%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL050-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:33:35 PM UTC 2026
% Result : Unsatisfiable 1.20s 0.63s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 92
% Number of leaves : 16
% Syntax : Number of clauses : 457 ( 457 unt; 0 nHn; 87 RR)
% Number of literals : 457 ( 456 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 505 ( 67 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(c2,axiom,
converse(converse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c3,plain,
converse(converse(composition(complement(composition(X,top)),top))) = composition(complement(composition(X,top)),top),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
composition(complement(composition(X,top)),top) = converse(converse(composition(complement(composition(X,top)),top))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
converse(composition(A2,B)) = composition(converse(B),converse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c6,plain,
converse(composition(X,top)) = composition(converse(top),converse(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
converse(join(A2,B2)) = join(converse(A2),converse(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(c11,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
top = join(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
cnf(c14,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c12,c16]) ).
cnf(c18,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c9,c18]) ).
cnf(c20,plain,
join(top,converse(complement(converse(top)))) = converse(top),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
converse(top) = join(top,converse(complement(converse(top)))),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
join(A2,B2) = join(B2,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c23,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c26,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c28,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c31,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c33,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c22]) ).
cnf(c36,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c31,c36]) ).
cnf(c38,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c29,c37]) ).
cnf(c39,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c42,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c45,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c47,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c45,c48]) ).
cnf(c50,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c43,c52]) ).
cnf(c54,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c53]) ).
cnf(c58,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,axiom,
composition(A2,composition(B2,C2)) = composition(composition(A2,B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
cnf(c60,plain,
composition(X2,composition(one,X)) = composition(composition(X2,one),X),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c62,plain,
composition(composition(X2,one),X) = composition(X2,X),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
composition(X2,composition(one,X)) = composition(X2,X),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c64,c53]) ).
cnf(c66,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c58,c65]) ).
cnf(c67,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,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)],[c22]) ).
cnf(c72,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)],[c71]) ).
cnf(c73,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c74,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c72,c74]) ).
cnf(c76,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c70,c76]) ).
cnf(c78,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c56,c77]) ).
cnf(c79,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c81,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c79,c81]) ).
cnf(c83,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c40,c82]) ).
cnf(c84,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c26,c83]) ).
cnf(c85,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c38]) ).
cnf(c88,plain,
join(complement(zero),top) = join(top,complement(zero)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c89,plain,
join(top,complement(zero)) = join(complement(zero),top),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c91,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
join(top,join(zero,X)) = join(top,join(X,zero)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c22]) ).
cnf(c94,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
join(top,join(X,zero)) = join(top,join(zero,X)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
join(top,join(zero,X)) = join(join(top,zero),X),
inference(substitution,[status(thm)],[c30]) ).
cnf(c97,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c98,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,axiom,
meet(A2,B2) = complement(join(complement(A2),complement(B2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c100,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c103,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c101,c104]) ).
cnf(c106,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c98,c105]) ).
cnf(c107,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
join(top,zero) = join(top,complement(top)),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
top = join(top,complement(top)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c110,plain,
join(top,complement(top)) = top,
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
join(top,zero) = top,
inference(transitivity,[status(thm)],[c108,c110]) ).
cnf(c112,plain,
join(join(top,zero),X) = join(top,X),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c22]) ).
cnf(c114,plain,
join(join(top,zero),X) = join(X,top),
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
join(top,join(zero,X)) = join(X,top),
inference(transitivity,[status(thm)],[c96,c114]) ).
cnf(c116,plain,
join(top,join(X,zero)) = join(X,top),
inference(transitivity,[status(thm)],[c95,c115]) ).
cnf(c117,plain,
join(top,join(zero,X)) = join(X,top),
inference(transitivity,[status(thm)],[c92,c116]) ).
cnf(c118,plain,
join(top,join(zero,complement(zero))) = join(complement(zero),top),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
join(complement(zero),top) = join(top,join(zero,complement(zero))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c121,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
join(top,join(zero,complement(zero))) = join(top,top),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
join(complement(zero),top) = join(top,top),
inference(transitivity,[status(thm)],[c119,c122]) ).
cnf(c124,plain,
join(top,complement(zero)) = join(top,top),
inference(transitivity,[status(thm)],[c89,c123]) ).
cnf(c125,plain,
join(top,top) = join(top,complement(zero)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
join(top,complement(zero)) = top,
inference(substitution,[status(thm)],[c84]) ).
cnf(c127,plain,
join(top,top) = top,
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
join(X,join(top,complement(X))) = top,
inference(transitivity,[status(thm)],[c87,c127]) ).
cnf(c129,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c86,c128]) ).
cnf(c130,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c24,c129]) ).
cnf(c131,plain,
join(top,converse(complement(converse(top)))) = top,
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c21,c131]) ).
cnf(c133,plain,
composition(converse(top),converse(X)) = composition(top,converse(X)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
converse(composition(X,top)) = composition(top,converse(X)),
inference(transitivity,[status(thm)],[c6,c133]) ).
cnf(c135,plain,
converse(composition(complement(composition(X,top)),top)) = composition(top,converse(complement(composition(X,top)))),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c130]) ).
cnf(c137,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
composition(top,converse(complement(composition(X,top)))) = composition(join(top,one),converse(complement(composition(X,top)))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c140,plain,
join(X2,composition(X,X2)) = join(composition(one,X2),composition(X,X2)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c142,plain,
composition(join(one,X),X2) = join(composition(one,X2),composition(X,X2)),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
join(composition(one,X2),composition(X,X2)) = composition(join(one,X),X2),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c22]) ).
cnf(c145,plain,
composition(join(one,X),X2) = composition(join(X,one),X2),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
join(composition(one,X2),composition(X,X2)) = composition(join(X,one),X2),
inference(transitivity,[status(thm)],[c143,c145]) ).
cnf(c147,plain,
join(X2,composition(X,X2)) = composition(join(X,one),X2),
inference(transitivity,[status(thm)],[c140,c146]) ).
cnf(c148,plain,
join(converse(complement(composition(X,top))),composition(top,converse(complement(composition(X,top))))) = composition(join(top,one),converse(complement(composition(X,top)))),
inference(substitution,[status(thm)],[c147]) ).
cnf(c149,plain,
composition(join(top,one),converse(complement(composition(X,top)))) = join(converse(complement(composition(X,top))),composition(top,converse(complement(composition(X,top))))),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
converse(composition(complement(composition(X,top)),top)) = composition(top,converse(complement(composition(X,top)))),
inference(substitution,[status(thm)],[c134]) ).
cnf(c151,plain,
composition(top,converse(complement(composition(X,top)))) = converse(composition(complement(composition(X,top)),top)),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
join(converse(complement(composition(X,top))),composition(top,converse(complement(composition(X,top))))) = join(converse(complement(composition(X,top))),converse(composition(complement(composition(X,top)),top))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
converse(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))) = join(converse(complement(composition(X2,top))),converse(composition(complement(composition(X2,top)),X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c154,plain,
join(converse(complement(composition(X2,top))),converse(composition(complement(composition(X2,top)),X))) = converse(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c156,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c159,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c161,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c162,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c165,plain,
complement(join(complement(X2),complement(X))) = meet(X2,X),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
complement(join(complement(X),complement(X2))) = meet(X2,X),
inference(transitivity,[status(thm)],[c163,c165]) ).
cnf(c167,plain,
meet(X,X2) = meet(X2,X),
inference(transitivity,[status(thm)],[c160,c166]) ).
cnf(c168,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c167]) ).
cnf(c169,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c159,c169]) ).
cnf(c171,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c157,c170]) ).
cnf(c172,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c167]) ).
cnf(c174,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c171]) ).
cnf(c175,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c102]) ).
cnf(c177,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c179,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c182,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)],[c181]) ).
cnf(c183,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(c184,plain,
X2 = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))) = X2,
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
join(meet(X2,X),complement(join(complement(X2),X))) = X2,
inference(transitivity,[status(thm)],[c182,c185]) ).
cnf(c187,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c180,c187]) ).
cnf(c189,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c177,c188]) ).
cnf(c190,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c175,c190]) ).
cnf(c192,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c173,c191]) ).
cnf(c193,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c167]) ).
cnf(c196,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c198,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c200,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c129]) ).
cnf(c202,plain,
top = join(complement(X),top),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
complement(top) = complement(join(complement(X),top)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
join(meet(X,top),complement(top)) = join(meet(X,top),complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
join(meet(X,top),complement(join(complement(X),top))) = X,
inference(substitution,[status(thm)],[c186]) ).
cnf(c206,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c204,c205]) ).
cnf(c207,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c200,c206]) ).
cnf(c208,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c198,c207]) ).
cnf(c209,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c196,c208]) ).
cnf(c210,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c194,c210]) ).
cnf(c212,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c211]) ).
cnf(c213,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c171]) ).
cnf(c215,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c214,c208]) ).
cnf(c216,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c213,c215]) ).
cnf(c217,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c172,c216]) ).
cnf(c218,plain,
meet(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)),top) = join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)) = meet(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)),top),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
complement(join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))))) = meet(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)),top),
inference(substitution,[status(thm)],[c171]) ).
cnf(c221,plain,
meet(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)),top) = complement(join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))))),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)))) = complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))),
inference(substitution,[status(thm)],[c211]) ).
cnf(c223,plain,
complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))) = join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)))),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
meet(composition(X2,top),composition(complement(composition(X2,top)),X)) = meet(composition(complement(composition(X2,top)),X),composition(X2,top)),
inference(substitution,[status(thm)],[c167]) ).
cnf(c225,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c226,plain,
join(X,zero) = join(X,complement(top)),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c129]) ).
cnf(c228,plain,
top = join(complement(X),top),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
complement(top) = complement(join(complement(X),top)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
join(X,complement(top)) = join(X,complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c232,plain,
join(X,complement(join(complement(X),top))) = join(meet(X,top),complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
join(meet(X,top),complement(join(complement(X),top))) = X,
inference(substitution,[status(thm)],[c186]) ).
cnf(c234,plain,
join(X,complement(join(complement(X),top))) = X,
inference(transitivity,[status(thm)],[c232,c233]) ).
cnf(c235,plain,
join(X,complement(top)) = X,
inference(transitivity,[status(thm)],[c230,c234]) ).
cnf(c236,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c226,c235]) ).
cnf(c237,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),zero) = meet(composition(complement(composition(X2,top)),X),composition(X2,top)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
meet(composition(complement(composition(X2,top)),X),composition(X2,top)) = join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),zero),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c240,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c240,c236]) ).
cnf(c242,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c241]) ).
cnf(c243,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c245,plain,
composition(top,zero) = composition(top,complement(top)),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c130]) ).
cnf(c247,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
composition(top,complement(top)) = composition(join(top,one),complement(top)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c250,plain,
join(top,one) = join(converse(top),one),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
composition(join(top,one),complement(top)) = composition(join(converse(top),one),complement(top)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(join(converse(top),one),complement(top)),
inference(substitution,[status(thm)],[c147]) ).
cnf(c253,plain,
composition(join(converse(top),one),complement(top)) = join(complement(top),composition(converse(top),complement(top))),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c130]) ).
cnf(c255,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
composition(top,top) = composition(join(top,one),top),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
join(top,composition(X,top)) = composition(join(X,one),top),
inference(substitution,[status(thm)],[c147]) ).
cnf(c258,plain,
composition(join(X,one),top) = join(top,composition(X,top)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c259,plain,
join(top,composition(X,top)) = top,
inference(substitution,[status(thm)],[c130]) ).
cnf(c260,plain,
composition(join(X,one),top) = top,
inference(transitivity,[status(thm)],[c258,c259]) ).
cnf(c261,plain,
composition(join(top,one),top) = top,
inference(substitution,[status(thm)],[c260]) ).
cnf(c262,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c256,c261]) ).
cnf(c263,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c75]) ).
cnf(c268,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c267,c106]) ).
cnf(c269,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c266,c268]) ).
cnf(c270,plain,
composition(join(converse(top),one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c253,c269]) ).
cnf(c271,plain,
composition(join(top,one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c251,c270]) ).
cnf(c272,plain,
composition(top,complement(top)) = zero,
inference(transitivity,[status(thm)],[c248,c271]) ).
cnf(c273,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c245,c272]) ).
cnf(c274,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c141]) ).
cnf(c277,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c130]) ).
cnf(c279,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c278,c273]) ).
cnf(c280,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c277,c279]) ).
cnf(c281,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c275,c280]) ).
cnf(c282,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c243,c281]) ).
cnf(c283,plain,
composition(zero,zero) = zero,
inference(substitution,[status(thm)],[c282]) ).
cnf(c284,plain,
zero = composition(zero,zero),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),zero) = join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,zero)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c167]) ).
cnf(c287,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c288,plain,
join(zero,complement(zero)) = complement(zero),
inference(substitution,[status(thm)],[c211]) ).
cnf(c289,plain,
complement(zero) = join(zero,complement(zero)),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c291,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c289,c291]) ).
cnf(c293,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c84]) ).
cnf(c296,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c295,c106]) ).
cnf(c297,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c294,c296]) ).
cnf(c298,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c287,c297]) ).
cnf(c299,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c286,c298]) ).
cnf(c300,plain,
zero = meet(X,zero),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
composition(zero,zero) = composition(zero,meet(X,zero)),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,zero)) = join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,zero))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
meet(converse(zero),top) = converse(zero),
inference(substitution,[status(thm)],[c217]) ).
cnf(c304,plain,
converse(zero) = meet(converse(zero),top),
inference(symmetry,[status(thm)],[c303]) ).
cnf(c305,plain,
converse(converse(complement(converse(zero)))) = complement(converse(zero)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c306,plain,
complement(converse(zero)) = converse(converse(complement(converse(zero)))),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
join(zero,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(substitution,[status(thm)],[c241]) ).
cnf(c308,plain,
converse(complement(converse(zero))) = join(zero,converse(complement(converse(zero)))),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(substitution,[status(thm)],[c19]) ).
cnf(c310,plain,
join(zero,converse(complement(converse(zero)))) = top,
inference(transitivity,[status(thm)],[c309,c132]) ).
cnf(c311,plain,
converse(complement(converse(zero))) = top,
inference(transitivity,[status(thm)],[c308,c310]) ).
cnf(c312,plain,
converse(converse(complement(converse(zero)))) = converse(top),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
converse(converse(complement(converse(zero)))) = top,
inference(transitivity,[status(thm)],[c312,c132]) ).
cnf(c314,plain,
complement(converse(zero)) = top,
inference(transitivity,[status(thm)],[c306,c313]) ).
cnf(c315,plain,
top = complement(converse(zero)),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
meet(converse(zero),top) = meet(converse(zero),complement(converse(zero))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(substitution,[status(thm)],[c102]) ).
cnf(c318,plain,
meet(converse(zero),complement(converse(zero))) = zero,
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
meet(converse(zero),top) = zero,
inference(transitivity,[status(thm)],[c316,c318]) ).
cnf(c320,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c304,c319]) ).
cnf(c321,plain,
zero = converse(zero),
inference(symmetry,[status(thm)],[c320]) ).
cnf(c322,plain,
meet(X,zero) = meet(X,converse(zero)),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
composition(zero,meet(X,zero)) = composition(zero,meet(X,converse(zero))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,zero))) = join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,converse(zero)))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
converse(converse(composition(X,top))) = composition(X,top),
inference(substitution,[status(thm)],[c2]) ).
cnf(c326,plain,
composition(X,top) = converse(converse(composition(X,top))),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
composition(converse(complement(composition(X,top))),composition(X,top)) = composition(converse(complement(composition(X,top))),converse(converse(composition(X,top)))),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
converse(composition(converse(composition(X,top)),complement(composition(X,top)))) = composition(converse(complement(composition(X,top))),converse(converse(composition(X,top)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c329,plain,
composition(converse(complement(composition(X,top))),converse(converse(composition(X,top)))) = converse(composition(converse(composition(X,top)),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
join(zero,composition(converse(composition(X,top)),complement(composition(X,top)))) = composition(converse(composition(X,top)),complement(composition(X,top))),
inference(substitution,[status(thm)],[c241]) ).
cnf(c331,plain,
composition(converse(composition(X,top)),complement(composition(X,top))) = join(zero,composition(converse(composition(X,top)),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c333,plain,
join(zero,composition(converse(composition(X,top)),complement(composition(X,top)))) = join(complement(top),composition(converse(composition(X,top)),complement(composition(X,top)))),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
composition(X,composition(top,top)) = composition(composition(X,top),top),
inference(substitution,[status(thm)],[c59]) ).
cnf(c335,plain,
composition(composition(X,top),top) = composition(X,composition(top,top)),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
composition(X,composition(top,top)) = composition(X,top),
inference(congruence,[status(thm)],[c262]) ).
cnf(c337,plain,
composition(composition(X,top),top) = composition(X,top),
inference(transitivity,[status(thm)],[c335,c336]) ).
cnf(c338,plain,
composition(X,top) = composition(composition(X,top),top),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
complement(composition(X,top)) = complement(composition(composition(X,top),top)),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
composition(converse(composition(X,top)),complement(composition(X,top))) = composition(converse(composition(X,top)),complement(composition(composition(X,top),top))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
join(complement(top),composition(converse(composition(X,top)),complement(composition(X,top)))) = join(complement(top),composition(converse(composition(X,top)),complement(composition(composition(X,top),top)))),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
join(complement(top),composition(converse(composition(X,top)),complement(composition(composition(X,top),top)))) = complement(top),
inference(substitution,[status(thm)],[c75]) ).
cnf(c343,plain,
join(complement(top),composition(converse(composition(X,top)),complement(composition(composition(X,top),top)))) = zero,
inference(transitivity,[status(thm)],[c342,c106]) ).
cnf(c344,plain,
join(complement(top),composition(converse(composition(X,top)),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c341,c343]) ).
cnf(c345,plain,
join(zero,composition(converse(composition(X,top)),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c333,c344]) ).
cnf(c346,plain,
composition(converse(composition(X,top)),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c331,c345]) ).
cnf(c347,plain,
converse(composition(converse(composition(X,top)),complement(composition(X,top)))) = converse(zero),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
composition(converse(complement(composition(X,top))),converse(converse(composition(X,top)))) = converse(zero),
inference(transitivity,[status(thm)],[c329,c347]) ).
cnf(c349,plain,
composition(converse(complement(composition(X,top))),composition(X,top)) = converse(zero),
inference(transitivity,[status(thm)],[c327,c348]) ).
cnf(c350,plain,
converse(zero) = composition(converse(complement(composition(X,top))),composition(X,top)),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
meet(X,converse(zero)) = meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
composition(zero,meet(X,converse(zero))) = composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,converse(zero)))) = join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
composition(X2,composition(X,X3)) = composition(composition(X2,X),X3),
inference(substitution,[status(thm)],[c59]) ).
cnf(c355,plain,
composition(composition(X3,X2),X) = composition(X3,composition(X2,X)),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
meet(complement(composition(X3,top)),composition(composition(X3,X2),X)) = meet(complement(composition(X3,top)),composition(X3,composition(X2,X))),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
meet(complement(composition(X2,top)),composition(X2,X)) = meet(composition(X2,X),complement(composition(X2,top))),
inference(substitution,[status(thm)],[c167]) ).
cnf(c358,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = meet(composition(X2,X),complement(composition(X2,top))),
inference(substitution,[status(thm)],[c236]) ).
cnf(c359,plain,
meet(composition(X2,X),complement(composition(X2,top))) = join(meet(composition(X2,X),complement(composition(X2,top))),zero),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
meet(zero,X) = meet(X,zero),
inference(substitution,[status(thm)],[c167]) ).
cnf(c361,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c360,c299]) ).
cnf(c362,plain,
meet(zero,complement(composition(X,top))) = zero,
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
zero = meet(zero,complement(composition(X,top))),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(zero,complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
zero = composition(X,zero),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c366,plain,
meet(zero,complement(composition(X,top))) = meet(composition(X,zero),complement(composition(X,top))),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(zero,complement(composition(X2,top)))) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,zero),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
zero = meet(X,zero),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c369,plain,
composition(X2,zero) = composition(X2,meet(X,zero)),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
meet(composition(X2,zero),complement(composition(X2,top))) = meet(composition(X2,meet(X,zero)),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,zero),complement(composition(X2,top)))) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,zero)),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = composition(converse(X),complement(composition(X,top))),
inference(substitution,[status(thm)],[c241]) ).
cnf(c373,plain,
composition(converse(X),complement(composition(X,top))) = join(zero,composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c375,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = join(complement(top),composition(converse(X),complement(composition(X,top)))),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = complement(top),
inference(substitution,[status(thm)],[c75]) ).
cnf(c377,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c376,c106]) ).
cnf(c378,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c375,c377]) ).
cnf(c379,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c373,c378]) ).
cnf(c380,plain,
zero = composition(converse(X),complement(composition(X,top))),
inference(symmetry,[status(thm)],[c379]) ).
cnf(c381,plain,
meet(X,zero) = meet(X,composition(converse(X2),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
composition(X2,meet(X,zero)) = composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,zero)),complement(composition(X2,top)))) = join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top)))),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,axiom,
join(meet(composition(A2,B2),C2),meet(composition(A2,meet(B2,composition(converse(A2),C2))),C2)) = meet(composition(A2,meet(B2,composition(converse(A2),C2))),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1_15) ).
cnf(c386,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top)))) = meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))),
inference(substitution,[status(thm)],[c385]) ).
cnf(c387,plain,
meet(X,composition(converse(X2),complement(composition(X2,top)))) = meet(X,zero),
inference(congruence,[status(thm)],[c379]) ).
cnf(c388,plain,
composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))) = composition(X2,meet(X,zero)),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))) = meet(composition(X2,meet(X,zero)),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
composition(X2,meet(X,zero)) = composition(X2,zero),
inference(congruence,[status(thm)],[c299]) ).
cnf(c391,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = meet(composition(X2,zero),complement(composition(X2,top))),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
meet(composition(X,zero),complement(composition(X,top))) = meet(zero,complement(composition(X,top))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c393,plain,
meet(zero,complement(composition(X,top))) = zero,
inference(substitution,[status(thm)],[c361]) ).
cnf(c394,plain,
meet(composition(X,zero),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c392,c393]) ).
cnf(c395,plain,
meet(composition(X2,meet(X,zero)),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c391,c394]) ).
cnf(c396,plain,
meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c389,c395]) ).
cnf(c397,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,composition(converse(X2),complement(composition(X2,top))))),complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c386,c396]) ).
cnf(c398,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,meet(X,zero)),complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c384,c397]) ).
cnf(c399,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(composition(X2,zero),complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c371,c398]) ).
cnf(c400,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),meet(zero,complement(composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c367,c399]) ).
cnf(c401,plain,
join(meet(composition(X2,X),complement(composition(X2,top))),zero) = zero,
inference(transitivity,[status(thm)],[c364,c400]) ).
cnf(c402,plain,
meet(composition(X2,X),complement(composition(X2,top))) = zero,
inference(transitivity,[status(thm)],[c359,c401]) ).
cnf(c403,plain,
meet(complement(composition(X2,top)),composition(X2,X)) = zero,
inference(transitivity,[status(thm)],[c357,c402]) ).
cnf(c404,plain,
meet(complement(composition(X3,top)),composition(X3,composition(X2,X))) = zero,
inference(substitution,[status(thm)],[c403]) ).
cnf(c405,plain,
meet(complement(composition(X3,top)),composition(composition(X3,X2),X)) = zero,
inference(transitivity,[status(thm)],[c356,c404]) ).
cnf(c406,plain,
meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))) = zero,
inference(substitution,[status(thm)],[c405]) ).
cnf(c407,plain,
zero = meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))) = composition(meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))))) = join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,axiom,
join(meet(composition(A2,B2),C2),composition(meet(A2,composition(C2,converse(B2))),meet(B2,composition(converse(A2),C2)))) = composition(meet(A2,composition(C2,converse(B2))),meet(B2,composition(converse(A2),C2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law_14) ).
cnf(c411,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))))) = composition(meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))),
inference(substitution,[status(thm)],[c410]) ).
cnf(c412,plain,
meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))) = zero,
inference(substitution,[status(thm)],[c405]) ).
cnf(c413,plain,
composition(meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))) = composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))) = meet(X,converse(zero)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c415,plain,
composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))) = composition(zero,meet(X,converse(zero))),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
meet(X,converse(zero)) = meet(X,zero),
inference(congruence,[status(thm)],[c320]) ).
cnf(c417,plain,
composition(zero,meet(X,converse(zero))) = composition(zero,meet(X,zero)),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
composition(zero,meet(X,zero)) = composition(zero,zero),
inference(congruence,[status(thm)],[c299]) ).
cnf(c419,plain,
composition(zero,zero) = zero,
inference(substitution,[status(thm)],[c282]) ).
cnf(c420,plain,
composition(zero,meet(X,zero)) = zero,
inference(transitivity,[status(thm)],[c418,c419]) ).
cnf(c421,plain,
composition(zero,meet(X,converse(zero))) = zero,
inference(transitivity,[status(thm)],[c417,c420]) ).
cnf(c422,plain,
composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c415,c421]) ).
cnf(c423,plain,
composition(meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top)))) = zero,
inference(transitivity,[status(thm)],[c413,c422]) ).
cnf(c424,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(meet(complement(composition(X2,top)),composition(composition(X2,top),converse(X))),meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))))) = zero,
inference(transitivity,[status(thm)],[c411,c423]) ).
cnf(c425,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,composition(converse(complement(composition(X2,top))),composition(X2,top))))) = zero,
inference(transitivity,[status(thm)],[c409,c424]) ).
cnf(c426,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,converse(zero)))) = zero,
inference(transitivity,[status(thm)],[c353,c425]) ).
cnf(c427,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,meet(X,zero))) = zero,
inference(transitivity,[status(thm)],[c324,c426]) ).
cnf(c428,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),composition(zero,zero)) = zero,
inference(transitivity,[status(thm)],[c302,c427]) ).
cnf(c429,plain,
join(meet(composition(complement(composition(X2,top)),X),composition(X2,top)),zero) = zero,
inference(transitivity,[status(thm)],[c285,c428]) ).
cnf(c430,plain,
meet(composition(complement(composition(X2,top)),X),composition(X2,top)) = zero,
inference(transitivity,[status(thm)],[c238,c429]) ).
cnf(c431,plain,
meet(composition(X2,top),composition(complement(composition(X2,top)),X)) = zero,
inference(transitivity,[status(thm)],[c224,c430]) ).
cnf(c432,plain,
zero = meet(composition(X2,top),composition(complement(composition(X2,top)),X)),
inference(symmetry,[status(thm)],[c431]) ).
cnf(c433,plain,
join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)))) = join(meet(composition(X2,top),composition(complement(composition(X2,top)),X)),complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
join(meet(composition(X2,top),composition(complement(composition(X2,top)),X)),complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)))) = composition(X2,top),
inference(substitution,[status(thm)],[c186]) ).
cnf(c435,plain,
join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)))) = composition(X2,top),
inference(transitivity,[status(thm)],[c433,c434]) ).
cnf(c436,plain,
complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))) = composition(X2,top),
inference(transitivity,[status(thm)],[c223,c435]) ).
cnf(c437,plain,
join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)))) = join(zero,composition(X2,top)),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
complement(join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))))) = complement(join(zero,composition(X2,top))),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
join(zero,composition(X,top)) = composition(X,top),
inference(substitution,[status(thm)],[c241]) ).
cnf(c440,plain,
complement(join(zero,composition(X,top))) = complement(composition(X,top)),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
complement(join(zero,complement(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))))) = complement(composition(X2,top)),
inference(transitivity,[status(thm)],[c438,c440]) ).
cnf(c442,plain,
meet(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)),top) = complement(composition(X2,top)),
inference(transitivity,[status(thm)],[c221,c441]) ).
cnf(c443,plain,
join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X)) = complement(composition(X2,top)),
inference(transitivity,[status(thm)],[c219,c442]) ).
cnf(c444,plain,
converse(join(complement(composition(X2,top)),composition(complement(composition(X2,top)),X))) = converse(complement(composition(X2,top))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
join(converse(complement(composition(X2,top))),converse(composition(complement(composition(X2,top)),X))) = converse(complement(composition(X2,top))),
inference(transitivity,[status(thm)],[c154,c444]) ).
cnf(c446,plain,
join(converse(complement(composition(X,top))),converse(composition(complement(composition(X,top)),top))) = converse(complement(composition(X,top))),
inference(substitution,[status(thm)],[c445]) ).
cnf(c447,plain,
join(converse(complement(composition(X,top))),composition(top,converse(complement(composition(X,top))))) = converse(complement(composition(X,top))),
inference(transitivity,[status(thm)],[c152,c446]) ).
cnf(c448,plain,
composition(join(top,one),converse(complement(composition(X,top)))) = converse(complement(composition(X,top))),
inference(transitivity,[status(thm)],[c149,c447]) ).
cnf(c449,plain,
composition(top,converse(complement(composition(X,top)))) = converse(complement(composition(X,top))),
inference(transitivity,[status(thm)],[c138,c448]) ).
cnf(c450,plain,
converse(composition(complement(composition(X,top)),top)) = converse(complement(composition(X,top))),
inference(transitivity,[status(thm)],[c135,c449]) ).
cnf(c451,plain,
converse(converse(composition(complement(composition(X,top)),top))) = converse(converse(complement(composition(X,top)))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
converse(converse(complement(composition(X,top)))) = complement(composition(X,top)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c453,plain,
converse(converse(composition(complement(composition(X,top)),top))) = complement(composition(X,top)),
inference(transitivity,[status(thm)],[c451,c452]) ).
cnf(c454,plain,
composition(complement(composition(X,top)),top) = complement(composition(X,top)),
inference(transitivity,[status(thm)],[c4,c453]) ).
cnf(c455,plain,
composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)),
inference(substitution,[status(thm)],[c454]) ).
cnf(c456,plain,
complement(composition(sk1,top)) = composition(complement(composition(sk1,top)),top),
inference(symmetry,[status(thm)],[c455]) ).
cnf(c457,plain,
$false,
inference(resolution,[status(thm)],[c1,c456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:57:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/0.63 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.20/0.63
% 1.20/0.63 % SZS status Unsatisfiable
% 1.20/0.63
% 1.73/0.66 % SZS output start CNFRefutation
% See solution above
% 2.41/0.88
% 2.41/0.88 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------