,complement(join(X,top))),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
join(X,join(X2,complement(top))) = join(X,join(X2,complement(join(X,top)))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
meet(X2,join(X,join(X2,complement(top)))) = meet(X2,join(X,join(X2,complement(join(X,top))))),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c417,plain,
join(X2,complement(join(X,top))) = join(complement(complement(X2)),complement(join(X,top))),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
join(X,join(X2,complement(join(X,top)))) = join(X,join(complement(complement(X2)),complement(join(X,top)))),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
meet(X2,join(X,join(X2,complement(join(X,top))))) = meet(X2,join(X,join(complement(complement(X2)),complement(join(X,top))))),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
join(X,join(complement(complement(X2)),complement(join(X,top)))) = join(join(X,complement(complement(X2))),complement(join(X,top))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c421,plain,
meet(X2,join(X,join(complement(complement(X2)),complement(join(X,top))))) = meet(X2,join(join(X,complement(complement(X2))),complement(join(X,top)))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
join(complement(X2),join(X,complement(complement(X2)))) = join(X,top),
inference(substitution,[status(thm)],[c74]) ).
cnf(c423,plain,
join(X,top) = join(complement(X2),join(X,complement(complement(X2)))),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c424,plain,
complement(join(X,top)) = complement(join(complement(X2),join(X,complement(complement(X2))))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
join(join(X,complement(complement(X2))),complement(join(X,top))) = join(join(X,complement(complement(X2))),complement(join(complement(X2),join(X,complement(complement(X2)))))),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
meet(X2,join(join(X,complement(complement(X2))),complement(join(X,top)))) = meet(X2,join(join(X,complement(complement(X2))),complement(join(complement(X2),join(X,complement(complement(X2))))))),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c428,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
complement(join(complement(X2),X)) = complement(join(X,complement(X2))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
join(X,complement(join(complement(X2),X))) = join(X,complement(join(X,complement(X2)))),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
meet(X2,join(X,complement(join(complement(X2),X)))) = meet(X2,join(X,complement(join(X,complement(X2))))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c433,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c432]) ).
cnf(c434,plain,
complement(join(X,complement(X2))) = complement(join(complement(X2),X)),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
join(X,complement(join(X,complement(X2)))) = join(X,complement(join(complement(X2),X))),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
meet(X2,join(X,complement(join(X,complement(X2))))) = meet(X2,join(X,complement(join(complement(X2),X)))),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
join(meet(X2,join(X,complement(join(complement(X2),X)))),zero) = meet(X2,join(X,complement(join(complement(X2),X)))),
inference(substitution,[status(thm)],[c403]) ).
cnf(c438,plain,
meet(X2,join(X,complement(join(complement(X2),X)))) = join(meet(X2,join(X,complement(join(complement(X2),X)))),zero),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c440,plain,
join(meet(X2,join(X,complement(join(complement(X2),X)))),zero) = join(meet(X2,join(X,complement(join(complement(X2),X)))),complement(top)),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
join(complement(X2),join(X,complement(join(complement(X2),X)))) = top,
inference(substitution,[status(thm)],[c118]) ).
cnf(c442,plain,
top = join(complement(X2),join(X,complement(join(complement(X2),X)))),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
complement(top) = complement(join(complement(X2),join(X,complement(join(complement(X2),X))))),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
join(meet(X2,join(X,complement(join(complement(X2),X)))),complement(top)) = join(meet(X2,join(X,complement(join(complement(X2),X)))),complement(join(complement(X2),join(X,complement(join(complement(X2),X)))))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
join(meet(X2,join(X,complement(join(complement(X2),X)))),complement(join(complement(X2),join(X,complement(join(complement(X2),X)))))) = X2,
inference(substitution,[status(thm)],[c41]) ).
cnf(c446,plain,
join(meet(X2,join(X,complement(join(complement(X2),X)))),complement(top)) = X2,
inference(transitivity,[status(thm)],[c444,c445]) ).
cnf(c447,plain,
join(meet(X2,join(X,complement(join(complement(X2),X)))),zero) = X2,
inference(transitivity,[status(thm)],[c440,c446]) ).
cnf(c448,plain,
meet(X2,join(X,complement(join(complement(X2),X)))) = X2,
inference(transitivity,[status(thm)],[c438,c447]) ).
cnf(c449,plain,
meet(X2,join(X,complement(join(X,complement(X2))))) = X2,
inference(transitivity,[status(thm)],[c436,c448]) ).
cnf(c450,plain,
meet(X2,join(X,complement(join(complement(X2),X)))) = X2,
inference(transitivity,[status(thm)],[c431,c449]) ).
cnf(c451,plain,
meet(X2,join(join(X,complement(complement(X2))),complement(join(complement(X2),join(X,complement(complement(X2))))))) = X2,
inference(substitution,[status(thm)],[c450]) ).
cnf(c452,plain,
meet(X2,join(join(X,complement(complement(X2))),complement(join(X,top)))) = X2,
inference(transitivity,[status(thm)],[c426,c451]) ).
cnf(c453,plain,
meet(X2,join(X,join(complement(complement(X2)),complement(join(X,top))))) = X2,
inference(transitivity,[status(thm)],[c421,c452]) ).
cnf(c454,plain,
meet(X2,join(X,join(X2,complement(join(X,top))))) = X2,
inference(transitivity,[status(thm)],[c419,c453]) ).
cnf(c455,plain,
meet(X2,join(X,join(X2,complement(top)))) = X2,
inference(transitivity,[status(thm)],[c415,c454]) ).
cnf(c456,plain,
meet(X2,join(X,join(X2,zero))) = X2,
inference(transitivity,[status(thm)],[c410,c455]) ).
cnf(c457,plain,
meet(X2,join(X,X2)) = X2,
inference(transitivity,[status(thm)],[c406,c456]) ).
cnf(c458,plain,
meet(X2,join(X2,X)) = X2,
inference(transitivity,[status(thm)],[c397,c457]) ).
cnf(c459,plain,
meet(meet(X3,complement(X2)),join(meet(X3,complement(X2)),join(X,meet(X2,X3)))) = meet(X3,complement(X2)),
inference(substitution,[status(thm)],[c458]) ).
cnf(c460,plain,
meet(meet(X3,complement(X2)),join(X,X3)) = meet(X3,complement(X2)),
inference(transitivity,[status(thm)],[c394,c459]) ).
cnf(c461,plain,
meet(meet(X,complement(X2)),join(X2,X)) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c460]) ).
cnf(c462,plain,
meet(X,complement(X2)) = meet(meet(X,complement(X2)),join(X2,X)),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
join(meet(X,complement(X2)),complement(complement(X2))) = join(meet(meet(X,complement(X2)),join(X2,X)),complement(complement(X2))),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c465,plain,
join(X,X2) = join(X2,X),
inference(symmetry,[status(thm)],[c464]) ).
cnf(c466,plain,
complement(join(X,X2)) = complement(join(X2,X)),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
join(meet(X2,complement(X)),complement(join(X,X2))) = join(meet(X2,complement(X)),complement(join(X2,X))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
join(complement(join(X2,X)),meet(X2,complement(X))) = join(meet(X2,complement(X)),complement(join(X2,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c469,plain,
join(meet(X2,complement(X)),complement(join(X2,X))) = join(complement(join(X2,X)),meet(X2,complement(X))),
inference(symmetry,[status(thm)],[c468]) ).
cnf(c470,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c471,plain,
join(X2,X) = join(X2,complement(complement(X))),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
complement(join(X2,X)) = complement(join(X2,complement(complement(X)))),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
join(complement(join(X2,X)),meet(X2,complement(X))) = join(complement(join(X2,complement(complement(X)))),meet(X2,complement(X))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
join(meet(X2,complement(X)),complement(join(X2,complement(complement(X))))) = join(complement(join(X2,complement(complement(X)))),meet(X2,complement(X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c475,plain,
join(complement(join(X2,complement(complement(X)))),meet(X2,complement(X))) = join(meet(X2,complement(X)),complement(join(X2,complement(complement(X))))),
inference(symmetry,[status(thm)],[c474]) ).
cnf(c476,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c477,plain,
join(X2,complement(X)) = join(complement(X),X2),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c478,plain,
complement(join(X2,complement(X))) = complement(join(complement(X),X2)),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
join(meet(X2,X),complement(join(X2,complement(X)))) = join(meet(X2,X),complement(join(complement(X),X2))),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,plain,
join(meet(X2,X),complement(join(X2,complement(X)))) = X,
inference(transitivity,[status(thm)],[c479,c43]) ).
cnf(c481,plain,
join(meet(X2,complement(X)),complement(join(X2,complement(complement(X))))) = complement(X),
inference(substitution,[status(thm)],[c480]) ).
cnf(c482,plain,
join(complement(join(X2,complement(complement(X)))),meet(X2,complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c475,c481]) ).
cnf(c483,plain,
join(complement(join(X2,X)),meet(X2,complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c473,c482]) ).
cnf(c484,plain,
join(meet(X2,complement(X)),complement(join(X2,X))) = complement(X),
inference(transitivity,[status(thm)],[c469,c483]) ).
cnf(c485,plain,
join(meet(X2,complement(X)),complement(join(X,X2))) = complement(X),
inference(transitivity,[status(thm)],[c467,c484]) ).
cnf(c486,plain,
join(meet(X,complement(X2)),complement(join(X2,X))) = complement(X2),
inference(substitution,[status(thm)],[c485]) ).
cnf(c487,plain,
complement(X2) = join(meet(X,complement(X2)),complement(join(X2,X))),
inference(symmetry,[status(thm)],[c486]) ).
cnf(c488,plain,
complement(complement(X2)) = complement(join(meet(X,complement(X2)),complement(join(X2,X)))),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
join(meet(meet(X,complement(X2)),join(X2,X)),complement(complement(X2))) = join(meet(meet(X,complement(X2)),join(X2,X)),complement(join(meet(X,complement(X2)),complement(join(X2,X))))),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
join(meet(meet(X,complement(X2)),join(X2,X)),complement(join(meet(X,complement(X2)),complement(join(X2,X))))) = join(X2,X),
inference(substitution,[status(thm)],[c480]) ).
cnf(c491,plain,
join(meet(meet(X,complement(X2)),join(X2,X)),complement(complement(X2))) = join(X2,X),
inference(transitivity,[status(thm)],[c489,c490]) ).
cnf(c492,plain,
join(meet(X,complement(X2)),complement(complement(X2))) = join(X2,X),
inference(transitivity,[status(thm)],[c463,c491]) ).
cnf(c493,plain,
join(meet(X,complement(X2)),X2) = join(X2,X),
inference(transitivity,[status(thm)],[c367,c492]) ).
cnf(c494,plain,
join(X2,meet(X,complement(X2))) = join(X2,X),
inference(transitivity,[status(thm)],[c355,c493]) ).
cnf(c495,plain,
join(X,meet(X2,complement(X))) = join(X,X2),
inference(substitution,[status(thm)],[c494]) ).
cnf(c496,plain,
composition(X3,join(X,meet(X2,complement(X)))) = composition(X3,join(X,X2)),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
composition(X3,join(X,X2)) = join(composition(X3,X2),composition(X3,X)),
inference(symmetry,[status(thm)],[c350]) ).
cnf(c498,plain,
composition(X3,join(X,meet(X2,complement(X)))) = join(composition(X3,X2),composition(X3,X)),
inference(transitivity,[status(thm)],[c496,c497]) ).
cnf(c499,plain,
composition(X3,join(meet(X2,complement(X)),X)) = join(composition(X3,X2),composition(X3,X)),
inference(transitivity,[status(thm)],[c353,c498]) ).
cnf(c500,plain,
join(composition(X3,X),composition(X3,meet(X2,complement(X)))) = join(composition(X3,X2),composition(X3,X)),
inference(transitivity,[status(thm)],[c351,c499]) ).
cnf(c501,plain,
join(composition(X3,meet(X2,complement(X))),composition(X3,X)) = join(composition(X3,X2),composition(X3,X)),
inference(transitivity,[status(thm)],[c287,c500]) ).
cnf(c502,plain,
join(composition(X3,X2),composition(X3,X)) = join(composition(X3,meet(X2,complement(X))),composition(X3,X)),
inference(symmetry,[status(thm)],[c501]) ).
cnf(c503,plain,
join(complement(composition(X3,meet(X2,complement(X)))),join(composition(X3,X2),composition(X3,X))) = join(complement(composition(X3,meet(X2,complement(X)))),join(composition(X3,meet(X2,complement(X))),composition(X3,X))),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c505,plain,
join(X2,X) = join(X,X2),
inference(symmetry,[status(thm)],[c504]) ).
cnf(c506,plain,
join(complement(X2),join(X2,X)) = join(complement(X2),join(X,X2)),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c508,plain,
join(X,X2) = join(X2,X),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
join(complement(X2),join(X,X2)) = join(complement(X2),join(X2,X)),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
join(complement(X2),join(X2,X)) = join(join(complement(X2),X2),X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c511,plain,
join(X,complement(X)) = join(complement(X),X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c512,plain,
join(complement(X),X) = join(X,complement(X)),
inference(symmetry,[status(thm)],[c511]) ).
cnf(c513,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c514,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c513]) ).
cnf(c515,plain,
join(complement(X),X) = top,
inference(transitivity,[status(thm)],[c512,c514]) ).
cnf(c516,plain,
join(join(complement(X2),X2),X) = join(top,X),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c19]) ).
cnf(c518,plain,
join(join(complement(X2),X2),X) = join(X,top),
inference(transitivity,[status(thm)],[c516,c517]) ).
cnf(c519,plain,
join(complement(X2),join(X2,X)) = join(X,top),
inference(transitivity,[status(thm)],[c510,c518]) ).
cnf(c520,plain,
join(complement(X2),join(X,X2)) = join(X,top),
inference(transitivity,[status(thm)],[c509,c519]) ).
cnf(c521,plain,
join(complement(X2),join(X,X2)) = top,
inference(transitivity,[status(thm)],[c520,c133]) ).
cnf(c522,plain,
join(complement(X2),join(X2,X)) = top,
inference(transitivity,[status(thm)],[c506,c521]) ).
cnf(c523,plain,
join(complement(composition(X3,meet(X2,complement(X)))),join(composition(X3,meet(X2,complement(X))),composition(X3,X))) = top,
inference(substitution,[status(thm)],[c522]) ).
cnf(c524,plain,
join(complement(composition(X3,meet(X2,complement(X)))),join(composition(X3,X2),composition(X3,X))) = top,
inference(transitivity,[status(thm)],[c503,c523]) ).
cnf(c525,plain,
join(composition(X3,X2),join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X))) = top,
inference(transitivity,[status(thm)],[c285,c524]) ).
cnf(c526,plain,
join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),composition(X3,X2)) = top,
inference(transitivity,[status(thm)],[c283,c525]) ).
cnf(c527,plain,
top = join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),composition(X3,X2)),
inference(symmetry,[status(thm)],[c526]) ).
cnf(c528,plain,
meet(join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),top) = meet(join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),composition(X3,X2))),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c530,plain,
join(X2,X) = join(X,X2),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
meet(join(X2,complement(X)),join(X2,X)) = meet(join(X2,complement(X)),join(X,X2)),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c533,plain,
join(X2,complement(X)) = join(complement(X),X2),
inference(symmetry,[status(thm)],[c532]) ).
cnf(c534,plain,
meet(join(X2,complement(X)),join(X,X2)) = meet(join(complement(X),X2),join(X,X2)),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c536,plain,
join(X,X2) = join(X,meet(X2,top)),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
meet(join(complement(X),X2),join(X,X2)) = meet(join(complement(X),X2),join(X,meet(X2,top))),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c539,plain,
join(X,meet(X2,top)) = join(X,complement(join(zero,complement(X2)))),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
meet(join(complement(X),X2),join(X,meet(X2,top))) = meet(join(complement(X),X2),join(X,complement(join(zero,complement(X2))))),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c542,plain,
join(complement(X),X2) = join(complement(X),meet(X2,top)),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
meet(join(complement(X),X2),join(X,complement(join(zero,complement(X2))))) = meet(join(complement(X),meet(X2,top)),join(X,complement(join(zero,complement(X2))))),
inference(congruence,[status(thm)],[c542]) ).
cnf(c544,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c545,plain,
join(complement(X),meet(X2,top)) = join(complement(X),complement(join(zero,complement(X2)))),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
meet(join(complement(X),meet(X2,top)),join(X,complement(join(zero,complement(X2))))) = meet(join(complement(X),complement(join(zero,complement(X2)))),join(X,complement(join(zero,complement(X2))))),
inference(congruence,[status(thm)],[c545]) ).
cnf(c547,plain,
meet(join(complement(X2),complement(X)),join(X2,complement(X))) = meet(join(X2,complement(X)),join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c548,plain,
meet(join(complement(X2),complement(X)),join(X2,complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c547,c240]) ).
cnf(c549,plain,
meet(join(complement(X),complement(join(zero,complement(X2)))),join(X,complement(join(zero,complement(X2))))) = complement(join(zero,complement(X2))),
inference(substitution,[status(thm)],[c548]) ).
cnf(c550,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c30,c279]) ).
cnf(c551,plain,
meet(join(complement(X),complement(join(zero,complement(X2)))),join(X,complement(join(zero,complement(X2))))) = X2,
inference(transitivity,[status(thm)],[c549,c550]) ).
cnf(c552,plain,
meet(join(complement(X),meet(X2,top)),join(X,complement(join(zero,complement(X2))))) = X2,
inference(transitivity,[status(thm)],[c546,c551]) ).
cnf(c553,plain,
meet(join(complement(X),X2),join(X,complement(join(zero,complement(X2))))) = X2,
inference(transitivity,[status(thm)],[c543,c552]) ).
cnf(c554,plain,
meet(join(complement(X),X2),join(X,meet(X2,top))) = X2,
inference(transitivity,[status(thm)],[c540,c553]) ).
cnf(c555,plain,
meet(join(complement(X),X2),join(X,X2)) = X2,
inference(transitivity,[status(thm)],[c537,c554]) ).
cnf(c556,plain,
meet(join(X2,complement(X)),join(X,X2)) = X2,
inference(transitivity,[status(thm)],[c534,c555]) ).
cnf(c557,plain,
meet(join(X2,complement(X)),join(X2,X)) = X2,
inference(transitivity,[status(thm)],[c531,c556]) ).
cnf(c558,plain,
meet(join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),composition(X3,X2))) = join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),
inference(substitution,[status(thm)],[c557]) ).
cnf(c559,plain,
meet(join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),top) = join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),
inference(transitivity,[status(thm)],[c528,c558]) ).
cnf(c560,plain,
join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))) = join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),
inference(transitivity,[status(thm)],[c281,c559]) ).
cnf(c561,plain,
join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)) = join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
join(X,join(X3,X2)) = join(join(X3,X2),X),
inference(substitution,[status(thm)],[c19]) ).
cnf(c563,plain,
join(join(X3,X2),X) = join(X,join(X3,X2)),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
join(X3,join(X,X2)) = join(X,join(X3,X2)),
inference(substitution,[status(thm)],[c89]) ).
cnf(c565,plain,
join(X,join(X3,X2)) = join(X3,join(X,X2)),
inference(symmetry,[status(thm)],[c564]) ).
cnf(c566,plain,
join(X3,join(X,X2)) = join(join(X,X2),X3),
inference(substitution,[status(thm)],[c19]) ).
cnf(c567,plain,
join(X,join(X3,X2)) = join(join(X,X2),X3),
inference(transitivity,[status(thm)],[c565,c566]) ).
cnf(c568,plain,
join(join(X3,X2),X) = join(join(X,X2),X3),
inference(transitivity,[status(thm)],[c563,c567]) ).
cnf(c569,plain,
join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))) = join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))),
inference(substitution,[status(thm)],[c568]) ).
cnf(c570,plain,
join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))) = join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),
inference(symmetry,[status(thm)],[c569]) ).
cnf(c571,plain,
meet(join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),top) = join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),
inference(substitution,[status(thm)],[c279]) ).
cnf(c572,plain,
join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))) = meet(join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),top),
inference(symmetry,[status(thm)],[c571]) ).
cnf(c573,plain,
join(composition(X3,meet(X2,complement(X))),join(complement(composition(X3,X2)),composition(X3,X))) = join(join(complement(composition(X3,X2)),composition(X3,X)),composition(X3,meet(X2,complement(X)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c574,plain,
join(join(complement(composition(X3,X2)),composition(X3,X)),composition(X3,meet(X2,complement(X)))) = join(composition(X3,meet(X2,complement(X))),join(complement(composition(X3,X2)),composition(X3,X))),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
join(complement(composition(X3,X2)),join(composition(X3,meet(X2,complement(X))),composition(X3,X))) = join(composition(X3,meet(X2,complement(X))),join(complement(composition(X3,X2)),composition(X3,X))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c576,plain,
join(composition(X3,meet(X2,complement(X))),join(complement(composition(X3,X2)),composition(X3,X))) = join(complement(composition(X3,X2)),join(composition(X3,meet(X2,complement(X))),composition(X3,X))),
inference(symmetry,[status(thm)],[c575]) ).
cnf(c577,plain,
join(complement(composition(X3,X2)),join(composition(X3,meet(X2,complement(X))),composition(X3,X))) = join(complement(composition(X3,X2)),join(composition(X3,X2),composition(X3,X))),
inference(congruence,[status(thm)],[c501]) ).
cnf(c578,plain,
join(complement(composition(X3,X2)),join(composition(X3,X2),composition(X3,X))) = top,
inference(substitution,[status(thm)],[c522]) ).
cnf(c579,plain,
join(complement(composition(X3,X2)),join(composition(X3,meet(X2,complement(X))),composition(X3,X))) = top,
inference(transitivity,[status(thm)],[c577,c578]) ).
cnf(c580,plain,
join(composition(X3,meet(X2,complement(X))),join(complement(composition(X3,X2)),composition(X3,X))) = top,
inference(transitivity,[status(thm)],[c576,c579]) ).
cnf(c581,plain,
join(join(complement(composition(X3,X2)),composition(X3,X)),composition(X3,meet(X2,complement(X)))) = top,
inference(transitivity,[status(thm)],[c574,c580]) ).
cnf(c582,plain,
top = join(join(complement(composition(X3,X2)),composition(X3,X)),composition(X3,meet(X2,complement(X)))),
inference(symmetry,[status(thm)],[c581]) ).
cnf(c583,plain,
meet(join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),top) = meet(join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),join(join(complement(composition(X3,X2)),composition(X3,X)),composition(X3,meet(X2,complement(X))))),
inference(congruence,[status(thm)],[c582]) ).
cnf(c584,plain,
meet(join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),join(join(complement(composition(X3,X2)),composition(X3,X)),composition(X3,meet(X2,complement(X))))) = join(complement(composition(X3,X2)),composition(X3,X)),
inference(substitution,[status(thm)],[c557]) ).
cnf(c585,plain,
meet(join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))),top) = join(complement(composition(X3,X2)),composition(X3,X)),
inference(transitivity,[status(thm)],[c583,c584]) ).
cnf(c586,plain,
join(join(complement(composition(X3,X2)),composition(X3,X)),complement(composition(X3,meet(X2,complement(X))))) = join(complement(composition(X3,X2)),composition(X3,X)),
inference(transitivity,[status(thm)],[c572,c585]) ).
cnf(c587,plain,
join(join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)),complement(composition(X3,X2))) = join(complement(composition(X3,X2)),composition(X3,X)),
inference(transitivity,[status(thm)],[c570,c586]) ).
cnf(c588,plain,
join(complement(composition(X3,meet(X2,complement(X)))),composition(X3,X)) = join(complement(composition(X3,X2)),composition(X3,X)),
inference(transitivity,[status(thm)],[c561,c587]) ).
cnf(c589,plain,
join(complement(composition(sk1,meet(sk2,complement(sk3)))),composition(sk1,sk3)) = join(complement(composition(sk1,sk2)),composition(sk1,sk3)),
inference(substitution,[status(thm)],[c588]) ).
cnf(c590,plain,
join(complement(composition(sk1,sk2)),composition(sk1,sk3)) = join(complement(composition(sk1,meet(sk2,complement(sk3)))),composition(sk1,sk3)),
inference(symmetry,[status(thm)],[c589]) ).
cnf(c591,plain,
$false,
inference(resolution,[status(thm)],[c1,c590]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL017-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 22:50:51 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.85/4.21 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 29.85/4.21
% 29.85/4.21 % SZS status Unsatisfiable
% 29.85/4.21
% 29.85/4.26 % SZS output start CNFRefutation
% See solution above
% 32.39/4.53
% 32.39/4.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------