TSTP Solution File: REL023-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL023-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:43:52 EDT 2022
% Result : Unsatisfiable 5.23s 5.44s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 122
% Number of leaves : 238
% Syntax : Number of clauses : 992 ( 508 unt; 0 nHn; 535 RR)
% Number of literals : 1689 (1688 equ; 700 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 1181 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maddux1_join_commutativity_1,axiom,
join(A,B) = join(B,A) ).
cnf(maddux2_join_associativity_2,axiom,
join(A,join(B,C)) = join(join(A,B),C) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(A,B) = complement(join(complement(A),complement(B))) ).
cnf(composition_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_14,negated_conjecture,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_4,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(meet(sk1,converse(sk2)),sk1) = join(sk1,meet(sk1,converse(sk2))),
inference(subst,[],[refute_0_4:[bind(A,$fot(sk1)),bind(B,$fot(meet(sk1,converse(sk2))))]]) ).
cnf(refute_0_6,plain,
composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),
introduced(tautology,[refl,[$fot(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)))]]) ).
cnf(refute_0_7,plain,
( composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) != composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))
| join(meet(sk1,converse(sk2)),sk1) != join(sk1,meet(sk1,converse(sk2)))
| composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))) ),[1,0],$fot(join(sk1,meet(sk1,converse(sk2))))]]) ).
cnf(refute_0_8,plain,
( join(meet(sk1,converse(sk2)),sk1) != join(sk1,meet(sk1,converse(sk2)))
| composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(meet(sk1,converse(sk2)),sk1),join(sk1,meet(sk1,converse(sk2)))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( composition(join(A,B),C) != join(composition(A,C),composition(B,C))
| join(composition(A,C),composition(B,C)) = composition(join(A,B),C) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(A,B),C))),bind(Y,$fot(join(composition(A,C),composition(B,C))))]]) ).
cnf(refute_0_11,plain,
join(composition(A,C),composition(B,C)) = composition(join(A,B),C),
inference(resolve,[$cnf( $equal(composition(join(A,B),C),join(composition(A,C),composition(B,C))) )],[composition_distributivity_7,refute_0_10]) ).
cnf(refute_0_12,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),
inference(subst,[],[refute_0_11:[bind(A,$fot(meet(sk1,converse(sk2)))),bind(B,$fot(sk1)),bind(C,$fot(meet(sk2,sk3)))]]) ).
cnf(refute_0_13,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))))),bind(Y,$fot(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)))),bind(Z,$fot(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))))]]) ).
cnf(refute_0_16,plain,
( composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(sk1,meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) ),[1],$fot(composition(sk1,meet(sk2,sk3)))]]) ).
cnf(refute_0_19,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(sk1,meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(sk1,meet(sk2,sk3))) )],[refute_0_19,goals_14]) ).
cnf(refute_0_21,plain,
join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)) = join(join(meet(X_24,B),meet(X_24,complement(B))),X_78),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(meet(X_24,B))),bind(B,$fot(meet(X_24,complement(B)))),bind(C,$fot(X_78))]]) ).
cnf(refute_0_22,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_23,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[0],$fot(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))))]]) ).
cnf(refute_0_24,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_24]) ).
cnf(refute_0_26,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_27,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_28,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_27]) ).
cnf(refute_0_29,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_30,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[1,1],$fot(meet(A,B))]]) ).
cnf(refute_0_31,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))),bind(Y,$fot(join(complement(join(complement(A),B)),meet(A,B)))),bind(Z,$fot(join(meet(A,B),complement(join(complement(A),B)))))]]) ).
cnf(refute_0_34,plain,
( join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_26,refute_0_34]) ).
cnf(refute_0_36,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(meet(A,B),complement(join(complement(A),B)))) ),[0],$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_37,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_25,refute_0_37]) ).
cnf(refute_0_39,plain,
X_24 = join(meet(X_24,complement(B)),complement(join(complement(X_24),complement(B)))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_24)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_40,plain,
meet(X_24,B) = complement(join(complement(X_24),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_41,plain,
( meet(X_24,B) != complement(join(complement(X_24),complement(B)))
| complement(join(complement(X_24),complement(B))) = meet(X_24,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_24,B))),bind(Y,$fot(complement(join(complement(X_24),complement(B)))))]]) ).
cnf(refute_0_42,plain,
complement(join(complement(X_24),complement(B))) = meet(X_24,B),
inference(resolve,[$cnf( $equal(meet(X_24,B),complement(join(complement(X_24),complement(B)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( X_24 != join(meet(X_24,complement(B)),complement(join(complement(X_24),complement(B))))
| complement(join(complement(X_24),complement(B))) != meet(X_24,B)
| X_24 = join(meet(X_24,complement(B)),meet(X_24,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_24,join(meet(X_24,complement(B)),complement(join(complement(X_24),complement(B))))) ),[1,1],$fot(meet(X_24,B))]]) ).
cnf(refute_0_44,plain,
( X_24 != join(meet(X_24,complement(B)),complement(join(complement(X_24),complement(B))))
| X_24 = join(meet(X_24,complement(B)),meet(X_24,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_24),complement(B))),meet(X_24,B)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
X_24 = join(meet(X_24,complement(B)),meet(X_24,B)),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,complement(B)),complement(join(complement(X_24),complement(B))))) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
join(meet(X_24,complement(B)),meet(X_24,B)) = join(meet(X_24,B),meet(X_24,complement(B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(X_24,B))),bind(B,$fot(meet(X_24,complement(B))))]]) ).
cnf(refute_0_47,plain,
( X_24 != join(meet(X_24,complement(B)),meet(X_24,B))
| join(meet(X_24,complement(B)),meet(X_24,B)) != join(meet(X_24,B),meet(X_24,complement(B)))
| X_24 = join(meet(X_24,B),meet(X_24,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(meet(X_24,B),meet(X_24,complement(B)))) ),[0],$fot(join(meet(X_24,complement(B)),meet(X_24,B)))]]) ).
cnf(refute_0_48,plain,
( X_24 != join(meet(X_24,complement(B)),meet(X_24,B))
| X_24 = join(meet(X_24,B),meet(X_24,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,complement(B)),meet(X_24,B)),join(meet(X_24,B),meet(X_24,complement(B)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
X_24 = join(meet(X_24,B),meet(X_24,complement(B))),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,complement(B)),meet(X_24,B))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( X_24 != join(meet(X_24,B),meet(X_24,complement(B)))
| join(meet(X_24,B),meet(X_24,complement(B))) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(join(meet(X_24,B),meet(X_24,complement(B)))))]]) ).
cnf(refute_0_51,plain,
join(meet(X_24,B),meet(X_24,complement(B))) = X_24,
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,B),meet(X_24,complement(B)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)) != join(join(meet(X_24,B),meet(X_24,complement(B))),X_78)
| join(meet(X_24,B),meet(X_24,complement(B))) != X_24
| join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)) = join(X_24,X_78) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)),join(join(meet(X_24,B),meet(X_24,complement(B))),X_78)) ),[1,0],$fot(X_24)]]) ).
cnf(refute_0_53,plain,
( join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)) != join(join(meet(X_24,B),meet(X_24,complement(B))),X_78)
| join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)) = join(X_24,X_78) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,B),meet(X_24,complement(B))),X_24) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)) = join(X_24,X_78),
inference(resolve,[$cnf( $equal(join(meet(X_24,B),join(meet(X_24,complement(B)),X_78)),join(join(meet(X_24,B),meet(X_24,complement(B))),X_78)) )],[refute_0_21,refute_0_53]) ).
cnf(refute_0_55,plain,
join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))) = join(X_361,meet(X_361,complement(complement(X_360)))),
inference(subst,[],[refute_0_54:[bind(B,$fot(X_360)),bind(X_24,$fot(X_361)),bind(X_78,$fot(meet(X_361,complement(complement(X_360)))))]]) ).
cnf(refute_0_56,plain,
X_361 = join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360)))),
inference(subst,[],[refute_0_49:[bind(B,$fot(complement(X_360))),bind(X_24,$fot(X_361))]]) ).
cnf(refute_0_57,plain,
( X_361 != join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))
| join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360)))) = X_361 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_361)),bind(Y,$fot(join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))))]]) ).
cnf(refute_0_58,plain,
join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360)))) = X_361,
inference(resolve,[$cnf( $equal(X_361,join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))) != join(X_361,meet(X_361,complement(complement(X_360))))
| join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360)))) != X_361
| join(meet(X_361,X_360),X_361) = join(X_361,meet(X_361,complement(complement(X_360)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))),join(X_361,meet(X_361,complement(complement(X_360))))) ),[0,1],$fot(X_361)]]) ).
cnf(refute_0_60,plain,
( join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))) != join(X_361,meet(X_361,complement(complement(X_360))))
| join(meet(X_361,X_360),X_361) = join(X_361,meet(X_361,complement(complement(X_360)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360)))),X_361) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
join(meet(X_361,X_360),X_361) = join(X_361,meet(X_361,complement(complement(X_360)))),
inference(resolve,[$cnf( $equal(join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(complement(X_360))))),join(X_361,meet(X_361,complement(complement(X_360))))) )],[refute_0_55,refute_0_60]) ).
cnf(refute_0_62,plain,
join(meet(X_361,X_360),X_361) = join(X_361,meet(X_361,X_360)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_361)),bind(B,$fot(meet(X_361,X_360)))]]) ).
cnf(refute_0_63,plain,
( join(meet(X_361,X_360),X_361) != join(X_361,meet(X_361,X_360))
| join(meet(X_361,X_360),X_361) != join(X_361,meet(X_361,complement(complement(X_360))))
| join(X_361,meet(X_361,X_360)) = join(X_361,meet(X_361,complement(complement(X_360)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_361,X_360),X_361),join(X_361,meet(X_361,complement(complement(X_360))))) ),[0],$fot(join(X_361,meet(X_361,X_360)))]]) ).
cnf(refute_0_64,plain,
( join(meet(X_361,X_360),X_361) != join(X_361,meet(X_361,complement(complement(X_360))))
| join(X_361,meet(X_361,X_360)) = join(X_361,meet(X_361,complement(complement(X_360)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_361,X_360),X_361),join(X_361,meet(X_361,X_360))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360)))) = join(X_361,meet(X_361,complement(X_360))),
inference(subst,[],[refute_0_54:[bind(B,$fot(X_360)),bind(X_24,$fot(X_361)),bind(X_78,$fot(meet(X_361,complement(X_360))))]]) ).
cnf(refute_0_66,plain,
X_24 = join(meet(X_24,X_25),complement(join(complement(X_24),X_25))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_24)),bind(B,$fot(X_25))]]) ).
cnf(refute_0_67,plain,
meet(X_6,X_7) = complement(join(complement(X_6),complement(X_7))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_68,plain,
join(complement(X_7),complement(X_6)) = join(complement(X_6),complement(X_7)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_7))),bind(B,$fot(complement(X_6)))]]) ).
cnf(refute_0_69,plain,
( join(complement(X_7),complement(X_6)) != join(complement(X_6),complement(X_7))
| join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_7),complement(X_6)))),bind(Y,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_70,plain,
join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)),
inference(resolve,[$cnf( $equal(join(complement(X_7),complement(X_6)),join(complement(X_6),complement(X_7))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( join(complement(X_6),complement(X_7)) != join(complement(X_7),complement(X_6))
| meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) ),[1,0],$fot(join(complement(X_7),complement(X_6)))]]) ).
cnf(refute_0_72,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))) ),
inference(resolve,[$cnf( $equal(join(complement(X_6),complement(X_7)),join(complement(X_7),complement(X_6))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
complement(join(complement(X_7),complement(X_6))) = meet(X_7,X_6),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_7)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_75,plain,
( complement(join(complement(X_7),complement(X_6))) != meet(X_7,X_6)
| meet(X_6,X_7) != complement(join(complement(X_7),complement(X_6)))
| meet(X_6,X_7) = meet(X_7,X_6) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_7),complement(X_6)))) ),[1],$fot(meet(X_7,X_6))]]) ).
cnf(refute_0_76,plain,
( meet(X_6,X_7) != complement(join(complement(X_7),complement(X_6)))
| meet(X_6,X_7) = meet(X_7,X_6) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_7),complement(X_6))),meet(X_7,X_6)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
meet(X_6,X_7) = meet(X_7,X_6),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_7),complement(X_6)))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
meet(X_25,X_24) = meet(X_24,X_25),
inference(subst,[],[refute_0_77:[bind(X_6,$fot(X_25)),bind(X_7,$fot(X_24))]]) ).
cnf(refute_0_79,plain,
( meet(X_25,X_24) != meet(X_24,X_25)
| meet(X_24,X_25) = meet(X_25,X_24) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_25,X_24))),bind(Y,$fot(meet(X_24,X_25)))]]) ).
cnf(refute_0_80,plain,
meet(X_24,X_25) = meet(X_25,X_24),
inference(resolve,[$cnf( $equal(meet(X_25,X_24),meet(X_24,X_25)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( X_24 != join(meet(X_24,X_25),complement(join(complement(X_24),X_25)))
| meet(X_24,X_25) != meet(X_25,X_24)
| X_24 = join(meet(X_25,X_24),complement(join(complement(X_24),X_25))) ),
introduced(tautology,[equality,[$cnf( $equal(X_24,join(meet(X_24,X_25),complement(join(complement(X_24),X_25)))) ),[1,0],$fot(meet(X_25,X_24))]]) ).
cnf(refute_0_82,plain,
( X_24 != join(meet(X_24,X_25),complement(join(complement(X_24),X_25)))
| X_24 = join(meet(X_25,X_24),complement(join(complement(X_24),X_25))) ),
inference(resolve,[$cnf( $equal(meet(X_24,X_25),meet(X_25,X_24)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
X_24 = join(meet(X_25,X_24),complement(join(complement(X_24),X_25))),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,X_25),complement(join(complement(X_24),X_25)))) )],[refute_0_66,refute_0_82]) ).
cnf(refute_0_84,plain,
join(X_119,X_119) = join(meet(complement(X_119),join(X_119,X_119)),complement(join(complement(join(X_119,X_119)),complement(X_119)))),
inference(subst,[],[refute_0_83:[bind(X_24,$fot(join(X_119,X_119))),bind(X_25,$fot(complement(X_119)))]]) ).
cnf(refute_0_85,plain,
zero = meet(join(X_118,X_118),complement(join(X_118,X_118))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(X_118,X_118)))]]) ).
cnf(refute_0_86,plain,
complement(X_52) = join(meet(X_52,complement(X_52)),complement(join(complement(complement(X_52)),X_52))),
inference(subst,[],[refute_0_83:[bind(X_24,$fot(complement(X_52))),bind(X_25,$fot(X_52))]]) ).
cnf(refute_0_87,plain,
zero = meet(X_52,complement(X_52)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_52))]]) ).
cnf(refute_0_88,plain,
( zero != meet(X_52,complement(X_52))
| meet(X_52,complement(X_52)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_52,complement(X_52))))]]) ).
cnf(refute_0_89,plain,
meet(X_52,complement(X_52)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_52,complement(X_52))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( complement(X_52) != join(meet(X_52,complement(X_52)),complement(join(complement(complement(X_52)),X_52)))
| meet(X_52,complement(X_52)) != zero
| complement(X_52) = join(zero,complement(join(complement(complement(X_52)),X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_52),join(meet(X_52,complement(X_52)),complement(join(complement(complement(X_52)),X_52)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_91,plain,
( complement(X_52) != join(meet(X_52,complement(X_52)),complement(join(complement(complement(X_52)),X_52)))
| complement(X_52) = join(zero,complement(join(complement(complement(X_52)),X_52))) ),
inference(resolve,[$cnf( $equal(meet(X_52,complement(X_52)),zero) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
complement(X_52) = join(zero,complement(join(complement(complement(X_52)),X_52))),
inference(resolve,[$cnf( $equal(complement(X_52),join(meet(X_52,complement(X_52)),complement(join(complement(complement(X_52)),X_52)))) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
join(complement(complement(X_52)),X_52) = join(X_52,complement(complement(X_52))),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_52)),bind(B,$fot(complement(complement(X_52))))]]) ).
cnf(refute_0_94,plain,
complement(join(complement(complement(X_52)),X_52)) = complement(join(complement(complement(X_52)),X_52)),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(X_52)),X_52)))]]) ).
cnf(refute_0_95,plain,
( complement(join(complement(complement(X_52)),X_52)) != complement(join(complement(complement(X_52)),X_52))
| join(complement(complement(X_52)),X_52) != join(X_52,complement(complement(X_52)))
| complement(join(complement(complement(X_52)),X_52)) = complement(join(X_52,complement(complement(X_52)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(X_52)),X_52)),complement(join(complement(complement(X_52)),X_52))) ),[1,0],$fot(join(X_52,complement(complement(X_52))))]]) ).
cnf(refute_0_96,plain,
( join(complement(complement(X_52)),X_52) != join(X_52,complement(complement(X_52)))
| complement(join(complement(complement(X_52)),X_52)) = complement(join(X_52,complement(complement(X_52)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_52)),X_52)),complement(join(complement(complement(X_52)),X_52))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
complement(join(complement(complement(X_52)),X_52)) = complement(join(X_52,complement(complement(X_52)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_52)),X_52),join(X_52,complement(complement(X_52)))) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
join(zero,complement(join(complement(complement(X_52)),X_52))) = join(zero,complement(join(complement(complement(X_52)),X_52))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(complement(X_52)),X_52))))]]) ).
cnf(refute_0_99,plain,
( complement(join(complement(complement(X_52)),X_52)) != complement(join(X_52,complement(complement(X_52))))
| join(zero,complement(join(complement(complement(X_52)),X_52))) != join(zero,complement(join(complement(complement(X_52)),X_52)))
| join(zero,complement(join(complement(complement(X_52)),X_52))) = join(zero,complement(join(X_52,complement(complement(X_52))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(complement(X_52)),X_52))),join(zero,complement(join(complement(complement(X_52)),X_52)))) ),[1,1],$fot(complement(join(X_52,complement(complement(X_52)))))]]) ).
cnf(refute_0_100,plain,
( complement(join(complement(complement(X_52)),X_52)) != complement(join(X_52,complement(complement(X_52))))
| join(zero,complement(join(complement(complement(X_52)),X_52))) = join(zero,complement(join(X_52,complement(complement(X_52))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_52)),X_52))),join(zero,complement(join(complement(complement(X_52)),X_52)))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
join(zero,complement(join(complement(complement(X_52)),X_52))) = join(zero,complement(join(X_52,complement(complement(X_52))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_52)),X_52)),complement(join(X_52,complement(complement(X_52))))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
( complement(X_52) != join(zero,complement(join(complement(complement(X_52)),X_52)))
| join(zero,complement(join(complement(complement(X_52)),X_52))) != join(zero,complement(join(X_52,complement(complement(X_52)))))
| complement(X_52) = join(zero,complement(join(X_52,complement(complement(X_52))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_52),join(zero,complement(join(X_52,complement(complement(X_52)))))) ),[0],$fot(join(zero,complement(join(complement(complement(X_52)),X_52))))]]) ).
cnf(refute_0_103,plain,
( complement(X_52) != join(zero,complement(join(complement(complement(X_52)),X_52)))
| complement(X_52) = join(zero,complement(join(X_52,complement(complement(X_52))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_52)),X_52))),join(zero,complement(join(X_52,complement(complement(X_52)))))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
complement(X_52) = join(zero,complement(join(X_52,complement(complement(X_52))))),
inference(resolve,[$cnf( $equal(complement(X_52),join(zero,complement(join(complement(complement(X_52)),X_52)))) )],[refute_0_92,refute_0_103]) ).
cnf(refute_0_105,plain,
X_24 = join(meet(X_24,complement(complement(X_24))),complement(join(complement(X_24),complement(complement(X_24))))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_24)),bind(B,$fot(complement(complement(X_24))))]]) ).
cnf(refute_0_106,plain,
top = join(complement(X_24),complement(complement(X_24))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_24)))]]) ).
cnf(refute_0_107,plain,
( top != join(complement(X_24),complement(complement(X_24)))
| join(complement(X_24),complement(complement(X_24))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_24),complement(complement(X_24)))))]]) ).
cnf(refute_0_108,plain,
join(complement(X_24),complement(complement(X_24))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_24),complement(complement(X_24)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( X_24 != join(meet(X_24,complement(complement(X_24))),complement(join(complement(X_24),complement(complement(X_24)))))
| join(complement(X_24),complement(complement(X_24))) != top
| X_24 = join(meet(X_24,complement(complement(X_24))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_24,join(meet(X_24,complement(complement(X_24))),complement(join(complement(X_24),complement(complement(X_24)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_110,plain,
( X_24 != join(meet(X_24,complement(complement(X_24))),complement(join(complement(X_24),complement(complement(X_24)))))
| X_24 = join(meet(X_24,complement(complement(X_24))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),complement(complement(X_24))),top) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
X_24 = join(meet(X_24,complement(complement(X_24))),complement(top)),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,complement(complement(X_24))),complement(join(complement(X_24),complement(complement(X_24)))))) )],[refute_0_105,refute_0_110]) ).
cnf(refute_0_112,plain,
zero = meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_113,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(complement(join(complement(X_6),complement(X_7)))))]]) ).
cnf(refute_0_114,plain,
complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_67,refute_0_113]) ).
cnf(refute_0_115,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) ),[1,1],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_116,plain,
( zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_112,refute_0_116]) ).
cnf(refute_0_118,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_119,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_118]) ).
cnf(refute_0_120,plain,
join(meet(X_6,X_7),complement(meet(X_6,X_7))) = top,
inference(subst,[],[refute_0_119:[bind(A,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_121,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))]]) ).
cnf(refute_0_122,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_123,plain,
( join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_6,X_7),complement(meet(X_6,X_7))),top) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
meet(join(complement(X_6),complement(X_7)),B) = complement(join(complement(join(complement(X_6),complement(X_7))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_126,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| meet(join(complement(X_6),complement(X_7)),B) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))
| meet(join(complement(X_6),complement(X_7)),B) = complement(join(meet(X_6,X_7),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))) ),[1,0,0],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_127,plain,
( meet(join(complement(X_6),complement(X_7)),B) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))
| meet(join(complement(X_6),complement(X_7)),B) = complement(join(meet(X_6,X_7),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_114,refute_0_126]) ).
cnf(refute_0_128,plain,
meet(join(complement(X_6),complement(X_7)),B) = complement(join(meet(X_6,X_7),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))) )],[refute_0_125,refute_0_127]) ).
cnf(refute_0_129,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
inference(subst,[],[refute_0_128:[bind(B,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_130,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)))),bind(Y,$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_131,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(top)) )],[refute_0_124,refute_0_131]) ).
cnf(refute_0_133,plain,
( meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(top)
| zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_134,plain,
( zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(top)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_117,refute_0_134]) ).
cnf(refute_0_136,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_137,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
join(complement(top),meet(X_24,complement(complement(X_24)))) = join(complement(top),meet(X_24,complement(complement(X_24)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_24,complement(complement(X_24)))))]]) ).
cnf(refute_0_139,plain,
( complement(top) != zero
| join(complement(top),meet(X_24,complement(complement(X_24)))) != join(complement(top),meet(X_24,complement(complement(X_24))))
| join(complement(top),meet(X_24,complement(complement(X_24)))) = join(zero,meet(X_24,complement(complement(X_24)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_24,complement(complement(X_24)))),join(complement(top),meet(X_24,complement(complement(X_24))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_140,plain,
( complement(top) != zero
| join(complement(top),meet(X_24,complement(complement(X_24)))) = join(zero,meet(X_24,complement(complement(X_24)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_24,complement(complement(X_24)))),join(complement(top),meet(X_24,complement(complement(X_24))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
join(complement(top),meet(X_24,complement(complement(X_24)))) = join(zero,meet(X_24,complement(complement(X_24)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
join(meet(X_24,complement(complement(X_24))),complement(top)) = join(complement(top),meet(X_24,complement(complement(X_24)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_24,complement(complement(X_24)))))]]) ).
cnf(refute_0_143,plain,
( join(complement(top),meet(X_24,complement(complement(X_24)))) != join(zero,meet(X_24,complement(complement(X_24))))
| join(meet(X_24,complement(complement(X_24))),complement(top)) != join(complement(top),meet(X_24,complement(complement(X_24))))
| join(meet(X_24,complement(complement(X_24))),complement(top)) = join(zero,meet(X_24,complement(complement(X_24)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(X_24,complement(complement(X_24))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_24,complement(complement(X_24)))))),bind(Z,$fot(join(zero,meet(X_24,complement(complement(X_24))))))]]) ).
cnf(refute_0_144,plain,
( join(complement(top),meet(X_24,complement(complement(X_24)))) != join(zero,meet(X_24,complement(complement(X_24))))
| join(meet(X_24,complement(complement(X_24))),complement(top)) = join(zero,meet(X_24,complement(complement(X_24)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,complement(complement(X_24))),complement(top)),join(complement(top),meet(X_24,complement(complement(X_24))))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
join(meet(X_24,complement(complement(X_24))),complement(top)) = join(zero,meet(X_24,complement(complement(X_24)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_24,complement(complement(X_24)))),join(zero,meet(X_24,complement(complement(X_24))))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( X_24 != join(meet(X_24,complement(complement(X_24))),complement(top))
| join(meet(X_24,complement(complement(X_24))),complement(top)) != join(zero,meet(X_24,complement(complement(X_24))))
| X_24 = join(zero,meet(X_24,complement(complement(X_24)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(zero,meet(X_24,complement(complement(X_24))))) ),[0],$fot(join(meet(X_24,complement(complement(X_24))),complement(top)))]]) ).
cnf(refute_0_147,plain,
( X_24 != join(meet(X_24,complement(complement(X_24))),complement(top))
| X_24 = join(zero,meet(X_24,complement(complement(X_24)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,complement(complement(X_24))),complement(top)),join(zero,meet(X_24,complement(complement(X_24))))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
X_24 = join(zero,meet(X_24,complement(complement(X_24)))),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,complement(complement(X_24))),complement(top))) )],[refute_0_111,refute_0_147]) ).
cnf(refute_0_149,plain,
join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B)))))),
inference(subst,[],[refute_0_148:[bind(X_24,$fot(join(zero,complement(B))))]]) ).
cnf(refute_0_150,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_151,plain,
( complement(top) != zero
| meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_152,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_151]) ).
cnf(refute_0_153,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_150,refute_0_152]) ).
cnf(refute_0_154,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_155,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( complement(join(zero,complement(B))) != meet(top,B)
| join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))
| join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))) ),[1,1,1,0],$fot(meet(top,B))]]) ).
cnf(refute_0_157,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))
| join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),meet(top,B)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))) )],[refute_0_149,refute_0_157]) ).
cnf(refute_0_159,plain,
( meet(X_6,X_7) != meet(X_7,X_6)
| meet(X_7,X_6) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(meet(X_7,X_6)))]]) ).
cnf(refute_0_160,plain,
meet(X_7,X_6) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),meet(X_7,X_6)) )],[refute_0_77,refute_0_159]) ).
cnf(refute_0_161,plain,
meet(join(zero,complement(B)),complement(meet(top,B))) = meet(complement(meet(top,B)),join(zero,complement(B))),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(complement(meet(top,B)))),bind(X_7,$fot(join(zero,complement(B))))]]) ).
cnf(refute_0_162,plain,
join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))))]]) ).
cnf(refute_0_163,plain,
( join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| meet(join(zero,complement(B)),complement(meet(top,B))) != meet(complement(meet(top,B)),join(zero,complement(B)))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) ),[1,1],$fot(meet(complement(meet(top,B)),join(zero,complement(B))))]]) ).
cnf(refute_0_164,plain,
( meet(join(zero,complement(B)),complement(meet(top,B))) != meet(complement(meet(top,B)),join(zero,complement(B)))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),complement(meet(top,B))),meet(complement(meet(top,B)),join(zero,complement(B)))) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(B)),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) ),[0],$fot(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))))]]) ).
cnf(refute_0_167,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) )],[refute_0_158,refute_0_167]) ).
cnf(refute_0_169,plain,
X_24 = join(meet(X_24,complement(X_24)),complement(join(complement(X_24),complement(X_24)))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_24)),bind(B,$fot(complement(X_24)))]]) ).
cnf(refute_0_170,plain,
zero = meet(X_24,complement(X_24)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_171,plain,
( zero != meet(X_24,complement(X_24))
| meet(X_24,complement(X_24)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_24,complement(X_24))))]]) ).
cnf(refute_0_172,plain,
meet(X_24,complement(X_24)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_24,complement(X_24))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( X_24 != join(meet(X_24,complement(X_24)),complement(join(complement(X_24),complement(X_24))))
| meet(X_24,complement(X_24)) != zero
| X_24 = join(zero,complement(join(complement(X_24),complement(X_24)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_24,join(meet(X_24,complement(X_24)),complement(join(complement(X_24),complement(X_24))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_174,plain,
( X_24 != join(meet(X_24,complement(X_24)),complement(join(complement(X_24),complement(X_24))))
| X_24 = join(zero,complement(join(complement(X_24),complement(X_24)))) ),
inference(resolve,[$cnf( $equal(meet(X_24,complement(X_24)),zero) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
X_24 = join(zero,complement(join(complement(X_24),complement(X_24)))),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,complement(X_24)),complement(join(complement(X_24),complement(X_24))))) )],[refute_0_169,refute_0_174]) ).
cnf(refute_0_176,plain,
complement(join(complement(X_24),complement(X_24))) = meet(X_24,X_24),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_24)),bind(B,$fot(X_24))]]) ).
cnf(refute_0_177,plain,
join(zero,complement(join(complement(X_24),complement(X_24)))) = join(zero,complement(join(complement(X_24),complement(X_24)))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(X_24),complement(X_24)))))]]) ).
cnf(refute_0_178,plain,
( complement(join(complement(X_24),complement(X_24))) != meet(X_24,X_24)
| join(zero,complement(join(complement(X_24),complement(X_24)))) != join(zero,complement(join(complement(X_24),complement(X_24))))
| join(zero,complement(join(complement(X_24),complement(X_24)))) = join(zero,meet(X_24,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(X_24),complement(X_24)))),join(zero,complement(join(complement(X_24),complement(X_24))))) ),[1,1],$fot(meet(X_24,X_24))]]) ).
cnf(refute_0_179,plain,
( complement(join(complement(X_24),complement(X_24))) != meet(X_24,X_24)
| join(zero,complement(join(complement(X_24),complement(X_24)))) = join(zero,meet(X_24,X_24)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_24),complement(X_24)))),join(zero,complement(join(complement(X_24),complement(X_24))))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
join(zero,complement(join(complement(X_24),complement(X_24)))) = join(zero,meet(X_24,X_24)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_24),complement(X_24))),meet(X_24,X_24)) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
( X_24 != join(zero,complement(join(complement(X_24),complement(X_24))))
| join(zero,complement(join(complement(X_24),complement(X_24)))) != join(zero,meet(X_24,X_24))
| X_24 = join(zero,meet(X_24,X_24)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(zero,meet(X_24,X_24))) ),[0],$fot(join(zero,complement(join(complement(X_24),complement(X_24)))))]]) ).
cnf(refute_0_182,plain,
( X_24 != join(zero,complement(join(complement(X_24),complement(X_24))))
| X_24 = join(zero,meet(X_24,X_24)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_24),complement(X_24)))),join(zero,meet(X_24,X_24))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
X_24 = join(zero,meet(X_24,X_24)),
inference(resolve,[$cnf( $equal(X_24,join(zero,complement(join(complement(X_24),complement(X_24))))) )],[refute_0_175,refute_0_182]) ).
cnf(refute_0_184,plain,
( X_24 != join(zero,meet(X_24,X_24))
| join(zero,meet(X_24,X_24)) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(join(zero,meet(X_24,X_24))))]]) ).
cnf(refute_0_185,plain,
join(zero,meet(X_24,X_24)) = X_24,
inference(resolve,[$cnf( $equal(X_24,join(zero,meet(X_24,X_24))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) = complement(meet(top,B)),
inference(subst,[],[refute_0_185:[bind(X_24,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_187,plain,
meet(A,join(zero,complement(X_10))) = complement(join(complement(A),complement(join(zero,complement(X_10))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(zero,complement(X_10))))]]) ).
cnf(refute_0_188,plain,
meet(top,X_10) = complement(join(zero,complement(X_10))),
inference(subst,[],[refute_0_153:[bind(B,$fot(X_10))]]) ).
cnf(refute_0_189,plain,
( meet(top,X_10) != complement(join(zero,complement(X_10)))
| complement(join(zero,complement(X_10))) = meet(top,X_10) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,X_10))),bind(Y,$fot(complement(join(zero,complement(X_10)))))]]) ).
cnf(refute_0_190,plain,
complement(join(zero,complement(X_10))) = meet(top,X_10),
inference(resolve,[$cnf( $equal(meet(top,X_10),complement(join(zero,complement(X_10)))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( complement(join(zero,complement(X_10))) != meet(top,X_10)
| meet(A,join(zero,complement(X_10))) != complement(join(complement(A),complement(join(zero,complement(X_10)))))
| meet(A,join(zero,complement(X_10))) = complement(join(complement(A),meet(top,X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_10))),complement(join(complement(A),complement(join(zero,complement(X_10)))))) ),[1,0,1],$fot(meet(top,X_10))]]) ).
cnf(refute_0_192,plain,
( meet(A,join(zero,complement(X_10))) != complement(join(complement(A),complement(join(zero,complement(X_10)))))
| meet(A,join(zero,complement(X_10))) = complement(join(complement(A),meet(top,X_10))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_10))),meet(top,X_10)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
meet(A,join(zero,complement(X_10))) = complement(join(complement(A),meet(top,X_10))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_10))),complement(join(complement(A),complement(join(zero,complement(X_10)))))) )],[refute_0_187,refute_0_192]) ).
cnf(refute_0_194,plain,
meet(A,join(complement(X_6),complement(X_7))) = complement(join(complement(A),complement(join(complement(X_6),complement(X_7))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_195,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| meet(A,join(complement(X_6),complement(X_7))) != complement(join(complement(A),complement(join(complement(X_6),complement(X_7)))))
| meet(A,join(complement(X_6),complement(X_7))) = complement(join(complement(A),meet(X_6,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_6),complement(X_7))),complement(join(complement(A),complement(join(complement(X_6),complement(X_7)))))) ),[1,0,1],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_196,plain,
( meet(A,join(complement(X_6),complement(X_7))) != complement(join(complement(A),complement(join(complement(X_6),complement(X_7)))))
| meet(A,join(complement(X_6),complement(X_7))) = complement(join(complement(A),meet(X_6,X_7))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_114,refute_0_195]) ).
cnf(refute_0_197,plain,
meet(A,join(complement(X_6),complement(X_7))) = complement(join(complement(A),meet(X_6,X_7))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_6),complement(X_7))),complement(join(complement(A),complement(join(complement(X_6),complement(X_7)))))) )],[refute_0_194,refute_0_196]) ).
cnf(refute_0_198,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B)))))),
inference(subst,[],[refute_0_148:[bind(X_24,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_199,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) ),[1,1,1,0],$fot(meet(A,B))]]) ).
cnf(refute_0_200,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_28,refute_0_199]) ).
cnf(refute_0_201,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) )],[refute_0_198,refute_0_200]) ).
cnf(refute_0_202,plain,
join(complement(complement(meet(A,B))),meet(A,B)) = join(meet(A,B),complement(complement(meet(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_203,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))]]) ).
cnf(refute_0_204,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) ),[1,0],$fot(join(meet(A,B),complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_205,plain,
( join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(join(complement(complement(meet(A,B))),meet(A,B)),join(meet(A,B),complement(complement(meet(A,B))))) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
meet(complement(meet(A,B)),join(complement(A),complement(B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(subst,[],[refute_0_197:[bind(A,$fot(complement(meet(A,B)))),bind(X_6,$fot(A)),bind(X_7,$fot(B))]]) ).
cnf(refute_0_208,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = meet(complement(meet(A,B)),join(complement(A),complement(B))),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(complement(meet(A,B)))),bind(X_7,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_209,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != meet(complement(meet(A,B)),join(complement(A),complement(B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(meet(complement(meet(A,B)),join(complement(A),complement(B))))),bind(Z,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B)))))]]) ).
cnf(refute_0_210,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),meet(complement(meet(A,B)),join(complement(A),complement(B)))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(resolve,[$cnf( $equal(meet(complement(meet(A,B)),join(complement(A),complement(B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))),bind(Z,$fot(complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_213,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_206,refute_0_213]) ).
cnf(refute_0_215,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_216,plain,
( join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) ),[1,1],$fot(complement(join(meet(A,B),complement(complement(meet(A,B))))))]]) ).
cnf(refute_0_217,plain,
( meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) ),[0],$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_220,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_201,refute_0_220]) ).
cnf(refute_0_222,plain,
( complement(X_52) != join(zero,complement(join(X_52,complement(complement(X_52)))))
| join(zero,complement(join(X_52,complement(complement(X_52))))) = complement(X_52) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_52))),bind(Y,$fot(join(zero,complement(join(X_52,complement(complement(X_52)))))))]]) ).
cnf(refute_0_223,plain,
join(zero,complement(join(X_52,complement(complement(X_52))))) = complement(X_52),
inference(resolve,[$cnf( $equal(complement(X_52),join(zero,complement(join(X_52,complement(complement(X_52)))))) )],[refute_0_104,refute_0_222]) ).
cnf(refute_0_224,plain,
join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) = complement(meet(A,B)),
inference(subst,[],[refute_0_223:[bind(X_52,$fot(meet(A,B)))]]) ).
cnf(refute_0_225,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) != complement(meet(A,B))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),complement(meet(A,B))) ),[0],$fot(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_226,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),complement(meet(A,B))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_221,refute_0_226]) ).
cnf(refute_0_228,plain,
join(complement(X_6),complement(X_7)) = complement(meet(X_6,X_7)),
inference(subst,[],[refute_0_227:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_229,plain,
meet(A,join(complement(X_6),complement(X_7))) = meet(A,join(complement(X_6),complement(X_7))),
introduced(tautology,[refl,[$fot(meet(A,join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_230,plain,
( join(complement(X_6),complement(X_7)) != complement(meet(X_6,X_7))
| meet(A,join(complement(X_6),complement(X_7))) != meet(A,join(complement(X_6),complement(X_7)))
| meet(A,join(complement(X_6),complement(X_7))) = meet(A,complement(meet(X_6,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_6),complement(X_7))),meet(A,join(complement(X_6),complement(X_7)))) ),[1,1],$fot(complement(meet(X_6,X_7)))]]) ).
cnf(refute_0_231,plain,
( join(complement(X_6),complement(X_7)) != complement(meet(X_6,X_7))
| meet(A,join(complement(X_6),complement(X_7))) = meet(A,complement(meet(X_6,X_7))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_6),complement(X_7))),meet(A,join(complement(X_6),complement(X_7)))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
meet(A,join(complement(X_6),complement(X_7))) = meet(A,complement(meet(X_6,X_7))),
inference(resolve,[$cnf( $equal(join(complement(X_6),complement(X_7)),complement(meet(X_6,X_7))) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( meet(A,join(complement(X_6),complement(X_7))) != complement(join(complement(A),meet(X_6,X_7)))
| meet(A,join(complement(X_6),complement(X_7))) != meet(A,complement(meet(X_6,X_7)))
| meet(A,complement(meet(X_6,X_7))) = complement(join(complement(A),meet(X_6,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_6),complement(X_7))),complement(join(complement(A),meet(X_6,X_7)))) ),[0],$fot(meet(A,complement(meet(X_6,X_7))))]]) ).
cnf(refute_0_234,plain,
( meet(A,join(complement(X_6),complement(X_7))) != complement(join(complement(A),meet(X_6,X_7)))
| meet(A,complement(meet(X_6,X_7))) = complement(join(complement(A),meet(X_6,X_7))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_6),complement(X_7))),meet(A,complement(meet(X_6,X_7)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
meet(A,complement(meet(X_6,X_7))) = complement(join(complement(A),meet(X_6,X_7))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_6),complement(X_7))),complement(join(complement(A),meet(X_6,X_7)))) )],[refute_0_197,refute_0_234]) ).
cnf(refute_0_236,plain,
( meet(A,complement(meet(X_6,X_7))) != complement(join(complement(A),meet(X_6,X_7)))
| complement(join(complement(A),meet(X_6,X_7))) = meet(A,complement(meet(X_6,X_7))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,complement(meet(X_6,X_7))))),bind(Y,$fot(complement(join(complement(A),meet(X_6,X_7)))))]]) ).
cnf(refute_0_237,plain,
complement(join(complement(A),meet(X_6,X_7))) = meet(A,complement(meet(X_6,X_7))),
inference(resolve,[$cnf( $equal(meet(A,complement(meet(X_6,X_7))),complement(join(complement(A),meet(X_6,X_7)))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
complement(join(complement(A),meet(top,X_10))) = meet(A,complement(meet(top,X_10))),
inference(subst,[],[refute_0_237:[bind(X_6,$fot(top)),bind(X_7,$fot(X_10))]]) ).
cnf(refute_0_239,plain,
( complement(join(complement(A),meet(top,X_10))) != meet(A,complement(meet(top,X_10)))
| meet(A,join(zero,complement(X_10))) != complement(join(complement(A),meet(top,X_10)))
| meet(A,join(zero,complement(X_10))) = meet(A,complement(meet(top,X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_10))),complement(join(complement(A),meet(top,X_10)))) ),[1],$fot(meet(A,complement(meet(top,X_10))))]]) ).
cnf(refute_0_240,plain,
( meet(A,join(zero,complement(X_10))) != complement(join(complement(A),meet(top,X_10)))
| meet(A,join(zero,complement(X_10))) = meet(A,complement(meet(top,X_10))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_10))),meet(A,complement(meet(top,X_10)))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
meet(A,join(zero,complement(X_10))) = meet(A,complement(meet(top,X_10))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_10))),complement(join(complement(A),meet(top,X_10)))) )],[refute_0_193,refute_0_240]) ).
cnf(refute_0_242,plain,
meet(complement(meet(top,B)),join(zero,complement(B))) = meet(complement(meet(top,B)),complement(meet(top,B))),
inference(subst,[],[refute_0_241:[bind(A,$fot(complement(meet(top,B)))),bind(X_10,$fot(B))]]) ).
cnf(refute_0_243,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))]]) ).
cnf(refute_0_244,plain,
( join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| meet(complement(meet(top,B)),join(zero,complement(B))) != meet(complement(meet(top,B)),complement(meet(top,B)))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) ),[1,1],$fot(meet(complement(meet(top,B)),complement(meet(top,B))))]]) ).
cnf(refute_0_245,plain,
( meet(complement(meet(top,B)),join(zero,complement(B))) != meet(complement(meet(top,B)),complement(meet(top,B)))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),join(zero,complement(B))),meet(complement(meet(top,B)),complement(meet(top,B)))) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
( join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != join(zero,meet(complement(meet(top,B)),complement(meet(top,B))))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))),bind(Y,$fot(join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))))),bind(Z,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_248,plain,
( join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),complement(meet(top,B))))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))),complement(meet(top,B))) )],[refute_0_186,refute_0_248]) ).
cnf(refute_0_250,plain,
( join(zero,complement(B)) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != complement(meet(top,B))
| join(zero,complement(B)) = complement(meet(top,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(B)),complement(meet(top,B))) ),[0],$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))]]) ).
cnf(refute_0_251,plain,
( join(zero,complement(B)) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,complement(B)) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),complement(meet(top,B))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
join(zero,complement(B)) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_168,refute_0_251]) ).
cnf(refute_0_253,plain,
join(zero,complement(join(X_52,complement(complement(X_52))))) = complement(meet(top,join(X_52,complement(complement(X_52))))),
inference(subst,[],[refute_0_252:[bind(B,$fot(join(X_52,complement(complement(X_52)))))]]) ).
cnf(refute_0_254,plain,
( complement(X_52) != join(zero,complement(join(X_52,complement(complement(X_52)))))
| join(zero,complement(join(X_52,complement(complement(X_52))))) != complement(meet(top,join(X_52,complement(complement(X_52)))))
| complement(X_52) = complement(meet(top,join(X_52,complement(complement(X_52))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_52),complement(meet(top,join(X_52,complement(complement(X_52)))))) ),[0],$fot(join(zero,complement(join(X_52,complement(complement(X_52))))))]]) ).
cnf(refute_0_255,plain,
( complement(X_52) != join(zero,complement(join(X_52,complement(complement(X_52)))))
| complement(X_52) = complement(meet(top,join(X_52,complement(complement(X_52))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(X_52,complement(complement(X_52))))),complement(meet(top,join(X_52,complement(complement(X_52)))))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
complement(X_52) = complement(meet(top,join(X_52,complement(complement(X_52))))),
inference(resolve,[$cnf( $equal(complement(X_52),join(zero,complement(join(X_52,complement(complement(X_52)))))) )],[refute_0_104,refute_0_255]) ).
cnf(refute_0_257,plain,
X_36 = join(meet(X_36,top),meet(X_36,complement(top))),
inference(subst,[],[refute_0_49:[bind(B,$fot(top)),bind(X_24,$fot(X_36))]]) ).
cnf(refute_0_258,plain,
( X_36 != join(meet(X_36,top),meet(X_36,complement(top)))
| complement(top) != zero
| X_36 = join(meet(X_36,top),meet(X_36,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(X_36,join(meet(X_36,top),meet(X_36,complement(top)))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_259,plain,
( X_36 != join(meet(X_36,top),meet(X_36,complement(top)))
| X_36 = join(meet(X_36,top),meet(X_36,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_258]) ).
cnf(refute_0_260,plain,
X_36 = join(meet(X_36,top),meet(X_36,zero)),
inference(resolve,[$cnf( $equal(X_36,join(meet(X_36,top),meet(X_36,complement(top)))) )],[refute_0_257,refute_0_259]) ).
cnf(refute_0_261,plain,
X_37 = join(meet(X_37,top),meet(X_37,zero)),
inference(subst,[],[refute_0_260:[bind(X_36,$fot(X_37))]]) ).
cnf(refute_0_262,plain,
meet(zero,X_37) = meet(X_37,zero),
inference(subst,[],[refute_0_77:[bind(X_6,$fot(zero)),bind(X_7,$fot(X_37))]]) ).
cnf(refute_0_263,plain,
( meet(zero,X_37) != meet(X_37,zero)
| meet(X_37,zero) = meet(zero,X_37) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(zero,X_37))),bind(Y,$fot(meet(X_37,zero)))]]) ).
cnf(refute_0_264,plain,
meet(X_37,zero) = meet(zero,X_37),
inference(resolve,[$cnf( $equal(meet(zero,X_37),meet(X_37,zero)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
( X_37 != join(meet(X_37,top),meet(X_37,zero))
| meet(X_37,zero) != meet(zero,X_37)
| X_37 = join(meet(X_37,top),meet(zero,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(X_37,join(meet(X_37,top),meet(X_37,zero))) ),[1,1],$fot(meet(zero,X_37))]]) ).
cnf(refute_0_266,plain,
( X_37 != join(meet(X_37,top),meet(X_37,zero))
| X_37 = join(meet(X_37,top),meet(zero,X_37)) ),
inference(resolve,[$cnf( $equal(meet(X_37,zero),meet(zero,X_37)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
X_37 = join(meet(X_37,top),meet(zero,X_37)),
inference(resolve,[$cnf( $equal(X_37,join(meet(X_37,top),meet(X_37,zero))) )],[refute_0_261,refute_0_266]) ).
cnf(refute_0_268,plain,
X_38 = join(meet(X_38,top),meet(zero,X_38)),
inference(subst,[],[refute_0_267:[bind(X_37,$fot(X_38))]]) ).
cnf(refute_0_269,plain,
meet(top,X_38) = meet(X_38,top),
inference(subst,[],[refute_0_77:[bind(X_6,$fot(top)),bind(X_7,$fot(X_38))]]) ).
cnf(refute_0_270,plain,
( meet(top,X_38) != meet(X_38,top)
| meet(X_38,top) = meet(top,X_38) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,X_38))),bind(Y,$fot(meet(X_38,top)))]]) ).
cnf(refute_0_271,plain,
meet(X_38,top) = meet(top,X_38),
inference(resolve,[$cnf( $equal(meet(top,X_38),meet(X_38,top)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
( X_38 != join(meet(X_38,top),meet(zero,X_38))
| meet(X_38,top) != meet(top,X_38)
| X_38 = join(meet(top,X_38),meet(zero,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(X_38,top),meet(zero,X_38))) ),[1,0],$fot(meet(top,X_38))]]) ).
cnf(refute_0_273,plain,
( X_38 != join(meet(X_38,top),meet(zero,X_38))
| X_38 = join(meet(top,X_38),meet(zero,X_38)) ),
inference(resolve,[$cnf( $equal(meet(X_38,top),meet(top,X_38)) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
X_38 = join(meet(top,X_38),meet(zero,X_38)),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,top),meet(zero,X_38))) )],[refute_0_268,refute_0_273]) ).
cnf(refute_0_275,plain,
join(meet(top,X_38),zero) = join(zero,meet(top,X_38)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(meet(top,X_38)))]]) ).
cnf(refute_0_276,plain,
meet(zero,B) = complement(join(complement(zero),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(zero))]]) ).
cnf(refute_0_277,plain,
X_24 = join(meet(X_24,join(zero,meet(X_24,top))),complement(join(complement(X_24),join(zero,meet(X_24,top))))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_24)),bind(B,$fot(join(zero,meet(X_24,top))))]]) ).
cnf(refute_0_278,plain,
top = join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_279,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| top != join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) ),[1,1],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_280,plain,
( top != join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_114,refute_0_279]) ).
cnf(refute_0_281,plain,
top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_278,refute_0_280]) ).
cnf(refute_0_282,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_283,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_282]) ).
cnf(refute_0_284,plain,
join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))),
inference(subst,[],[refute_0_283:[bind(A,$fot(complement(X_6))),bind(B,$fot(complement(X_7))),bind(C,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_285,plain,
( join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != join(complement(X_6),join(complement(X_7),meet(X_6,X_7)))
| top != join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| top = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) ),[1],$fot(join(complement(X_6),join(complement(X_7),meet(X_6,X_7))))]]) ).
cnf(refute_0_286,plain,
( top != join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| top = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),join(complement(X_6),join(complement(X_7),meet(X_6,X_7)))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
top = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_281,refute_0_286]) ).
cnf(refute_0_288,plain,
top = join(complement(X_18),join(complement(top),meet(X_18,top))),
inference(subst,[],[refute_0_287:[bind(X_6,$fot(X_18)),bind(X_7,$fot(top))]]) ).
cnf(refute_0_289,plain,
( complement(top) != zero
| top != join(complement(X_18),join(complement(top),meet(X_18,top)))
| top = join(complement(X_18),join(zero,meet(X_18,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_18),join(complement(top),meet(X_18,top)))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_290,plain,
( top != join(complement(X_18),join(complement(top),meet(X_18,top)))
| top = join(complement(X_18),join(zero,meet(X_18,top))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_289]) ).
cnf(refute_0_291,plain,
top = join(complement(X_18),join(zero,meet(X_18,top))),
inference(resolve,[$cnf( $equal(top,join(complement(X_18),join(complement(top),meet(X_18,top)))) )],[refute_0_288,refute_0_290]) ).
cnf(refute_0_292,plain,
top = join(complement(X_24),join(zero,meet(X_24,top))),
inference(subst,[],[refute_0_291:[bind(X_18,$fot(X_24))]]) ).
cnf(refute_0_293,plain,
( top != join(complement(X_24),join(zero,meet(X_24,top)))
| join(complement(X_24),join(zero,meet(X_24,top))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_24),join(zero,meet(X_24,top)))))]]) ).
cnf(refute_0_294,plain,
join(complement(X_24),join(zero,meet(X_24,top))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_24),join(zero,meet(X_24,top)))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
( X_24 != join(meet(X_24,join(zero,meet(X_24,top))),complement(join(complement(X_24),join(zero,meet(X_24,top)))))
| join(complement(X_24),join(zero,meet(X_24,top))) != top
| X_24 = join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_24,join(meet(X_24,join(zero,meet(X_24,top))),complement(join(complement(X_24),join(zero,meet(X_24,top)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_296,plain,
( X_24 != join(meet(X_24,join(zero,meet(X_24,top))),complement(join(complement(X_24),join(zero,meet(X_24,top)))))
| X_24 = join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),join(zero,meet(X_24,top))),top) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
X_24 = join(meet(X_24,join(zero,meet(X_24,top))),complement(top)),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,join(zero,meet(X_24,top))),complement(join(complement(X_24),join(zero,meet(X_24,top)))))) )],[refute_0_277,refute_0_296]) ).
cnf(refute_0_298,plain,
join(complement(top),meet(X_24,join(zero,meet(X_24,top)))) = join(complement(top),meet(X_24,join(zero,meet(X_24,top)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_24,join(zero,meet(X_24,top)))))]]) ).
cnf(refute_0_299,plain,
( complement(top) != zero
| join(complement(top),meet(X_24,join(zero,meet(X_24,top)))) != join(complement(top),meet(X_24,join(zero,meet(X_24,top))))
| join(complement(top),meet(X_24,join(zero,meet(X_24,top)))) = join(zero,meet(X_24,join(zero,meet(X_24,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_24,join(zero,meet(X_24,top)))),join(complement(top),meet(X_24,join(zero,meet(X_24,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_300,plain,
( complement(top) != zero
| join(complement(top),meet(X_24,join(zero,meet(X_24,top)))) = join(zero,meet(X_24,join(zero,meet(X_24,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_24,join(zero,meet(X_24,top)))),join(complement(top),meet(X_24,join(zero,meet(X_24,top))))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
join(complement(top),meet(X_24,join(zero,meet(X_24,top)))) = join(zero,meet(X_24,join(zero,meet(X_24,top)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_300]) ).
cnf(refute_0_302,plain,
join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) = join(complement(top),meet(X_24,join(zero,meet(X_24,top)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_24,join(zero,meet(X_24,top)))))]]) ).
cnf(refute_0_303,plain,
( join(complement(top),meet(X_24,join(zero,meet(X_24,top)))) != join(zero,meet(X_24,join(zero,meet(X_24,top))))
| join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) != join(complement(top),meet(X_24,join(zero,meet(X_24,top))))
| join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) = join(zero,meet(X_24,join(zero,meet(X_24,top)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(X_24,join(zero,meet(X_24,top))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_24,join(zero,meet(X_24,top)))))),bind(Z,$fot(join(zero,meet(X_24,join(zero,meet(X_24,top))))))]]) ).
cnf(refute_0_304,plain,
( join(complement(top),meet(X_24,join(zero,meet(X_24,top)))) != join(zero,meet(X_24,join(zero,meet(X_24,top))))
| join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) = join(zero,meet(X_24,join(zero,meet(X_24,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,join(zero,meet(X_24,top))),complement(top)),join(complement(top),meet(X_24,join(zero,meet(X_24,top))))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) = join(zero,meet(X_24,join(zero,meet(X_24,top)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_24,join(zero,meet(X_24,top)))),join(zero,meet(X_24,join(zero,meet(X_24,top))))) )],[refute_0_301,refute_0_304]) ).
cnf(refute_0_306,plain,
( X_24 != join(meet(X_24,join(zero,meet(X_24,top))),complement(top))
| join(meet(X_24,join(zero,meet(X_24,top))),complement(top)) != join(zero,meet(X_24,join(zero,meet(X_24,top))))
| X_24 = join(zero,meet(X_24,join(zero,meet(X_24,top)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(zero,meet(X_24,join(zero,meet(X_24,top))))) ),[0],$fot(join(meet(X_24,join(zero,meet(X_24,top))),complement(top)))]]) ).
cnf(refute_0_307,plain,
( X_24 != join(meet(X_24,join(zero,meet(X_24,top))),complement(top))
| X_24 = join(zero,meet(X_24,join(zero,meet(X_24,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,join(zero,meet(X_24,top))),complement(top)),join(zero,meet(X_24,join(zero,meet(X_24,top))))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
X_24 = join(zero,meet(X_24,join(zero,meet(X_24,top)))),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,join(zero,meet(X_24,top))),complement(top))) )],[refute_0_297,refute_0_307]) ).
cnf(refute_0_309,plain,
X_28 = join(zero,meet(X_28,join(zero,meet(X_28,top)))),
inference(subst,[],[refute_0_308:[bind(X_24,$fot(X_28))]]) ).
cnf(refute_0_310,plain,
meet(top,X_28) = meet(X_28,top),
inference(subst,[],[refute_0_77:[bind(X_6,$fot(top)),bind(X_7,$fot(X_28))]]) ).
cnf(refute_0_311,plain,
( meet(top,X_28) != meet(X_28,top)
| meet(X_28,top) = meet(top,X_28) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,X_28))),bind(Y,$fot(meet(X_28,top)))]]) ).
cnf(refute_0_312,plain,
meet(X_28,top) = meet(top,X_28),
inference(resolve,[$cnf( $equal(meet(top,X_28),meet(X_28,top)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
( X_28 != join(zero,meet(X_28,join(zero,meet(X_28,top))))
| meet(X_28,top) != meet(top,X_28)
| X_28 = join(zero,meet(X_28,join(zero,meet(top,X_28)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_28,join(zero,meet(X_28,join(zero,meet(X_28,top))))) ),[1,1,1,1],$fot(meet(top,X_28))]]) ).
cnf(refute_0_314,plain,
( X_28 != join(zero,meet(X_28,join(zero,meet(X_28,top))))
| X_28 = join(zero,meet(X_28,join(zero,meet(top,X_28)))) ),
inference(resolve,[$cnf( $equal(meet(X_28,top),meet(top,X_28)) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
X_28 = join(zero,meet(X_28,join(zero,meet(top,X_28)))),
inference(resolve,[$cnf( $equal(X_28,join(zero,meet(X_28,join(zero,meet(X_28,top))))) )],[refute_0_309,refute_0_314]) ).
cnf(refute_0_316,plain,
complement(complement(top)) = join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top)))))),
inference(subst,[],[refute_0_315:[bind(X_28,$fot(complement(complement(top))))]]) ).
cnf(refute_0_317,plain,
top = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_148:[bind(X_24,$fot(top))]]) ).
cnf(refute_0_318,plain,
( top != join(zero,meet(top,complement(complement(top))))
| join(zero,meet(top,complement(complement(top)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(complement(top))))))]]) ).
cnf(refute_0_319,plain,
join(zero,meet(top,complement(complement(top)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))
| join(zero,meet(top,complement(complement(top)))) != top
| complement(complement(top)) = join(zero,meet(complement(complement(top)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))) ),[1,1,1],$fot(top)]]) ).
cnf(refute_0_321,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))
| complement(complement(top)) = join(zero,meet(complement(complement(top)),top)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(complement(top)))),top) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
complement(complement(top)) = join(zero,meet(complement(complement(top)),top)),
inference(resolve,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),join(zero,meet(top,complement(complement(top))))))) )],[refute_0_316,refute_0_321]) ).
cnf(refute_0_323,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_324,plain,
( complement(complement(top)) != complement(complement(top))
| complement(top) != zero
| complement(complement(top)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),complement(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_325,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_325]) ).
cnf(refute_0_327,plain,
( complement(complement(top)) != complement(zero)
| complement(complement(top)) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = join(zero,meet(complement(complement(top)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),top))) ),[0],$fot(complement(zero))]]) ).
cnf(refute_0_328,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = join(zero,meet(complement(complement(top)),top)) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
( complement(top) != zero
| top != join(zero,meet(top,complement(complement(top))))
| top = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) ),[1,1,1,0],$fot(zero)]]) ).
cnf(refute_0_330,plain,
( top != join(zero,meet(top,complement(complement(top))))
| top = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_329]) ).
cnf(refute_0_331,plain,
top = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_317,refute_0_330]) ).
cnf(refute_0_332,plain,
( top != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(zero)))))]]) ).
cnf(refute_0_333,plain,
join(zero,meet(top,complement(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(zero)))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
meet(top,complement(complement(top))) = meet(top,complement(complement(top))),
introduced(tautology,[refl,[$fot(meet(top,complement(complement(top))))]]) ).
cnf(refute_0_335,plain,
( complement(complement(top)) != complement(zero)
| meet(top,complement(complement(top))) != meet(top,complement(complement(top)))
| meet(top,complement(complement(top))) = meet(top,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(complement(top))),meet(top,complement(complement(top)))) ),[1,1],$fot(complement(zero))]]) ).
cnf(refute_0_336,plain,
( complement(complement(top)) != complement(zero)
| meet(top,complement(complement(top))) = meet(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(meet(top,complement(complement(top))),meet(top,complement(complement(top)))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
meet(top,complement(complement(top))) = meet(top,complement(zero)),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_326,refute_0_336]) ).
cnf(refute_0_338,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_339,plain,
( complement(top) != zero
| meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_340,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_339]) ).
cnf(refute_0_341,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_338,refute_0_340]) ).
cnf(refute_0_342,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_155:[bind(B,$fot(A))]]) ).
cnf(refute_0_343,plain,
join(complement(A),zero) = join(zero,complement(A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(A)))]]) ).
cnf(refute_0_344,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_345,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_346,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_343,refute_0_346]) ).
cnf(refute_0_348,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_349,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_342,refute_0_349]) ).
cnf(refute_0_351,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_352,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_341,refute_0_352]) ).
cnf(refute_0_354,plain,
meet(complement(complement(top)),top) = meet(top,complement(complement(top))),
inference(subst,[],[refute_0_353:[bind(A,$fot(complement(complement(top))))]]) ).
cnf(refute_0_355,plain,
( meet(complement(complement(top)),top) != meet(top,complement(complement(top)))
| meet(top,complement(complement(top))) != meet(top,complement(zero))
| meet(complement(complement(top)),top) = meet(top,complement(zero)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(complement(complement(top)),top))),bind(Y,$fot(meet(top,complement(complement(top))))),bind(Z,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_356,plain,
( meet(top,complement(complement(top))) != meet(top,complement(zero))
| meet(complement(complement(top)),top) = meet(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(top)),top),meet(top,complement(complement(top)))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
meet(complement(complement(top)),top) = meet(top,complement(zero)),
inference(resolve,[$cnf( $equal(meet(top,complement(complement(top))),meet(top,complement(zero))) )],[refute_0_337,refute_0_356]) ).
cnf(refute_0_358,plain,
join(zero,meet(complement(complement(top)),top)) = join(zero,meet(complement(complement(top)),top)),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(complement(top)),top)))]]) ).
cnf(refute_0_359,plain,
( join(zero,meet(complement(complement(top)),top)) != join(zero,meet(complement(complement(top)),top))
| meet(complement(complement(top)),top) != meet(top,complement(zero))
| join(zero,meet(complement(complement(top)),top)) = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),join(zero,meet(complement(complement(top)),top))) ),[1,1],$fot(meet(top,complement(zero)))]]) ).
cnf(refute_0_360,plain,
( meet(complement(complement(top)),top) != meet(top,complement(zero))
| join(zero,meet(complement(complement(top)),top)) = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),join(zero,meet(complement(complement(top)),top))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
join(zero,meet(complement(complement(top)),top)) = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(meet(complement(complement(top)),top),meet(top,complement(zero))) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
( join(zero,meet(complement(complement(top)),top)) != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) != top
| join(zero,meet(complement(complement(top)),top)) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,meet(complement(complement(top)),top)))),bind(Y,$fot(join(zero,meet(top,complement(zero))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_363,plain,
( join(zero,meet(top,complement(zero))) != top
| join(zero,meet(complement(complement(top)),top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),join(zero,meet(top,complement(zero)))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
join(zero,meet(complement(complement(top)),top)) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(zero))),top) )],[refute_0_333,refute_0_363]) ).
cnf(refute_0_365,plain,
( complement(zero) != join(zero,meet(complement(complement(top)),top))
| join(zero,meet(complement(complement(top)),top)) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(zero,meet(complement(complement(top)),top)))]]) ).
cnf(refute_0_366,plain,
( complement(zero) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(top)),top)),top) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
( complement(complement(top)) != join(zero,meet(complement(complement(top)),top))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(complement(zero),join(zero,meet(complement(complement(top)),top))) )],[refute_0_328,refute_0_366]) ).
cnf(refute_0_368,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(complement(top)),join(zero,meet(complement(complement(top)),top))) )],[refute_0_322,refute_0_367]) ).
cnf(refute_0_369,plain,
( complement(zero) != top
| meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) ),[1,0,0],$fot(top)]]) ).
cnf(refute_0_370,plain,
( meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
meet(zero,B) = complement(join(top,complement(B))),
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) )],[refute_0_276,refute_0_370]) ).
cnf(refute_0_372,plain,
top = join(complement(X_6),join(complement(X_6),meet(X_6,X_6))),
inference(subst,[],[refute_0_287:[bind(X_7,$fot(X_6))]]) ).
cnf(refute_0_373,plain,
top = join(meet(X_92,X_92),complement(meet(X_92,X_92))),
inference(subst,[],[def_top_12:[bind(A,$fot(meet(X_92,X_92)))]]) ).
cnf(refute_0_374,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_375,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) ),[0],$fot(join(complement(B),composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_376,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_376]) ).
cnf(refute_0_378,plain,
join(complement(X_91),composition(converse(one),complement(composition(one,X_91)))) = complement(X_91),
inference(subst,[],[refute_0_377:[bind(A,$fot(one)),bind(B,$fot(X_91))]]) ).
cnf(refute_0_379,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_380,plain,
converse(composition(converse(A),X_17)) = composition(converse(X_17),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_17))]]) ).
cnf(refute_0_381,plain,
( converse(composition(converse(A),X_17)) != composition(converse(X_17),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_17)) = composition(converse(X_17),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_17)),composition(converse(X_17),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_382,plain,
( converse(composition(converse(A),X_17)) != composition(converse(X_17),converse(converse(A)))
| converse(composition(converse(A),X_17)) = composition(converse(X_17),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_381]) ).
cnf(refute_0_383,plain,
converse(composition(converse(A),X_17)) = composition(converse(X_17),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_17)),composition(converse(X_17),converse(converse(A)))) )],[refute_0_380,refute_0_382]) ).
cnf(refute_0_384,plain,
converse(composition(converse(X_44),one)) = composition(converse(one),X_44),
inference(subst,[],[refute_0_383:[bind(A,$fot(X_44)),bind(X_17,$fot(one))]]) ).
cnf(refute_0_385,plain,
composition(converse(X_44),one) = converse(X_44),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_44)))]]) ).
cnf(refute_0_386,plain,
( composition(converse(X_44),one) != converse(X_44)
| converse(composition(converse(X_44),one)) != composition(converse(one),X_44)
| converse(converse(X_44)) = composition(converse(one),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_44),one)),composition(converse(one),X_44)) ),[0,0],$fot(converse(X_44))]]) ).
cnf(refute_0_387,plain,
( converse(composition(converse(X_44),one)) != composition(converse(one),X_44)
| converse(converse(X_44)) = composition(converse(one),X_44) ),
inference(resolve,[$cnf( $equal(composition(converse(X_44),one),converse(X_44)) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
converse(converse(X_44)) = composition(converse(one),X_44),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_44),one)),composition(converse(one),X_44)) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
converse(converse(X_44)) = X_44,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_44))]]) ).
cnf(refute_0_390,plain,
( converse(converse(X_44)) != X_44
| converse(converse(X_44)) != composition(converse(one),X_44)
| X_44 = composition(converse(one),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_44)),composition(converse(one),X_44)) ),[0],$fot(X_44)]]) ).
cnf(refute_0_391,plain,
( converse(converse(X_44)) != composition(converse(one),X_44)
| X_44 = composition(converse(one),X_44) ),
inference(resolve,[$cnf( $equal(converse(converse(X_44)),X_44) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
X_44 = composition(converse(one),X_44),
inference(resolve,[$cnf( $equal(converse(converse(X_44)),composition(converse(one),X_44)) )],[refute_0_388,refute_0_391]) ).
cnf(refute_0_393,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_392:[bind(X_44,$fot(one))]]) ).
cnf(refute_0_394,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_395,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_397,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_379,refute_0_397]) ).
cnf(refute_0_399,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_400,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
( converse(one) != one
| join(complement(X_91),composition(converse(one),complement(composition(one,X_91)))) != complement(X_91)
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) = complement(X_91) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_91),composition(converse(one),complement(composition(one,X_91)))),complement(X_91)) ),[0,1,0],$fot(one)]]) ).
cnf(refute_0_402,plain,
( join(complement(X_91),composition(converse(one),complement(composition(one,X_91)))) != complement(X_91)
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) = complement(X_91) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
join(complement(X_91),composition(one,complement(composition(one,X_91)))) = complement(X_91),
inference(resolve,[$cnf( $equal(join(complement(X_91),composition(converse(one),complement(composition(one,X_91)))),complement(X_91)) )],[refute_0_378,refute_0_402]) ).
cnf(refute_0_404,plain,
join(complement(X_91),complement(X_91)) = complement(meet(X_91,X_91)),
inference(subst,[],[refute_0_227:[bind(A,$fot(X_91)),bind(B,$fot(X_91))]]) ).
cnf(refute_0_405,plain,
composition(converse(one),X_44) = composition(converse(one),X_44),
introduced(tautology,[refl,[$fot(composition(converse(one),X_44))]]) ).
cnf(refute_0_406,plain,
( composition(converse(one),X_44) != composition(converse(one),X_44)
| converse(one) != one
| composition(converse(one),X_44) = composition(one,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_44),composition(converse(one),X_44)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_407,plain,
( converse(one) != one
| composition(converse(one),X_44) = composition(one,X_44) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_44),composition(converse(one),X_44)) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
composition(converse(one),X_44) = composition(one,X_44),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_400,refute_0_407]) ).
cnf(refute_0_409,plain,
( X_44 != composition(converse(one),X_44)
| composition(converse(one),X_44) != composition(one,X_44)
| X_44 = composition(one,X_44) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_44,composition(one,X_44)) ),[0],$fot(composition(converse(one),X_44))]]) ).
cnf(refute_0_410,plain,
( X_44 != composition(converse(one),X_44)
| X_44 = composition(one,X_44) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_44),composition(one,X_44)) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
X_44 = composition(one,X_44),
inference(resolve,[$cnf( $equal(X_44,composition(converse(one),X_44)) )],[refute_0_392,refute_0_410]) ).
cnf(refute_0_412,plain,
( X_44 != composition(one,X_44)
| composition(one,X_44) = X_44 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_44)),bind(Y,$fot(composition(one,X_44)))]]) ).
cnf(refute_0_413,plain,
composition(one,X_44) = X_44,
inference(resolve,[$cnf( $equal(X_44,composition(one,X_44)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
composition(one,X_91) = X_91,
inference(subst,[],[refute_0_413:[bind(X_44,$fot(X_91))]]) ).
cnf(refute_0_415,plain,
complement(composition(one,X_91)) = complement(composition(one,X_91)),
introduced(tautology,[refl,[$fot(complement(composition(one,X_91)))]]) ).
cnf(refute_0_416,plain,
( complement(composition(one,X_91)) != complement(composition(one,X_91))
| composition(one,X_91) != X_91
| complement(composition(one,X_91)) = complement(X_91) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(one,X_91)),complement(composition(one,X_91))) ),[1,0],$fot(X_91)]]) ).
cnf(refute_0_417,plain,
( composition(one,X_91) != X_91
| complement(composition(one,X_91)) = complement(X_91) ),
inference(resolve,[$cnf( $equal(complement(composition(one,X_91)),complement(composition(one,X_91))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
complement(composition(one,X_91)) = complement(X_91),
inference(resolve,[$cnf( $equal(composition(one,X_91),X_91) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
composition(one,complement(composition(one,X_91))) = complement(composition(one,X_91)),
inference(subst,[],[refute_0_413:[bind(X_44,$fot(complement(composition(one,X_91))))]]) ).
cnf(refute_0_420,plain,
( complement(composition(one,X_91)) != complement(X_91)
| composition(one,complement(composition(one,X_91))) != complement(composition(one,X_91))
| composition(one,complement(composition(one,X_91))) = complement(X_91) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(one,complement(composition(one,X_91))))),bind(Y,$fot(complement(composition(one,X_91)))),bind(Z,$fot(complement(X_91)))]]) ).
cnf(refute_0_421,plain,
( complement(composition(one,X_91)) != complement(X_91)
| composition(one,complement(composition(one,X_91))) = complement(X_91) ),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,X_91))),complement(composition(one,X_91))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
composition(one,complement(composition(one,X_91))) = complement(X_91),
inference(resolve,[$cnf( $equal(complement(composition(one,X_91)),complement(X_91)) )],[refute_0_418,refute_0_421]) ).
cnf(refute_0_423,plain,
join(complement(X_91),composition(one,complement(composition(one,X_91)))) = join(complement(X_91),composition(one,complement(composition(one,X_91)))),
introduced(tautology,[refl,[$fot(join(complement(X_91),composition(one,complement(composition(one,X_91)))))]]) ).
cnf(refute_0_424,plain,
( composition(one,complement(composition(one,X_91))) != complement(X_91)
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) != join(complement(X_91),composition(one,complement(composition(one,X_91))))
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) = join(complement(X_91),complement(X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_91),composition(one,complement(composition(one,X_91)))),join(complement(X_91),composition(one,complement(composition(one,X_91))))) ),[1,1],$fot(complement(X_91))]]) ).
cnf(refute_0_425,plain,
( composition(one,complement(composition(one,X_91))) != complement(X_91)
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) = join(complement(X_91),complement(X_91)) ),
inference(resolve,[$cnf( $equal(join(complement(X_91),composition(one,complement(composition(one,X_91)))),join(complement(X_91),composition(one,complement(composition(one,X_91))))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
join(complement(X_91),composition(one,complement(composition(one,X_91)))) = join(complement(X_91),complement(X_91)),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,X_91))),complement(X_91)) )],[refute_0_422,refute_0_425]) ).
cnf(refute_0_427,plain,
( join(complement(X_91),complement(X_91)) != complement(meet(X_91,X_91))
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) != join(complement(X_91),complement(X_91))
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) = complement(meet(X_91,X_91)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(X_91),composition(one,complement(composition(one,X_91)))))),bind(Y,$fot(join(complement(X_91),complement(X_91)))),bind(Z,$fot(complement(meet(X_91,X_91))))]]) ).
cnf(refute_0_428,plain,
( join(complement(X_91),complement(X_91)) != complement(meet(X_91,X_91))
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) = complement(meet(X_91,X_91)) ),
inference(resolve,[$cnf( $equal(join(complement(X_91),composition(one,complement(composition(one,X_91)))),join(complement(X_91),complement(X_91))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
join(complement(X_91),composition(one,complement(composition(one,X_91)))) = complement(meet(X_91,X_91)),
inference(resolve,[$cnf( $equal(join(complement(X_91),complement(X_91)),complement(meet(X_91,X_91))) )],[refute_0_404,refute_0_428]) ).
cnf(refute_0_430,plain,
( join(complement(X_91),composition(one,complement(composition(one,X_91)))) != complement(X_91)
| join(complement(X_91),composition(one,complement(composition(one,X_91)))) != complement(meet(X_91,X_91))
| complement(meet(X_91,X_91)) = complement(X_91) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_91),composition(one,complement(composition(one,X_91)))),complement(X_91)) ),[0],$fot(complement(meet(X_91,X_91)))]]) ).
cnf(refute_0_431,plain,
( join(complement(X_91),composition(one,complement(composition(one,X_91)))) != complement(X_91)
| complement(meet(X_91,X_91)) = complement(X_91) ),
inference(resolve,[$cnf( $equal(join(complement(X_91),composition(one,complement(composition(one,X_91)))),complement(meet(X_91,X_91))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
complement(meet(X_91,X_91)) = complement(X_91),
inference(resolve,[$cnf( $equal(join(complement(X_91),composition(one,complement(composition(one,X_91)))),complement(X_91)) )],[refute_0_403,refute_0_431]) ).
cnf(refute_0_433,plain,
complement(meet(X_92,X_92)) = complement(X_92),
inference(subst,[],[refute_0_432:[bind(X_91,$fot(X_92))]]) ).
cnf(refute_0_434,plain,
( complement(meet(X_92,X_92)) != complement(X_92)
| top != join(meet(X_92,X_92),complement(meet(X_92,X_92)))
| top = join(meet(X_92,X_92),complement(X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(X_92,X_92),complement(meet(X_92,X_92)))) ),[1,1],$fot(complement(X_92))]]) ).
cnf(refute_0_435,plain,
( top != join(meet(X_92,X_92),complement(meet(X_92,X_92)))
| top = join(meet(X_92,X_92),complement(X_92)) ),
inference(resolve,[$cnf( $equal(complement(meet(X_92,X_92)),complement(X_92)) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
top = join(meet(X_92,X_92),complement(X_92)),
inference(resolve,[$cnf( $equal(top,join(meet(X_92,X_92),complement(meet(X_92,X_92)))) )],[refute_0_373,refute_0_435]) ).
cnf(refute_0_437,plain,
join(meet(X_92,X_92),complement(X_92)) = join(complement(X_92),meet(X_92,X_92)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_92))),bind(B,$fot(meet(X_92,X_92)))]]) ).
cnf(refute_0_438,plain,
( join(meet(X_92,X_92),complement(X_92)) != join(complement(X_92),meet(X_92,X_92))
| top != join(meet(X_92,X_92),complement(X_92))
| top = join(complement(X_92),meet(X_92,X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(X_92,X_92),complement(X_92))) ),[1],$fot(join(complement(X_92),meet(X_92,X_92)))]]) ).
cnf(refute_0_439,plain,
( top != join(meet(X_92,X_92),complement(X_92))
| top = join(complement(X_92),meet(X_92,X_92)) ),
inference(resolve,[$cnf( $equal(join(meet(X_92,X_92),complement(X_92)),join(complement(X_92),meet(X_92,X_92))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
top = join(complement(X_92),meet(X_92,X_92)),
inference(resolve,[$cnf( $equal(top,join(meet(X_92,X_92),complement(X_92))) )],[refute_0_436,refute_0_439]) ).
cnf(refute_0_441,plain,
top = join(complement(X_6),meet(X_6,X_6)),
inference(subst,[],[refute_0_440:[bind(X_92,$fot(X_6))]]) ).
cnf(refute_0_442,plain,
( top != join(complement(X_6),meet(X_6,X_6))
| join(complement(X_6),meet(X_6,X_6)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_6),meet(X_6,X_6))))]]) ).
cnf(refute_0_443,plain,
join(complement(X_6),meet(X_6,X_6)) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_6),meet(X_6,X_6))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
( join(complement(X_6),meet(X_6,X_6)) != top
| top != join(complement(X_6),join(complement(X_6),meet(X_6,X_6)))
| top = join(complement(X_6),top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_6),join(complement(X_6),meet(X_6,X_6)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_445,plain,
( top != join(complement(X_6),join(complement(X_6),meet(X_6,X_6)))
| top = join(complement(X_6),top) ),
inference(resolve,[$cnf( $equal(join(complement(X_6),meet(X_6,X_6)),top) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
top = join(complement(X_6),top),
inference(resolve,[$cnf( $equal(top,join(complement(X_6),join(complement(X_6),meet(X_6,X_6)))) )],[refute_0_372,refute_0_445]) ).
cnf(refute_0_447,plain,
join(X_76,join(one,join(one,complement(join(one,one))))) = join(join(X_76,one),join(one,complement(join(one,one)))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_76)),bind(B,$fot(one)),bind(C,$fot(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_448,plain,
converse(converse(join(one,join(one,complement(join(one,one)))))) = join(one,join(one,complement(join(one,one)))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(one,join(one,complement(join(one,one))))))]]) ).
cnf(refute_0_449,plain,
converse(join(converse(A),X_12)) = join(converse(converse(A)),converse(X_12)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_12))]]) ).
cnf(refute_0_450,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_12)) != join(converse(converse(A)),converse(X_12))
| converse(join(converse(A),X_12)) = join(A,converse(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_12)),join(converse(converse(A)),converse(X_12))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_451,plain,
( converse(join(converse(A),X_12)) != join(converse(converse(A)),converse(X_12))
| converse(join(converse(A),X_12)) = join(A,converse(X_12)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_450]) ).
cnf(refute_0_452,plain,
converse(join(converse(A),X_12)) = join(A,converse(X_12)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_12)),join(converse(converse(A)),converse(X_12))) )],[refute_0_449,refute_0_451]) ).
cnf(refute_0_453,plain,
converse(join(converse(X_13),complement(converse(X_13)))) = join(X_13,converse(complement(converse(X_13)))),
inference(subst,[],[refute_0_452:[bind(A,$fot(X_13)),bind(X_12,$fot(complement(converse(X_13))))]]) ).
cnf(refute_0_454,plain,
top = join(converse(X_13),complement(converse(X_13))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_13)))]]) ).
cnf(refute_0_455,plain,
( top != join(converse(X_13),complement(converse(X_13)))
| join(converse(X_13),complement(converse(X_13))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_13),complement(converse(X_13)))))]]) ).
cnf(refute_0_456,plain,
join(converse(X_13),complement(converse(X_13))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_13),complement(converse(X_13)))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
( converse(join(converse(X_13),complement(converse(X_13)))) != join(X_13,converse(complement(converse(X_13))))
| join(converse(X_13),complement(converse(X_13))) != top
| converse(top) = join(X_13,converse(complement(converse(X_13)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_13),complement(converse(X_13)))),join(X_13,converse(complement(converse(X_13))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_458,plain,
( converse(join(converse(X_13),complement(converse(X_13)))) != join(X_13,converse(complement(converse(X_13))))
| converse(top) = join(X_13,converse(complement(converse(X_13)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_13),complement(converse(X_13))),top) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
converse(top) = join(X_13,converse(complement(converse(X_13)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_13),complement(converse(X_13)))),join(X_13,converse(complement(converse(X_13))))) )],[refute_0_453,refute_0_458]) ).
cnf(refute_0_460,plain,
converse(top) = join(join(one,one),converse(complement(converse(join(one,one))))),
inference(subst,[],[refute_0_459:[bind(X_13,$fot(join(one,one)))]]) ).
cnf(refute_0_461,plain,
converse(join(X_11,converse(A))) = join(converse(X_11),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_11)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_462,plain,
( converse(converse(A)) != A
| converse(join(X_11,converse(A))) != join(converse(X_11),converse(converse(A)))
| converse(join(X_11,converse(A))) = join(converse(X_11),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_11,converse(A))),join(converse(X_11),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_463,plain,
( converse(join(X_11,converse(A))) != join(converse(X_11),converse(converse(A)))
| converse(join(X_11,converse(A))) = join(converse(X_11),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_462]) ).
cnf(refute_0_464,plain,
converse(join(X_11,converse(A))) = join(converse(X_11),A),
inference(resolve,[$cnf( $equal(converse(join(X_11,converse(A))),join(converse(X_11),converse(converse(A)))) )],[refute_0_461,refute_0_463]) ).
cnf(refute_0_465,plain,
converse(join(X_11,converse(one))) = join(converse(X_11),one),
inference(subst,[],[refute_0_464:[bind(A,$fot(one))]]) ).
cnf(refute_0_466,plain,
( converse(join(X_11,converse(one))) != join(converse(X_11),one)
| converse(one) != one
| converse(join(X_11,one)) = join(converse(X_11),one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_11,converse(one))),join(converse(X_11),one)) ),[0,0,1],$fot(one)]]) ).
cnf(refute_0_467,plain,
( converse(join(X_11,converse(one))) != join(converse(X_11),one)
| converse(join(X_11,one)) = join(converse(X_11),one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_400,refute_0_466]) ).
cnf(refute_0_468,plain,
converse(join(X_11,one)) = join(converse(X_11),one),
inference(resolve,[$cnf( $equal(converse(join(X_11,converse(one))),join(converse(X_11),one)) )],[refute_0_465,refute_0_467]) ).
cnf(refute_0_469,plain,
join(converse(X_11),one) = join(one,converse(X_11)),
inference(subst,[],[refute_0_4:[bind(A,$fot(one)),bind(B,$fot(converse(X_11)))]]) ).
cnf(refute_0_470,plain,
( converse(join(X_11,one)) != join(converse(X_11),one)
| join(converse(X_11),one) != join(one,converse(X_11))
| converse(join(X_11,one)) = join(one,converse(X_11)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_11,one)),join(one,converse(X_11))) ),[0],$fot(join(converse(X_11),one))]]) ).
cnf(refute_0_471,plain,
( converse(join(X_11,one)) != join(converse(X_11),one)
| converse(join(X_11,one)) = join(one,converse(X_11)) ),
inference(resolve,[$cnf( $equal(join(converse(X_11),one),join(one,converse(X_11))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
converse(join(X_11,one)) = join(one,converse(X_11)),
inference(resolve,[$cnf( $equal(converse(join(X_11,one)),join(converse(X_11),one)) )],[refute_0_468,refute_0_471]) ).
cnf(refute_0_473,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_472:[bind(X_11,$fot(one))]]) ).
cnf(refute_0_474,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(one) != one
| converse(join(one,one)) = join(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_475,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_400,refute_0_474]) ).
cnf(refute_0_476,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_473,refute_0_475]) ).
cnf(refute_0_477,plain,
( converse(join(one,one)) != join(one,one)
| converse(top) != join(join(one,one),converse(complement(converse(join(one,one)))))
| converse(top) = join(join(one,one),converse(complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(converse(join(one,one)))))) ),[1,1,0,0],$fot(join(one,one))]]) ).
cnf(refute_0_478,plain,
( converse(top) != join(join(one,one),converse(complement(converse(join(one,one)))))
| converse(top) = join(join(one,one),converse(complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
converse(top) = join(join(one,one),converse(complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(converse(join(one,one)))))) )],[refute_0_460,refute_0_478]) ).
cnf(refute_0_480,plain,
join(converse(X_12),converse(X_11)) = join(converse(X_11),converse(X_12)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(X_12))),bind(B,$fot(converse(X_11)))]]) ).
cnf(refute_0_481,plain,
converse(join(X_11,X_12)) = join(converse(X_11),converse(X_12)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_11)),bind(B,$fot(X_12))]]) ).
cnf(refute_0_482,plain,
( converse(join(X_11,X_12)) != join(converse(X_11),converse(X_12))
| join(converse(X_11),converse(X_12)) = converse(join(X_11,X_12)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_11,X_12)))),bind(Y,$fot(join(converse(X_11),converse(X_12))))]]) ).
cnf(refute_0_483,plain,
join(converse(X_11),converse(X_12)) = converse(join(X_11,X_12)),
inference(resolve,[$cnf( $equal(converse(join(X_11,X_12)),join(converse(X_11),converse(X_12))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
( join(converse(X_11),converse(X_12)) != converse(join(X_11,X_12))
| join(converse(X_12),converse(X_11)) != join(converse(X_11),converse(X_12))
| join(converse(X_12),converse(X_11)) = converse(join(X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_12),converse(X_11)),join(converse(X_11),converse(X_12))) ),[1],$fot(converse(join(X_11,X_12)))]]) ).
cnf(refute_0_485,plain,
( join(converse(X_12),converse(X_11)) != join(converse(X_11),converse(X_12))
| join(converse(X_12),converse(X_11)) = converse(join(X_11,X_12)) ),
inference(resolve,[$cnf( $equal(join(converse(X_11),converse(X_12)),converse(join(X_11,X_12))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
join(converse(X_12),converse(X_11)) = converse(join(X_11,X_12)),
inference(resolve,[$cnf( $equal(join(converse(X_12),converse(X_11)),join(converse(X_11),converse(X_12))) )],[refute_0_480,refute_0_485]) ).
cnf(refute_0_487,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_488,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_487]) ).
cnf(refute_0_489,plain,
join(converse(X_12),converse(X_11)) = converse(join(X_12,X_11)),
inference(subst,[],[refute_0_488:[bind(A,$fot(X_12)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_490,plain,
( join(converse(X_12),converse(X_11)) != converse(join(X_11,X_12))
| join(converse(X_12),converse(X_11)) != converse(join(X_12,X_11))
| converse(join(X_12,X_11)) = converse(join(X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_12),converse(X_11)),converse(join(X_11,X_12))) ),[0],$fot(converse(join(X_12,X_11)))]]) ).
cnf(refute_0_491,plain,
( join(converse(X_12),converse(X_11)) != converse(join(X_11,X_12))
| converse(join(X_12,X_11)) = converse(join(X_11,X_12)) ),
inference(resolve,[$cnf( $equal(join(converse(X_12),converse(X_11)),converse(join(X_12,X_11))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
converse(join(X_12,X_11)) = converse(join(X_11,X_12)),
inference(resolve,[$cnf( $equal(join(converse(X_12),converse(X_11)),converse(join(X_11,X_12))) )],[refute_0_486,refute_0_491]) ).
cnf(refute_0_493,plain,
( converse(join(X_12,X_11)) != converse(join(X_11,X_12))
| converse(join(X_11,X_12)) = converse(join(X_12,X_11)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_12,X_11)))),bind(Y,$fot(converse(join(X_11,X_12))))]]) ).
cnf(refute_0_494,plain,
converse(join(X_11,X_12)) = converse(join(X_12,X_11)),
inference(resolve,[$cnf( $equal(converse(join(X_12,X_11)),converse(join(X_11,X_12))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
converse(join(join(one,complement(join(one,one))),one)) = converse(join(one,join(one,complement(join(one,one))))),
inference(subst,[],[refute_0_494:[bind(X_11,$fot(join(one,complement(join(one,one))))),bind(X_12,$fot(one))]]) ).
cnf(refute_0_496,plain,
( converse(join(X_11,one)) != join(one,converse(X_11))
| join(one,converse(X_11)) = converse(join(X_11,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_11,one)))),bind(Y,$fot(join(one,converse(X_11))))]]) ).
cnf(refute_0_497,plain,
join(one,converse(X_11)) = converse(join(X_11,one)),
inference(resolve,[$cnf( $equal(converse(join(X_11,one)),join(one,converse(X_11))) )],[refute_0_472,refute_0_496]) ).
cnf(refute_0_498,plain,
join(one,converse(join(one,complement(join(one,one))))) = converse(join(join(one,complement(join(one,one))),one)),
inference(subst,[],[refute_0_497:[bind(X_11,$fot(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_499,plain,
( converse(join(join(one,complement(join(one,one))),one)) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,converse(join(one,complement(join(one,one))))) != converse(join(join(one,complement(join(one,one))),one))
| join(one,converse(join(one,complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,converse(join(one,complement(join(one,one))))))),bind(Y,$fot(converse(join(join(one,complement(join(one,one))),one)))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_500,plain,
( converse(join(join(one,complement(join(one,one))),one)) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,converse(join(one,complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,complement(join(one,one))))),converse(join(join(one,complement(join(one,one))),one))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
join(one,converse(join(one,complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(converse(join(join(one,complement(join(one,one))),one)),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_495,refute_0_500]) ).
cnf(refute_0_502,plain,
converse(join(complement(join(one,one)),one)) = converse(join(one,complement(join(one,one)))),
inference(subst,[],[refute_0_494:[bind(X_11,$fot(complement(join(one,one)))),bind(X_12,$fot(one))]]) ).
cnf(refute_0_503,plain,
join(one,converse(complement(join(one,one)))) = converse(join(complement(join(one,one)),one)),
inference(subst,[],[refute_0_497:[bind(X_11,$fot(complement(join(one,one))))]]) ).
cnf(refute_0_504,plain,
( converse(join(complement(join(one,one)),one)) != converse(join(one,complement(join(one,one))))
| join(one,converse(complement(join(one,one)))) != converse(join(complement(join(one,one)),one))
| join(one,converse(complement(join(one,one)))) = converse(join(one,complement(join(one,one)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,converse(complement(join(one,one)))))),bind(Y,$fot(converse(join(complement(join(one,one)),one)))),bind(Z,$fot(converse(join(one,complement(join(one,one))))))]]) ).
cnf(refute_0_505,plain,
( converse(join(complement(join(one,one)),one)) != converse(join(one,complement(join(one,one))))
| join(one,converse(complement(join(one,one)))) = converse(join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(one,converse(complement(join(one,one)))),converse(join(complement(join(one,one)),one))) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
join(one,converse(complement(join(one,one)))) = converse(join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(join(complement(join(one,one)),one)),converse(join(one,complement(join(one,one))))) )],[refute_0_502,refute_0_505]) ).
cnf(refute_0_507,plain,
join(one,join(one,converse(complement(join(one,one))))) = join(one,join(one,converse(complement(join(one,one))))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(complement(join(one,one))))))]]) ).
cnf(refute_0_508,plain,
( join(one,converse(complement(join(one,one)))) != converse(join(one,complement(join(one,one))))
| join(one,join(one,converse(complement(join(one,one))))) != join(one,join(one,converse(complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,join(one,converse(complement(join(one,one)))))) ),[1,1],$fot(converse(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_509,plain,
( join(one,converse(complement(join(one,one)))) != converse(join(one,complement(join(one,one))))
| join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,join(one,converse(complement(join(one,one)))))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,converse(complement(join(one,one)))),converse(join(one,complement(join(one,one))))) )],[refute_0_506,refute_0_509]) ).
cnf(refute_0_511,plain,
( join(one,converse(join(one,complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) != join(one,converse(join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,converse(complement(join(one,one))))))),bind(Y,$fot(join(one,converse(join(one,complement(join(one,one))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_512,plain,
( join(one,converse(join(one,complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,converse(join(one,complement(join(one,one)))))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,complement(join(one,one))))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_501,refute_0_512]) ).
cnf(refute_0_514,plain,
join(join(one,one),converse(complement(join(one,one)))) = join(one,join(one,converse(complement(join(one,one))))),
inference(subst,[],[refute_0_283:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(converse(complement(join(one,one)))))]]) ).
cnf(refute_0_515,plain,
( join(join(one,one),converse(complement(join(one,one)))) != join(one,join(one,converse(complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,one),converse(complement(join(one,one)))))),bind(Y,$fot(join(one,join(one,converse(complement(join(one,one))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_516,plain,
( join(one,join(one,converse(complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,one)))),join(one,join(one,converse(complement(join(one,one)))))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_513,refute_0_516]) ).
cnf(refute_0_518,plain,
( converse(top) != join(join(one,one),converse(complement(join(one,one))))
| join(join(one,one),converse(complement(join(one,one)))) != converse(join(one,join(one,complement(join(one,one)))))
| converse(top) = converse(join(one,join(one,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),converse(join(one,join(one,complement(join(one,one)))))) ),[0],$fot(join(join(one,one),converse(complement(join(one,one)))))]]) ).
cnf(refute_0_519,plain,
( converse(top) != join(join(one,one),converse(complement(join(one,one))))
| converse(top) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,one)))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
converse(top) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(join(one,one))))) )],[refute_0_479,refute_0_519]) ).
cnf(refute_0_521,plain,
( converse(top) != converse(join(one,join(one,complement(join(one,one)))))
| converse(join(one,join(one,complement(join(one,one))))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_522,plain,
converse(join(one,join(one,complement(join(one,one))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
( converse(converse(join(one,join(one,complement(join(one,one)))))) != join(one,join(one,complement(join(one,one))))
| converse(join(one,join(one,complement(join(one,one))))) != converse(top)
| converse(converse(top)) = join(one,join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(one,join(one,complement(join(one,one)))))),join(one,join(one,complement(join(one,one))))) ),[0,0],$fot(converse(top))]]) ).
cnf(refute_0_524,plain,
( converse(converse(join(one,join(one,complement(join(one,one)))))) != join(one,join(one,complement(join(one,one))))
| converse(converse(top)) = join(one,join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,complement(join(one,one))))),converse(top)) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
converse(converse(top)) = join(one,join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(converse(join(one,join(one,complement(join(one,one)))))),join(one,join(one,complement(join(one,one))))) )],[refute_0_448,refute_0_524]) ).
cnf(refute_0_526,plain,
converse(converse(top)) = top,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(top))]]) ).
cnf(refute_0_527,plain,
( converse(converse(top)) != join(one,join(one,complement(join(one,one))))
| converse(converse(top)) != top
| top = join(one,join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(top)),join(one,join(one,complement(join(one,one))))) ),[0],$fot(top)]]) ).
cnf(refute_0_528,plain,
( converse(converse(top)) != join(one,join(one,complement(join(one,one))))
| top = join(one,join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
top = join(one,join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(converse(top)),join(one,join(one,complement(join(one,one))))) )],[refute_0_525,refute_0_528]) ).
cnf(refute_0_530,plain,
( top != join(one,join(one,complement(join(one,one))))
| join(one,join(one,complement(join(one,one)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(one,join(one,complement(join(one,one))))))]]) ).
cnf(refute_0_531,plain,
join(one,join(one,complement(join(one,one)))) = top,
inference(resolve,[$cnf( $equal(top,join(one,join(one,complement(join(one,one))))) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
( join(X_76,join(one,join(one,complement(join(one,one))))) != join(join(X_76,one),join(one,complement(join(one,one))))
| join(one,join(one,complement(join(one,one)))) != top
| join(X_76,top) = join(join(X_76,one),join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_76,join(one,join(one,complement(join(one,one))))),join(join(X_76,one),join(one,complement(join(one,one))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_533,plain,
( join(X_76,join(one,join(one,complement(join(one,one))))) != join(join(X_76,one),join(one,complement(join(one,one))))
| join(X_76,top) = join(join(X_76,one),join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,complement(join(one,one)))),top) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
join(X_76,top) = join(join(X_76,one),join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(join(X_76,join(one,join(one,complement(join(one,one))))),join(join(X_76,one),join(one,complement(join(one,one))))) )],[refute_0_447,refute_0_533]) ).
cnf(refute_0_535,plain,
join(A,join(X_76,X_77)) = join(join(X_76,X_77),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_76,X_77)))]]) ).
cnf(refute_0_536,plain,
join(X_76,join(X_77,A)) = join(join(X_76,X_77),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_76)),bind(B,$fot(X_77)),bind(C,$fot(A))]]) ).
cnf(refute_0_537,plain,
( join(X_76,join(X_77,A)) != join(join(X_76,X_77),A)
| join(join(X_76,X_77),A) = join(X_76,join(X_77,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_76,join(X_77,A)))),bind(Y,$fot(join(join(X_76,X_77),A)))]]) ).
cnf(refute_0_538,plain,
join(join(X_76,X_77),A) = join(X_76,join(X_77,A)),
inference(resolve,[$cnf( $equal(join(X_76,join(X_77,A)),join(join(X_76,X_77),A)) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
( join(A,join(X_76,X_77)) != join(join(X_76,X_77),A)
| join(join(X_76,X_77),A) != join(X_76,join(X_77,A))
| join(A,join(X_76,X_77)) = join(X_76,join(X_77,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_76,X_77)),join(X_76,join(X_77,A))) ),[0],$fot(join(join(X_76,X_77),A))]]) ).
cnf(refute_0_540,plain,
( join(A,join(X_76,X_77)) != join(join(X_76,X_77),A)
| join(A,join(X_76,X_77)) = join(X_76,join(X_77,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_76,X_77),A),join(X_76,join(X_77,A))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
join(A,join(X_76,X_77)) = join(X_76,join(X_77,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_76,X_77)),join(join(X_76,X_77),A)) )],[refute_0_535,refute_0_540]) ).
cnf(refute_0_542,plain,
( join(A,join(X_76,X_77)) != join(X_76,join(X_77,A))
| join(X_76,join(X_77,A)) = join(A,join(X_76,X_77)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(X_76,X_77)))),bind(Y,$fot(join(X_76,join(X_77,A))))]]) ).
cnf(refute_0_543,plain,
join(X_76,join(X_77,A)) = join(A,join(X_76,X_77)),
inference(resolve,[$cnf( $equal(join(A,join(X_76,X_77)),join(X_76,join(X_77,A))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
join(complement(join(one,one)),join(X_76,one)) = join(one,join(complement(join(one,one)),X_76)),
inference(subst,[],[refute_0_543:[bind(A,$fot(one)),bind(X_76,$fot(complement(join(one,one)))),bind(X_77,$fot(X_76))]]) ).
cnf(refute_0_545,plain,
join(one,join(complement(join(one,one)),join(X_76,one))) = join(one,join(complement(join(one,one)),join(X_76,one))),
introduced(tautology,[refl,[$fot(join(one,join(complement(join(one,one)),join(X_76,one))))]]) ).
cnf(refute_0_546,plain,
( join(complement(join(one,one)),join(X_76,one)) != join(one,join(complement(join(one,one)),X_76))
| join(one,join(complement(join(one,one)),join(X_76,one))) != join(one,join(complement(join(one,one)),join(X_76,one)))
| join(one,join(complement(join(one,one)),join(X_76,one))) = join(one,join(one,join(complement(join(one,one)),X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(complement(join(one,one)),join(X_76,one))),join(one,join(complement(join(one,one)),join(X_76,one)))) ),[1,1],$fot(join(one,join(complement(join(one,one)),X_76)))]]) ).
cnf(refute_0_547,plain,
( join(complement(join(one,one)),join(X_76,one)) != join(one,join(complement(join(one,one)),X_76))
| join(one,join(complement(join(one,one)),join(X_76,one))) = join(one,join(one,join(complement(join(one,one)),X_76))) ),
inference(resolve,[$cnf( $equal(join(one,join(complement(join(one,one)),join(X_76,one))),join(one,join(complement(join(one,one)),join(X_76,one)))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
join(one,join(complement(join(one,one)),join(X_76,one))) = join(one,join(one,join(complement(join(one,one)),X_76))),
inference(resolve,[$cnf( $equal(join(complement(join(one,one)),join(X_76,one)),join(one,join(complement(join(one,one)),X_76))) )],[refute_0_544,refute_0_547]) ).
cnf(refute_0_549,plain,
join(join(X_76,one),join(one,complement(join(one,one)))) = join(one,join(complement(join(one,one)),join(X_76,one))),
inference(subst,[],[refute_0_541:[bind(A,$fot(join(X_76,one))),bind(X_76,$fot(one)),bind(X_77,$fot(complement(join(one,one))))]]) ).
cnf(refute_0_550,plain,
( join(join(X_76,one),join(one,complement(join(one,one)))) != join(one,join(complement(join(one,one)),join(X_76,one)))
| join(one,join(complement(join(one,one)),join(X_76,one))) != join(one,join(one,join(complement(join(one,one)),X_76)))
| join(join(X_76,one),join(one,complement(join(one,one)))) = join(one,join(one,join(complement(join(one,one)),X_76))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(X_76,one),join(one,complement(join(one,one)))))),bind(Y,$fot(join(one,join(complement(join(one,one)),join(X_76,one))))),bind(Z,$fot(join(one,join(one,join(complement(join(one,one)),X_76)))))]]) ).
cnf(refute_0_551,plain,
( join(one,join(complement(join(one,one)),join(X_76,one))) != join(one,join(one,join(complement(join(one,one)),X_76)))
| join(join(X_76,one),join(one,complement(join(one,one)))) = join(one,join(one,join(complement(join(one,one)),X_76))) ),
inference(resolve,[$cnf( $equal(join(join(X_76,one),join(one,complement(join(one,one)))),join(one,join(complement(join(one,one)),join(X_76,one)))) )],[refute_0_549,refute_0_550]) ).
cnf(refute_0_552,plain,
join(join(X_76,one),join(one,complement(join(one,one)))) = join(one,join(one,join(complement(join(one,one)),X_76))),
inference(resolve,[$cnf( $equal(join(one,join(complement(join(one,one)),join(X_76,one))),join(one,join(one,join(complement(join(one,one)),X_76)))) )],[refute_0_548,refute_0_551]) ).
cnf(refute_0_553,plain,
( join(X_76,top) != join(join(X_76,one),join(one,complement(join(one,one))))
| join(join(X_76,one),join(one,complement(join(one,one)))) != join(one,join(one,join(complement(join(one,one)),X_76)))
| join(X_76,top) = join(one,join(one,join(complement(join(one,one)),X_76))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_76,top),join(one,join(one,join(complement(join(one,one)),X_76)))) ),[0],$fot(join(join(X_76,one),join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_554,plain,
( join(X_76,top) != join(join(X_76,one),join(one,complement(join(one,one))))
| join(X_76,top) = join(one,join(one,join(complement(join(one,one)),X_76))) ),
inference(resolve,[$cnf( $equal(join(join(X_76,one),join(one,complement(join(one,one)))),join(one,join(one,join(complement(join(one,one)),X_76)))) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
join(X_76,top) = join(one,join(one,join(complement(join(one,one)),X_76))),
inference(resolve,[$cnf( $equal(join(X_76,top),join(join(X_76,one),join(one,complement(join(one,one))))) )],[refute_0_534,refute_0_554]) ).
cnf(refute_0_556,plain,
join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(join(A,join(X_83,complement(join(A,X_83)))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(B,$fot(join(X_83,complement(join(A,X_83)))))]]) ).
cnf(refute_0_557,plain,
top = join(join(X_76,X_77),complement(join(X_76,X_77))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(X_76,X_77)))]]) ).
cnf(refute_0_558,plain,
join(X_76,join(X_77,complement(join(X_76,X_77)))) = join(join(X_76,X_77),complement(join(X_76,X_77))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_76)),bind(B,$fot(X_77)),bind(C,$fot(complement(join(X_76,X_77))))]]) ).
cnf(refute_0_559,plain,
( join(X_76,join(X_77,complement(join(X_76,X_77)))) != join(join(X_76,X_77),complement(join(X_76,X_77)))
| join(join(X_76,X_77),complement(join(X_76,X_77))) = join(X_76,join(X_77,complement(join(X_76,X_77)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_76,join(X_77,complement(join(X_76,X_77)))))),bind(Y,$fot(join(join(X_76,X_77),complement(join(X_76,X_77)))))]]) ).
cnf(refute_0_560,plain,
join(join(X_76,X_77),complement(join(X_76,X_77))) = join(X_76,join(X_77,complement(join(X_76,X_77)))),
inference(resolve,[$cnf( $equal(join(X_76,join(X_77,complement(join(X_76,X_77)))),join(join(X_76,X_77),complement(join(X_76,X_77)))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
( join(join(X_76,X_77),complement(join(X_76,X_77))) != join(X_76,join(X_77,complement(join(X_76,X_77))))
| top != join(join(X_76,X_77),complement(join(X_76,X_77)))
| top = join(X_76,join(X_77,complement(join(X_76,X_77)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_76,X_77),complement(join(X_76,X_77)))) ),[1],$fot(join(X_76,join(X_77,complement(join(X_76,X_77)))))]]) ).
cnf(refute_0_562,plain,
( top != join(join(X_76,X_77),complement(join(X_76,X_77)))
| top = join(X_76,join(X_77,complement(join(X_76,X_77)))) ),
inference(resolve,[$cnf( $equal(join(join(X_76,X_77),complement(join(X_76,X_77))),join(X_76,join(X_77,complement(join(X_76,X_77))))) )],[refute_0_560,refute_0_561]) ).
cnf(refute_0_563,plain,
top = join(X_76,join(X_77,complement(join(X_76,X_77)))),
inference(resolve,[$cnf( $equal(top,join(join(X_76,X_77),complement(join(X_76,X_77)))) )],[refute_0_557,refute_0_562]) ).
cnf(refute_0_564,plain,
top = join(A,join(X_83,complement(join(A,X_83)))),
inference(subst,[],[refute_0_563:[bind(X_76,$fot(A)),bind(X_77,$fot(X_83))]]) ).
cnf(refute_0_565,plain,
( top != join(A,join(X_83,complement(join(A,X_83))))
| join(A,join(X_83,complement(join(A,X_83)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,join(X_83,complement(join(A,X_83))))))]]) ).
cnf(refute_0_566,plain,
join(A,join(X_83,complement(join(A,X_83)))) = top,
inference(resolve,[$cnf( $equal(top,join(A,join(X_83,complement(join(A,X_83))))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
( join(A,join(X_83,complement(join(A,X_83)))) != top
| join(A,join(join(X_83,complement(join(A,X_83))),C)) != join(join(A,join(X_83,complement(join(A,X_83)))),C)
| join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(X_83,complement(join(A,X_83))),C)),join(join(A,join(X_83,complement(join(A,X_83)))),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_568,plain,
( join(A,join(join(X_83,complement(join(A,X_83))),C)) != join(join(A,join(X_83,complement(join(A,X_83)))),C)
| join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(A,join(X_83,complement(join(A,X_83)))),top) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(top,C),
inference(resolve,[$cnf( $equal(join(A,join(join(X_83,complement(join(A,X_83))),C)),join(join(A,join(X_83,complement(join(A,X_83)))),C)) )],[refute_0_556,refute_0_568]) ).
cnf(refute_0_570,plain,
join(join(X_83,complement(join(A,X_83))),C) = join(X_83,join(complement(join(A,X_83)),C)),
inference(subst,[],[refute_0_283:[bind(A,$fot(X_83)),bind(B,$fot(complement(join(A,X_83))))]]) ).
cnf(refute_0_571,plain,
join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(A,join(join(X_83,complement(join(A,X_83))),C)),
introduced(tautology,[refl,[$fot(join(A,join(join(X_83,complement(join(A,X_83))),C)))]]) ).
cnf(refute_0_572,plain,
( join(A,join(join(X_83,complement(join(A,X_83))),C)) != join(A,join(join(X_83,complement(join(A,X_83))),C))
| join(join(X_83,complement(join(A,X_83))),C) != join(X_83,join(complement(join(A,X_83)),C))
| join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(A,join(X_83,join(complement(join(A,X_83)),C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(X_83,complement(join(A,X_83))),C)),join(A,join(join(X_83,complement(join(A,X_83))),C))) ),[1,1],$fot(join(X_83,join(complement(join(A,X_83)),C)))]]) ).
cnf(refute_0_573,plain,
( join(join(X_83,complement(join(A,X_83))),C) != join(X_83,join(complement(join(A,X_83)),C))
| join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(A,join(X_83,join(complement(join(A,X_83)),C))) ),
inference(resolve,[$cnf( $equal(join(A,join(join(X_83,complement(join(A,X_83))),C)),join(A,join(join(X_83,complement(join(A,X_83))),C))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
join(A,join(join(X_83,complement(join(A,X_83))),C)) = join(A,join(X_83,join(complement(join(A,X_83)),C))),
inference(resolve,[$cnf( $equal(join(join(X_83,complement(join(A,X_83))),C),join(X_83,join(complement(join(A,X_83)),C))) )],[refute_0_570,refute_0_573]) ).
cnf(refute_0_575,plain,
( join(A,join(join(X_83,complement(join(A,X_83))),C)) != join(A,join(X_83,join(complement(join(A,X_83)),C)))
| join(A,join(join(X_83,complement(join(A,X_83))),C)) != join(top,C)
| join(A,join(X_83,join(complement(join(A,X_83)),C))) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(X_83,complement(join(A,X_83))),C)),join(top,C)) ),[0],$fot(join(A,join(X_83,join(complement(join(A,X_83)),C))))]]) ).
cnf(refute_0_576,plain,
( join(A,join(join(X_83,complement(join(A,X_83))),C)) != join(top,C)
| join(A,join(X_83,join(complement(join(A,X_83)),C))) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(A,join(join(X_83,complement(join(A,X_83))),C)),join(A,join(X_83,join(complement(join(A,X_83)),C)))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
join(A,join(X_83,join(complement(join(A,X_83)),C))) = join(top,C),
inference(resolve,[$cnf( $equal(join(A,join(join(X_83,complement(join(A,X_83))),C)),join(top,C)) )],[refute_0_569,refute_0_576]) ).
cnf(refute_0_578,plain,
join(one,join(one,join(complement(join(one,one)),X_76))) = join(top,X_76),
inference(subst,[],[refute_0_577:[bind(A,$fot(one)),bind(C,$fot(X_76)),bind(X_83,$fot(one))]]) ).
cnf(refute_0_579,plain,
( join(X_76,top) != join(one,join(one,join(complement(join(one,one)),X_76)))
| join(one,join(one,join(complement(join(one,one)),X_76))) != join(top,X_76)
| join(X_76,top) = join(top,X_76) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_76,top),join(top,X_76)) ),[0],$fot(join(one,join(one,join(complement(join(one,one)),X_76))))]]) ).
cnf(refute_0_580,plain,
( join(X_76,top) != join(one,join(one,join(complement(join(one,one)),X_76)))
| join(X_76,top) = join(top,X_76) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(complement(join(one,one)),X_76))),join(top,X_76)) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
join(X_76,top) = join(top,X_76),
inference(resolve,[$cnf( $equal(join(X_76,top),join(one,join(one,join(complement(join(one,one)),X_76)))) )],[refute_0_555,refute_0_580]) ).
cnf(refute_0_582,plain,
join(complement(X_6),top) = join(top,complement(X_6)),
inference(subst,[],[refute_0_581:[bind(X_76,$fot(complement(X_6)))]]) ).
cnf(refute_0_583,plain,
( join(complement(X_6),top) != join(top,complement(X_6))
| top != join(complement(X_6),top)
| top = join(top,complement(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_6),top)) ),[1],$fot(join(top,complement(X_6)))]]) ).
cnf(refute_0_584,plain,
( top != join(complement(X_6),top)
| top = join(top,complement(X_6)) ),
inference(resolve,[$cnf( $equal(join(complement(X_6),top),join(top,complement(X_6))) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
top = join(top,complement(X_6)),
inference(resolve,[$cnf( $equal(top,join(complement(X_6),top)) )],[refute_0_446,refute_0_584]) ).
cnf(refute_0_586,plain,
( top != join(top,complement(X_6))
| join(top,complement(X_6)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_6))))]]) ).
cnf(refute_0_587,plain,
join(top,complement(X_6)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_6))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
join(top,complement(B)) = top,
inference(subst,[],[refute_0_587:[bind(X_6,$fot(B))]]) ).
cnf(refute_0_589,plain,
complement(join(top,complement(B))) = complement(join(top,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(top,complement(B))))]]) ).
cnf(refute_0_590,plain,
( complement(join(top,complement(B))) != complement(join(top,complement(B)))
| join(top,complement(B)) != top
| complement(join(top,complement(B))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,complement(B))),complement(join(top,complement(B)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_591,plain,
( join(top,complement(B)) != top
| complement(join(top,complement(B))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),complement(join(top,complement(B)))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
complement(join(top,complement(B))) = complement(top),
inference(resolve,[$cnf( $equal(join(top,complement(B)),top) )],[refute_0_588,refute_0_591]) ).
cnf(refute_0_593,plain,
( complement(join(top,complement(B))) != complement(top)
| complement(top) != zero
| complement(join(top,complement(B))) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(join(top,complement(B))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_594,plain,
( complement(top) != zero
| complement(join(top,complement(B))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),complement(top)) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
complement(join(top,complement(B))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_594]) ).
cnf(refute_0_596,plain,
( complement(join(top,complement(B))) != zero
| meet(zero,B) != complement(join(top,complement(B)))
| meet(zero,B) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,B),complement(join(top,complement(B)))) ),[1],$fot(zero)]]) ).
cnf(refute_0_597,plain,
( meet(zero,B) != complement(join(top,complement(B)))
| meet(zero,B) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),zero) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
meet(zero,B) = zero,
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(top,complement(B)))) )],[refute_0_371,refute_0_597]) ).
cnf(refute_0_599,plain,
meet(zero,X_38) = zero,
inference(subst,[],[refute_0_598:[bind(B,$fot(X_38))]]) ).
cnf(refute_0_600,plain,
join(meet(top,X_38),meet(zero,X_38)) = join(meet(top,X_38),meet(zero,X_38)),
introduced(tautology,[refl,[$fot(join(meet(top,X_38),meet(zero,X_38)))]]) ).
cnf(refute_0_601,plain,
( join(meet(top,X_38),meet(zero,X_38)) != join(meet(top,X_38),meet(zero,X_38))
| meet(zero,X_38) != zero
| join(meet(top,X_38),meet(zero,X_38)) = join(meet(top,X_38),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_38),meet(zero,X_38)),join(meet(top,X_38),meet(zero,X_38))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_602,plain,
( meet(zero,X_38) != zero
| join(meet(top,X_38),meet(zero,X_38)) = join(meet(top,X_38),zero) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),meet(zero,X_38)),join(meet(top,X_38),meet(zero,X_38))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
join(meet(top,X_38),meet(zero,X_38)) = join(meet(top,X_38),zero),
inference(resolve,[$cnf( $equal(meet(zero,X_38),zero) )],[refute_0_599,refute_0_602]) ).
cnf(refute_0_604,plain,
( join(meet(top,X_38),meet(zero,X_38)) != join(meet(top,X_38),zero)
| join(meet(top,X_38),zero) != join(zero,meet(top,X_38))
| join(meet(top,X_38),meet(zero,X_38)) = join(zero,meet(top,X_38)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(top,X_38),meet(zero,X_38)))),bind(Y,$fot(join(meet(top,X_38),zero))),bind(Z,$fot(join(zero,meet(top,X_38))))]]) ).
cnf(refute_0_605,plain,
( join(meet(top,X_38),zero) != join(zero,meet(top,X_38))
| join(meet(top,X_38),meet(zero,X_38)) = join(zero,meet(top,X_38)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),meet(zero,X_38)),join(meet(top,X_38),zero)) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
join(meet(top,X_38),meet(zero,X_38)) = join(zero,meet(top,X_38)),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),zero),join(zero,meet(top,X_38))) )],[refute_0_275,refute_0_605]) ).
cnf(refute_0_607,plain,
( X_38 != join(meet(top,X_38),meet(zero,X_38))
| join(meet(top,X_38),meet(zero,X_38)) != join(zero,meet(top,X_38))
| X_38 = join(zero,meet(top,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_38,join(zero,meet(top,X_38))) ),[0],$fot(join(meet(top,X_38),meet(zero,X_38)))]]) ).
cnf(refute_0_608,plain,
( X_38 != join(meet(top,X_38),meet(zero,X_38))
| X_38 = join(zero,meet(top,X_38)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),meet(zero,X_38)),join(zero,meet(top,X_38))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
X_38 = join(zero,meet(top,X_38)),
inference(resolve,[$cnf( $equal(X_38,join(meet(top,X_38),meet(zero,X_38))) )],[refute_0_274,refute_0_608]) ).
cnf(refute_0_610,plain,
meet(top,join(zero,complement(X_10))) = complement(join(zero,complement(join(zero,complement(X_10))))),
inference(subst,[],[refute_0_153:[bind(B,$fot(join(zero,complement(X_10))))]]) ).
cnf(refute_0_611,plain,
( complement(join(zero,complement(X_10))) != meet(top,X_10)
| meet(top,join(zero,complement(X_10))) != complement(join(zero,complement(join(zero,complement(X_10)))))
| meet(top,join(zero,complement(X_10))) = complement(join(zero,meet(top,X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,complement(X_10))),complement(join(zero,complement(join(zero,complement(X_10)))))) ),[1,0,1],$fot(meet(top,X_10))]]) ).
cnf(refute_0_612,plain,
( meet(top,join(zero,complement(X_10))) != complement(join(zero,complement(join(zero,complement(X_10)))))
| meet(top,join(zero,complement(X_10))) = complement(join(zero,meet(top,X_10))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_10))),meet(top,X_10)) )],[refute_0_190,refute_0_611]) ).
cnf(refute_0_613,plain,
meet(top,join(zero,complement(X_10))) = complement(join(zero,meet(top,X_10))),
inference(resolve,[$cnf( $equal(meet(top,join(zero,complement(X_10))),complement(join(zero,complement(join(zero,complement(X_10)))))) )],[refute_0_610,refute_0_612]) ).
cnf(refute_0_614,plain,
meet(top,join(zero,complement(X_10))) = meet(top,complement(meet(top,X_10))),
inference(subst,[],[refute_0_241:[bind(A,$fot(top))]]) ).
cnf(refute_0_615,plain,
( meet(top,join(zero,complement(X_10))) != complement(join(zero,meet(top,X_10)))
| meet(top,join(zero,complement(X_10))) != meet(top,complement(meet(top,X_10)))
| meet(top,complement(meet(top,X_10))) = complement(join(zero,meet(top,X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,complement(X_10))),complement(join(zero,meet(top,X_10)))) ),[0],$fot(meet(top,complement(meet(top,X_10))))]]) ).
cnf(refute_0_616,plain,
( meet(top,join(zero,complement(X_10))) != complement(join(zero,meet(top,X_10)))
| meet(top,complement(meet(top,X_10))) = complement(join(zero,meet(top,X_10))) ),
inference(resolve,[$cnf( $equal(meet(top,join(zero,complement(X_10))),meet(top,complement(meet(top,X_10)))) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
meet(top,complement(meet(top,X_10))) = complement(join(zero,meet(top,X_10))),
inference(resolve,[$cnf( $equal(meet(top,join(zero,complement(X_10))),complement(join(zero,meet(top,X_10)))) )],[refute_0_613,refute_0_616]) ).
cnf(refute_0_618,plain,
( X_38 != join(zero,meet(top,X_38))
| join(zero,meet(top,X_38)) = X_38 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_38)),bind(Y,$fot(join(zero,meet(top,X_38))))]]) ).
cnf(refute_0_619,plain,
join(zero,meet(top,X_38)) = X_38,
inference(resolve,[$cnf( $equal(X_38,join(zero,meet(top,X_38))) )],[refute_0_609,refute_0_618]) ).
cnf(refute_0_620,plain,
join(zero,meet(top,X_10)) = X_10,
inference(subst,[],[refute_0_619:[bind(X_38,$fot(X_10))]]) ).
cnf(refute_0_621,plain,
complement(join(zero,meet(top,X_10))) = complement(join(zero,meet(top,X_10))),
introduced(tautology,[refl,[$fot(complement(join(zero,meet(top,X_10))))]]) ).
cnf(refute_0_622,plain,
( complement(join(zero,meet(top,X_10))) != complement(join(zero,meet(top,X_10)))
| join(zero,meet(top,X_10)) != X_10
| complement(join(zero,meet(top,X_10))) = complement(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,meet(top,X_10))),complement(join(zero,meet(top,X_10)))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_623,plain,
( join(zero,meet(top,X_10)) != X_10
| complement(join(zero,meet(top,X_10))) = complement(X_10) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,X_10))),complement(join(zero,meet(top,X_10)))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
complement(join(zero,meet(top,X_10))) = complement(X_10),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_10)),X_10) )],[refute_0_620,refute_0_623]) ).
cnf(refute_0_625,plain,
( complement(join(zero,meet(top,X_10))) != complement(X_10)
| meet(top,complement(meet(top,X_10))) != complement(join(zero,meet(top,X_10)))
| meet(top,complement(meet(top,X_10))) = complement(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(meet(top,X_10))),complement(join(zero,meet(top,X_10)))) ),[1],$fot(complement(X_10))]]) ).
cnf(refute_0_626,plain,
( meet(top,complement(meet(top,X_10))) != complement(join(zero,meet(top,X_10)))
| meet(top,complement(meet(top,X_10))) = complement(X_10) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,X_10))),complement(X_10)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
meet(top,complement(meet(top,X_10))) = complement(X_10),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(top,X_10))),complement(join(zero,meet(top,X_10)))) )],[refute_0_617,refute_0_626]) ).
cnf(refute_0_628,plain,
meet(top,X_33) = join(meet(meet(top,X_33),join(zero,complement(X_33))),complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))),
inference(subst,[],[refute_0_38:[bind(A,$fot(meet(top,X_33))),bind(B,$fot(join(zero,complement(X_33))))]]) ).
cnf(refute_0_629,plain,
zero = meet(join(zero,complement(X_10)),complement(join(zero,complement(X_10)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(zero,complement(X_10))))]]) ).
cnf(refute_0_630,plain,
( complement(join(zero,complement(X_10))) != meet(top,X_10)
| zero != meet(join(zero,complement(X_10)),complement(join(zero,complement(X_10))))
| zero = meet(join(zero,complement(X_10)),meet(top,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,complement(X_10)),complement(join(zero,complement(X_10))))) ),[1,1],$fot(meet(top,X_10))]]) ).
cnf(refute_0_631,plain,
( zero != meet(join(zero,complement(X_10)),complement(join(zero,complement(X_10))))
| zero = meet(join(zero,complement(X_10)),meet(top,X_10)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_10))),meet(top,X_10)) )],[refute_0_190,refute_0_630]) ).
cnf(refute_0_632,plain,
zero = meet(join(zero,complement(X_10)),meet(top,X_10)),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,complement(X_10)),complement(join(zero,complement(X_10))))) )],[refute_0_629,refute_0_631]) ).
cnf(refute_0_633,plain,
meet(join(zero,complement(X_10)),meet(top,X_10)) = meet(meet(top,X_10),join(zero,complement(X_10))),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(meet(top,X_10))),bind(X_7,$fot(join(zero,complement(X_10))))]]) ).
cnf(refute_0_634,plain,
( meet(join(zero,complement(X_10)),meet(top,X_10)) != meet(meet(top,X_10),join(zero,complement(X_10)))
| zero != meet(join(zero,complement(X_10)),meet(top,X_10))
| zero = meet(meet(top,X_10),join(zero,complement(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,complement(X_10)),meet(top,X_10))) ),[1],$fot(meet(meet(top,X_10),join(zero,complement(X_10))))]]) ).
cnf(refute_0_635,plain,
( zero != meet(join(zero,complement(X_10)),meet(top,X_10))
| zero = meet(meet(top,X_10),join(zero,complement(X_10))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_10)),meet(top,X_10)),meet(meet(top,X_10),join(zero,complement(X_10)))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
zero = meet(meet(top,X_10),join(zero,complement(X_10))),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,complement(X_10)),meet(top,X_10))) )],[refute_0_632,refute_0_635]) ).
cnf(refute_0_637,plain,
zero = meet(meet(top,X_33),join(zero,complement(X_33))),
inference(subst,[],[refute_0_636:[bind(X_10,$fot(X_33))]]) ).
cnf(refute_0_638,plain,
( zero != meet(meet(top,X_33),join(zero,complement(X_33)))
| meet(meet(top,X_33),join(zero,complement(X_33))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(meet(top,X_33),join(zero,complement(X_33)))))]]) ).
cnf(refute_0_639,plain,
meet(meet(top,X_33),join(zero,complement(X_33))) = zero,
inference(resolve,[$cnf( $equal(zero,meet(meet(top,X_33),join(zero,complement(X_33)))) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
( meet(meet(top,X_33),join(zero,complement(X_33))) != zero
| meet(top,X_33) != join(meet(meet(top,X_33),join(zero,complement(X_33))),complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))
| meet(top,X_33) = join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_33),join(meet(meet(top,X_33),join(zero,complement(X_33))),complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_641,plain,
( meet(top,X_33) != join(meet(meet(top,X_33),join(zero,complement(X_33))),complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))
| meet(top,X_33) = join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) ),
inference(resolve,[$cnf( $equal(meet(meet(top,X_33),join(zero,complement(X_33))),zero) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
meet(top,X_33) = join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))),
inference(resolve,[$cnf( $equal(meet(top,X_33),join(meet(meet(top,X_33),join(zero,complement(X_33))),complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))) )],[refute_0_628,refute_0_641]) ).
cnf(refute_0_643,plain,
join(complement(meet(top,X_33)),complement(meet(top,X_33))) = complement(meet(meet(top,X_33),meet(top,X_33))),
inference(subst,[],[refute_0_227:[bind(A,$fot(meet(top,X_33))),bind(B,$fot(meet(top,X_33)))]]) ).
cnf(refute_0_644,plain,
join(zero,complement(X_33)) = complement(meet(top,X_33)),
inference(subst,[],[refute_0_252:[bind(B,$fot(X_33))]]) ).
cnf(refute_0_645,plain,
join(complement(meet(top,X_33)),join(zero,complement(X_33))) = join(complement(meet(top,X_33)),join(zero,complement(X_33))),
introduced(tautology,[refl,[$fot(join(complement(meet(top,X_33)),join(zero,complement(X_33))))]]) ).
cnf(refute_0_646,plain,
( join(complement(meet(top,X_33)),join(zero,complement(X_33))) != join(complement(meet(top,X_33)),join(zero,complement(X_33)))
| join(zero,complement(X_33)) != complement(meet(top,X_33))
| join(complement(meet(top,X_33)),join(zero,complement(X_33))) = join(complement(meet(top,X_33)),complement(meet(top,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(meet(top,X_33)),join(zero,complement(X_33))),join(complement(meet(top,X_33)),join(zero,complement(X_33)))) ),[1,1],$fot(complement(meet(top,X_33)))]]) ).
cnf(refute_0_647,plain,
( join(zero,complement(X_33)) != complement(meet(top,X_33))
| join(complement(meet(top,X_33)),join(zero,complement(X_33))) = join(complement(meet(top,X_33)),complement(meet(top,X_33))) ),
inference(resolve,[$cnf( $equal(join(complement(meet(top,X_33)),join(zero,complement(X_33))),join(complement(meet(top,X_33)),join(zero,complement(X_33)))) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
join(complement(meet(top,X_33)),join(zero,complement(X_33))) = join(complement(meet(top,X_33)),complement(meet(top,X_33))),
inference(resolve,[$cnf( $equal(join(zero,complement(X_33)),complement(meet(top,X_33))) )],[refute_0_644,refute_0_647]) ).
cnf(refute_0_649,plain,
( join(complement(meet(top,X_33)),complement(meet(top,X_33))) != complement(meet(meet(top,X_33),meet(top,X_33)))
| join(complement(meet(top,X_33)),join(zero,complement(X_33))) != join(complement(meet(top,X_33)),complement(meet(top,X_33)))
| join(complement(meet(top,X_33)),join(zero,complement(X_33))) = complement(meet(meet(top,X_33),meet(top,X_33))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(meet(top,X_33)),join(zero,complement(X_33))))),bind(Y,$fot(join(complement(meet(top,X_33)),complement(meet(top,X_33))))),bind(Z,$fot(complement(meet(meet(top,X_33),meet(top,X_33)))))]]) ).
cnf(refute_0_650,plain,
( join(complement(meet(top,X_33)),complement(meet(top,X_33))) != complement(meet(meet(top,X_33),meet(top,X_33)))
| join(complement(meet(top,X_33)),join(zero,complement(X_33))) = complement(meet(meet(top,X_33),meet(top,X_33))) ),
inference(resolve,[$cnf( $equal(join(complement(meet(top,X_33)),join(zero,complement(X_33))),join(complement(meet(top,X_33)),complement(meet(top,X_33)))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
join(complement(meet(top,X_33)),join(zero,complement(X_33))) = complement(meet(meet(top,X_33),meet(top,X_33))),
inference(resolve,[$cnf( $equal(join(complement(meet(top,X_33)),complement(meet(top,X_33))),complement(meet(meet(top,X_33),meet(top,X_33)))) )],[refute_0_643,refute_0_650]) ).
cnf(refute_0_652,plain,
meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))) = meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))),
introduced(tautology,[refl,[$fot(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))))]]) ).
cnf(refute_0_653,plain,
( join(complement(meet(top,X_33)),join(zero,complement(X_33))) != complement(meet(meet(top,X_33),meet(top,X_33)))
| meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))) != meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))
| meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))) = meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))),meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) ),[1,1],$fot(complement(meet(meet(top,X_33),meet(top,X_33))))]]) ).
cnf(refute_0_654,plain,
( join(complement(meet(top,X_33)),join(zero,complement(X_33))) != complement(meet(meet(top,X_33),meet(top,X_33)))
| meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))) = meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))),meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))) = meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))),
inference(resolve,[$cnf( $equal(join(complement(meet(top,X_33)),join(zero,complement(X_33))),complement(meet(meet(top,X_33),meet(top,X_33)))) )],[refute_0_651,refute_0_654]) ).
cnf(refute_0_656,plain,
complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))),
introduced(tautology,[refl,[$fot(complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))))]]) ).
cnf(refute_0_657,plain,
( complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) != complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))))
| meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))) != meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))
| complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))),complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))))) ),[1,0],$fot(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))]]) ).
cnf(refute_0_658,plain,
( meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))) != meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))
| complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) ),
inference(resolve,[$cnf( $equal(complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))),complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))))) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))),
inference(resolve,[$cnf( $equal(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))),meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) )],[refute_0_655,refute_0_658]) ).
cnf(refute_0_660,plain,
join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))),
inference(subst,[],[refute_0_252:[bind(B,$fot(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))]]) ).
cnf(refute_0_661,plain,
( complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) != complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))
| join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) != complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))))
| join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))))),bind(Y,$fot(complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))))),bind(Z,$fot(complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))))]]) ).
cnf(refute_0_662,plain,
( complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))) != complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))
| join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))),complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33)))))) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))),
inference(resolve,[$cnf( $equal(complement(meet(top,join(complement(meet(top,X_33)),join(zero,complement(X_33))))),complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))) )],[refute_0_659,refute_0_662]) ).
cnf(refute_0_664,plain,
( join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))) != complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))
| meet(top,X_33) != join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))
| meet(top,X_33) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_33),join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))) ),[1],$fot(complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))))]]) ).
cnf(refute_0_665,plain,
( meet(top,X_33) != join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))
| meet(top,X_33) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33))))),complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
meet(top,X_33) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))),
inference(resolve,[$cnf( $equal(meet(top,X_33),join(zero,complement(join(complement(meet(top,X_33)),join(zero,complement(X_33)))))) )],[refute_0_642,refute_0_665]) ).
cnf(refute_0_667,plain,
meet(top,complement(meet(top,X_33))) = complement(join(zero,meet(top,X_33))),
inference(subst,[],[refute_0_617:[bind(X_10,$fot(X_33))]]) ).
cnf(refute_0_668,plain,
complement(meet(meet(top,X_33),meet(top,X_33))) = complement(meet(top,X_33)),
inference(subst,[],[refute_0_432:[bind(X_91,$fot(meet(top,X_33)))]]) ).
cnf(refute_0_669,plain,
meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) = meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))),
introduced(tautology,[refl,[$fot(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))]]) ).
cnf(refute_0_670,plain,
( complement(meet(meet(top,X_33),meet(top,X_33))) != complement(meet(top,X_33))
| meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) != meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))
| meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) = meet(top,complement(meet(top,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))),meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) ),[1,1],$fot(complement(meet(top,X_33)))]]) ).
cnf(refute_0_671,plain,
( complement(meet(meet(top,X_33),meet(top,X_33))) != complement(meet(top,X_33))
| meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) = meet(top,complement(meet(top,X_33))) ),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))),meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) = meet(top,complement(meet(top,X_33))),
inference(resolve,[$cnf( $equal(complement(meet(meet(top,X_33),meet(top,X_33))),complement(meet(top,X_33))) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
( meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) != meet(top,complement(meet(top,X_33)))
| meet(top,complement(meet(top,X_33))) != complement(join(zero,meet(top,X_33)))
| meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) = complement(join(zero,meet(top,X_33))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))),bind(Y,$fot(meet(top,complement(meet(top,X_33))))),bind(Z,$fot(complement(join(zero,meet(top,X_33)))))]]) ).
cnf(refute_0_674,plain,
( meet(top,complement(meet(top,X_33))) != complement(join(zero,meet(top,X_33)))
| meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) = complement(join(zero,meet(top,X_33))) ),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))),meet(top,complement(meet(top,X_33)))) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) = complement(join(zero,meet(top,X_33))),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(top,X_33))),complement(join(zero,meet(top,X_33)))) )],[refute_0_667,refute_0_674]) ).
cnf(refute_0_676,plain,
complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) = complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))),
introduced(tautology,[refl,[$fot(complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))))]]) ).
cnf(refute_0_677,plain,
( complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) != complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))
| meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) != complement(join(zero,meet(top,X_33)))
| complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) = complement(complement(join(zero,meet(top,X_33)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))),complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))) ),[1,0],$fot(complement(join(zero,meet(top,X_33))))]]) ).
cnf(refute_0_678,plain,
( meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))) != complement(join(zero,meet(top,X_33)))
| complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) = complement(complement(join(zero,meet(top,X_33)))) ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))),complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) = complement(complement(join(zero,meet(top,X_33)))),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))),complement(join(zero,meet(top,X_33)))) )],[refute_0_675,refute_0_678]) ).
cnf(refute_0_680,plain,
( complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))) != complement(complement(join(zero,meet(top,X_33))))
| meet(top,X_33) != complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))
| meet(top,X_33) = complement(complement(join(zero,meet(top,X_33)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_33),complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))) ),[1],$fot(complement(complement(join(zero,meet(top,X_33)))))]]) ).
cnf(refute_0_681,plain,
( meet(top,X_33) != complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))
| meet(top,X_33) = complement(complement(join(zero,meet(top,X_33)))) ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33))))),complement(complement(join(zero,meet(top,X_33))))) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
meet(top,X_33) = complement(complement(join(zero,meet(top,X_33)))),
inference(resolve,[$cnf( $equal(meet(top,X_33),complement(meet(top,complement(meet(meet(top,X_33),meet(top,X_33)))))) )],[refute_0_666,refute_0_681]) ).
cnf(refute_0_683,plain,
join(zero,meet(top,X_33)) = X_33,
inference(subst,[],[refute_0_619:[bind(X_38,$fot(X_33))]]) ).
cnf(refute_0_684,plain,
complement(join(zero,meet(top,X_33))) = complement(join(zero,meet(top,X_33))),
introduced(tautology,[refl,[$fot(complement(join(zero,meet(top,X_33))))]]) ).
cnf(refute_0_685,plain,
( complement(join(zero,meet(top,X_33))) != complement(join(zero,meet(top,X_33)))
| join(zero,meet(top,X_33)) != X_33
| complement(join(zero,meet(top,X_33))) = complement(X_33) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,meet(top,X_33))),complement(join(zero,meet(top,X_33)))) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_686,plain,
( join(zero,meet(top,X_33)) != X_33
| complement(join(zero,meet(top,X_33))) = complement(X_33) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,X_33))),complement(join(zero,meet(top,X_33)))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
complement(join(zero,meet(top,X_33))) = complement(X_33),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_33)),X_33) )],[refute_0_683,refute_0_686]) ).
cnf(refute_0_688,plain,
complement(complement(join(zero,meet(top,X_33)))) = complement(complement(join(zero,meet(top,X_33)))),
introduced(tautology,[refl,[$fot(complement(complement(join(zero,meet(top,X_33)))))]]) ).
cnf(refute_0_689,plain,
( complement(complement(join(zero,meet(top,X_33)))) != complement(complement(join(zero,meet(top,X_33))))
| complement(join(zero,meet(top,X_33))) != complement(X_33)
| complement(complement(join(zero,meet(top,X_33)))) = complement(complement(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(join(zero,meet(top,X_33)))),complement(complement(join(zero,meet(top,X_33))))) ),[1,0],$fot(complement(X_33))]]) ).
cnf(refute_0_690,plain,
( complement(join(zero,meet(top,X_33))) != complement(X_33)
| complement(complement(join(zero,meet(top,X_33)))) = complement(complement(X_33)) ),
inference(resolve,[$cnf( $equal(complement(complement(join(zero,meet(top,X_33)))),complement(complement(join(zero,meet(top,X_33))))) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
complement(complement(join(zero,meet(top,X_33)))) = complement(complement(X_33)),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,X_33))),complement(X_33)) )],[refute_0_687,refute_0_690]) ).
cnf(refute_0_692,plain,
( complement(complement(join(zero,meet(top,X_33)))) != complement(complement(X_33))
| meet(top,X_33) != complement(complement(join(zero,meet(top,X_33))))
| meet(top,X_33) = complement(complement(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_33),complement(complement(join(zero,meet(top,X_33))))) ),[1],$fot(complement(complement(X_33)))]]) ).
cnf(refute_0_693,plain,
( meet(top,X_33) != complement(complement(join(zero,meet(top,X_33))))
| meet(top,X_33) = complement(complement(X_33)) ),
inference(resolve,[$cnf( $equal(complement(complement(join(zero,meet(top,X_33)))),complement(complement(X_33))) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
meet(top,X_33) = complement(complement(X_33)),
inference(resolve,[$cnf( $equal(meet(top,X_33),complement(complement(join(zero,meet(top,X_33))))) )],[refute_0_682,refute_0_693]) ).
cnf(refute_0_695,plain,
meet(top,X_10) = complement(complement(X_10)),
inference(subst,[],[refute_0_694:[bind(X_33,$fot(X_10))]]) ).
cnf(refute_0_696,plain,
complement(join(complement(A),complement(B))) = complement(join(complement(A),complement(B))),
introduced(tautology,[refl,[$fot(complement(join(complement(A),complement(B))))]]) ).
cnf(refute_0_697,plain,
( complement(join(complement(A),complement(B))) != complement(join(complement(A),complement(B)))
| join(complement(A),complement(B)) != complement(meet(A,B))
| complement(join(complement(A),complement(B))) = complement(complement(meet(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(B)))) ),[1,0],$fot(complement(meet(A,B)))]]) ).
cnf(refute_0_698,plain,
( join(complement(A),complement(B)) != complement(meet(A,B))
| complement(join(complement(A),complement(B))) = complement(complement(meet(A,B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(B)))) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
complement(join(complement(A),complement(B))) = complement(complement(meet(A,B))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),complement(meet(A,B))) )],[refute_0_227,refute_0_698]) ).
cnf(refute_0_700,plain,
( complement(join(complement(A),complement(B))) != complement(complement(meet(A,B)))
| meet(A,B) != complement(join(complement(A),complement(B)))
| meet(A,B) = complement(complement(meet(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) ),[1],$fot(complement(complement(meet(A,B))))]]) ).
cnf(refute_0_701,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| meet(A,B) = complement(complement(meet(A,B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),complement(complement(meet(A,B)))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
meet(A,B) = complement(complement(meet(A,B))),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_701]) ).
cnf(refute_0_703,plain,
( meet(A,B) != complement(complement(meet(A,B)))
| complement(complement(meet(A,B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_704,plain,
complement(complement(meet(A,B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(complement(meet(A,B)))) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
complement(complement(meet(top,X_10))) = meet(top,X_10),
inference(subst,[],[refute_0_704:[bind(A,$fot(top)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_706,plain,
( complement(complement(meet(top,X_10))) != meet(top,X_10)
| meet(top,X_10) != complement(complement(X_10))
| complement(complement(meet(top,X_10))) = complement(complement(X_10)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(complement(meet(top,X_10))))),bind(Y,$fot(meet(top,X_10))),bind(Z,$fot(complement(complement(X_10))))]]) ).
cnf(refute_0_707,plain,
( meet(top,X_10) != complement(complement(X_10))
| complement(complement(meet(top,X_10))) = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(complement(complement(meet(top,X_10))),meet(top,X_10)) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
complement(complement(meet(top,X_10))) = complement(complement(X_10)),
inference(resolve,[$cnf( $equal(meet(top,X_10),complement(complement(X_10))) )],[refute_0_695,refute_0_707]) ).
cnf(refute_0_709,plain,
complement(complement(complement(meet(top,X_10)))) = complement(complement(complement(meet(top,X_10)))),
introduced(tautology,[refl,[$fot(complement(complement(complement(meet(top,X_10)))))]]) ).
cnf(refute_0_710,plain,
( complement(complement(complement(meet(top,X_10)))) != complement(complement(complement(meet(top,X_10))))
| complement(complement(meet(top,X_10))) != complement(complement(X_10))
| complement(complement(complement(meet(top,X_10)))) = complement(complement(complement(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(complement(meet(top,X_10)))),complement(complement(complement(meet(top,X_10))))) ),[1,0],$fot(complement(complement(X_10)))]]) ).
cnf(refute_0_711,plain,
( complement(complement(meet(top,X_10))) != complement(complement(X_10))
| complement(complement(complement(meet(top,X_10)))) = complement(complement(complement(X_10))) ),
inference(resolve,[$cnf( $equal(complement(complement(complement(meet(top,X_10)))),complement(complement(complement(meet(top,X_10))))) )],[refute_0_709,refute_0_710]) ).
cnf(refute_0_712,plain,
complement(complement(complement(meet(top,X_10)))) = complement(complement(complement(X_10))),
inference(resolve,[$cnf( $equal(complement(complement(meet(top,X_10))),complement(complement(X_10))) )],[refute_0_708,refute_0_711]) ).
cnf(refute_0_713,plain,
meet(top,complement(meet(top,X_10))) = complement(complement(complement(meet(top,X_10)))),
inference(subst,[],[refute_0_694:[bind(X_33,$fot(complement(meet(top,X_10))))]]) ).
cnf(refute_0_714,plain,
( complement(complement(complement(meet(top,X_10)))) != complement(complement(complement(X_10)))
| meet(top,complement(meet(top,X_10))) != complement(complement(complement(meet(top,X_10))))
| meet(top,complement(meet(top,X_10))) = complement(complement(complement(X_10))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(top,complement(meet(top,X_10))))),bind(Y,$fot(complement(complement(complement(meet(top,X_10)))))),bind(Z,$fot(complement(complement(complement(X_10)))))]]) ).
cnf(refute_0_715,plain,
( complement(complement(complement(meet(top,X_10)))) != complement(complement(complement(X_10)))
| meet(top,complement(meet(top,X_10))) = complement(complement(complement(X_10))) ),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(top,X_10))),complement(complement(complement(meet(top,X_10))))) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
meet(top,complement(meet(top,X_10))) = complement(complement(complement(X_10))),
inference(resolve,[$cnf( $equal(complement(complement(complement(meet(top,X_10)))),complement(complement(complement(X_10)))) )],[refute_0_712,refute_0_715]) ).
cnf(refute_0_717,plain,
( meet(top,complement(meet(top,X_10))) != complement(X_10)
| meet(top,complement(meet(top,X_10))) != complement(complement(complement(X_10)))
| complement(complement(complement(X_10))) = complement(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(meet(top,X_10))),complement(X_10)) ),[0],$fot(complement(complement(complement(X_10))))]]) ).
cnf(refute_0_718,plain,
( meet(top,complement(meet(top,X_10))) != complement(X_10)
| complement(complement(complement(X_10))) = complement(X_10) ),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(top,X_10))),complement(complement(complement(X_10)))) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
complement(complement(complement(X_10))) = complement(X_10),
inference(resolve,[$cnf( $equal(meet(top,complement(meet(top,X_10))),complement(X_10)) )],[refute_0_627,refute_0_718]) ).
cnf(refute_0_720,plain,
complement(complement(complement(B))) = complement(B),
inference(subst,[],[refute_0_719:[bind(X_10,$fot(B))]]) ).
cnf(refute_0_721,plain,
meet(top,B) = complement(complement(B)),
inference(subst,[],[refute_0_694:[bind(X_33,$fot(B))]]) ).
cnf(refute_0_722,plain,
complement(meet(top,B)) = complement(meet(top,B)),
introduced(tautology,[refl,[$fot(complement(meet(top,B)))]]) ).
cnf(refute_0_723,plain,
( complement(meet(top,B)) != complement(meet(top,B))
| meet(top,B) != complement(complement(B))
| complement(meet(top,B)) = complement(complement(complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,B)),complement(meet(top,B))) ),[1,0],$fot(complement(complement(B)))]]) ).
cnf(refute_0_724,plain,
( meet(top,B) != complement(complement(B))
| complement(meet(top,B)) = complement(complement(complement(B))) ),
inference(resolve,[$cnf( $equal(complement(meet(top,B)),complement(meet(top,B))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
complement(meet(top,B)) = complement(complement(complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(complement(B))) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
( complement(complement(complement(B))) != complement(B)
| complement(meet(top,B)) != complement(complement(complement(B)))
| complement(meet(top,B)) = complement(B) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(meet(top,B)))),bind(Y,$fot(complement(complement(complement(B))))),bind(Z,$fot(complement(B)))]]) ).
cnf(refute_0_727,plain,
( complement(complement(complement(B))) != complement(B)
| complement(meet(top,B)) = complement(B) ),
inference(resolve,[$cnf( $equal(complement(meet(top,B)),complement(complement(complement(B)))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
complement(meet(top,B)) = complement(B),
inference(resolve,[$cnf( $equal(complement(complement(complement(B))),complement(B)) )],[refute_0_720,refute_0_727]) ).
cnf(refute_0_729,plain,
( complement(meet(top,B)) != complement(B)
| join(zero,complement(B)) != complement(meet(top,B))
| join(zero,complement(B)) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),complement(meet(top,B))) ),[1],$fot(complement(B))]]) ).
cnf(refute_0_730,plain,
( join(zero,complement(B)) != complement(meet(top,B))
| join(zero,complement(B)) = complement(B) ),
inference(resolve,[$cnf( $equal(complement(meet(top,B)),complement(B)) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
join(zero,complement(B)) = complement(B),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(meet(top,B))) )],[refute_0_252,refute_0_730]) ).
cnf(refute_0_732,plain,
join(zero,complement(complement(X_38))) = complement(complement(X_38)),
inference(subst,[],[refute_0_731:[bind(B,$fot(complement(X_38)))]]) ).
cnf(refute_0_733,plain,
meet(top,X_38) = complement(complement(X_38)),
inference(subst,[],[refute_0_694:[bind(X_33,$fot(X_38))]]) ).
cnf(refute_0_734,plain,
join(zero,meet(top,X_38)) = join(zero,meet(top,X_38)),
introduced(tautology,[refl,[$fot(join(zero,meet(top,X_38)))]]) ).
cnf(refute_0_735,plain,
( join(zero,meet(top,X_38)) != join(zero,meet(top,X_38))
| meet(top,X_38) != complement(complement(X_38))
| join(zero,meet(top,X_38)) = join(zero,complement(complement(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(top,X_38)),join(zero,meet(top,X_38))) ),[1,1],$fot(complement(complement(X_38)))]]) ).
cnf(refute_0_736,plain,
( meet(top,X_38) != complement(complement(X_38))
| join(zero,meet(top,X_38)) = join(zero,complement(complement(X_38))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_38)),join(zero,meet(top,X_38))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
join(zero,meet(top,X_38)) = join(zero,complement(complement(X_38))),
inference(resolve,[$cnf( $equal(meet(top,X_38),complement(complement(X_38))) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
( join(zero,complement(complement(X_38))) != complement(complement(X_38))
| join(zero,meet(top,X_38)) != join(zero,complement(complement(X_38)))
| join(zero,meet(top,X_38)) = complement(complement(X_38)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,meet(top,X_38)))),bind(Y,$fot(join(zero,complement(complement(X_38))))),bind(Z,$fot(complement(complement(X_38))))]]) ).
cnf(refute_0_739,plain,
( join(zero,complement(complement(X_38))) != complement(complement(X_38))
| join(zero,meet(top,X_38)) = complement(complement(X_38)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_38)),join(zero,complement(complement(X_38)))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
join(zero,meet(top,X_38)) = complement(complement(X_38)),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_38))),complement(complement(X_38))) )],[refute_0_732,refute_0_739]) ).
cnf(refute_0_741,plain,
( X_38 != join(zero,meet(top,X_38))
| join(zero,meet(top,X_38)) != complement(complement(X_38))
| X_38 = complement(complement(X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_38,complement(complement(X_38))) ),[0],$fot(join(zero,meet(top,X_38)))]]) ).
cnf(refute_0_742,plain,
( X_38 != join(zero,meet(top,X_38))
| X_38 = complement(complement(X_38)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_38)),complement(complement(X_38))) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
X_38 = complement(complement(X_38)),
inference(resolve,[$cnf( $equal(X_38,join(zero,meet(top,X_38))) )],[refute_0_609,refute_0_742]) ).
cnf(refute_0_744,plain,
( X_38 != complement(complement(X_38))
| complement(complement(X_38)) = X_38 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_38)),bind(Y,$fot(complement(complement(X_38))))]]) ).
cnf(refute_0_745,plain,
complement(complement(X_38)) = X_38,
inference(resolve,[$cnf( $equal(X_38,complement(complement(X_38))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
complement(complement(X_52)) = X_52,
inference(subst,[],[refute_0_745:[bind(X_38,$fot(X_52))]]) ).
cnf(refute_0_747,plain,
join(X_52,complement(complement(X_52))) = join(X_52,complement(complement(X_52))),
introduced(tautology,[refl,[$fot(join(X_52,complement(complement(X_52))))]]) ).
cnf(refute_0_748,plain,
( complement(complement(X_52)) != X_52
| join(X_52,complement(complement(X_52))) != join(X_52,complement(complement(X_52)))
| join(X_52,complement(complement(X_52))) = join(X_52,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_52,complement(complement(X_52))),join(X_52,complement(complement(X_52)))) ),[1,1],$fot(X_52)]]) ).
cnf(refute_0_749,plain,
( complement(complement(X_52)) != X_52
| join(X_52,complement(complement(X_52))) = join(X_52,X_52) ),
inference(resolve,[$cnf( $equal(join(X_52,complement(complement(X_52))),join(X_52,complement(complement(X_52)))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
join(X_52,complement(complement(X_52))) = join(X_52,X_52),
inference(resolve,[$cnf( $equal(complement(complement(X_52)),X_52) )],[refute_0_746,refute_0_749]) ).
cnf(refute_0_751,plain,
complement(complement(X_33)) = X_33,
inference(subst,[],[refute_0_745:[bind(X_38,$fot(X_33))]]) ).
cnf(refute_0_752,plain,
( complement(complement(X_33)) != X_33
| meet(top,X_33) != complement(complement(X_33))
| meet(top,X_33) = X_33 ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_33),complement(complement(X_33))) ),[1],$fot(X_33)]]) ).
cnf(refute_0_753,plain,
( meet(top,X_33) != complement(complement(X_33))
| meet(top,X_33) = X_33 ),
inference(resolve,[$cnf( $equal(complement(complement(X_33)),X_33) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
meet(top,X_33) = X_33,
inference(resolve,[$cnf( $equal(meet(top,X_33),complement(complement(X_33))) )],[refute_0_694,refute_0_753]) ).
cnf(refute_0_755,plain,
meet(top,join(X_52,complement(complement(X_52)))) = join(X_52,complement(complement(X_52))),
inference(subst,[],[refute_0_754:[bind(X_33,$fot(join(X_52,complement(complement(X_52)))))]]) ).
cnf(refute_0_756,plain,
( join(X_52,complement(complement(X_52))) != join(X_52,X_52)
| meet(top,join(X_52,complement(complement(X_52)))) != join(X_52,complement(complement(X_52)))
| meet(top,join(X_52,complement(complement(X_52)))) = join(X_52,X_52) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(top,join(X_52,complement(complement(X_52)))))),bind(Y,$fot(join(X_52,complement(complement(X_52))))),bind(Z,$fot(join(X_52,X_52)))]]) ).
cnf(refute_0_757,plain,
( join(X_52,complement(complement(X_52))) != join(X_52,X_52)
| meet(top,join(X_52,complement(complement(X_52)))) = join(X_52,X_52) ),
inference(resolve,[$cnf( $equal(meet(top,join(X_52,complement(complement(X_52)))),join(X_52,complement(complement(X_52)))) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
meet(top,join(X_52,complement(complement(X_52)))) = join(X_52,X_52),
inference(resolve,[$cnf( $equal(join(X_52,complement(complement(X_52))),join(X_52,X_52)) )],[refute_0_750,refute_0_757]) ).
cnf(refute_0_759,plain,
complement(meet(top,join(X_52,complement(complement(X_52))))) = complement(meet(top,join(X_52,complement(complement(X_52))))),
introduced(tautology,[refl,[$fot(complement(meet(top,join(X_52,complement(complement(X_52))))))]]) ).
cnf(refute_0_760,plain,
( complement(meet(top,join(X_52,complement(complement(X_52))))) != complement(meet(top,join(X_52,complement(complement(X_52)))))
| meet(top,join(X_52,complement(complement(X_52)))) != join(X_52,X_52)
| complement(meet(top,join(X_52,complement(complement(X_52))))) = complement(join(X_52,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,join(X_52,complement(complement(X_52))))),complement(meet(top,join(X_52,complement(complement(X_52)))))) ),[1,0],$fot(join(X_52,X_52))]]) ).
cnf(refute_0_761,plain,
( meet(top,join(X_52,complement(complement(X_52)))) != join(X_52,X_52)
| complement(meet(top,join(X_52,complement(complement(X_52))))) = complement(join(X_52,X_52)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,join(X_52,complement(complement(X_52))))),complement(meet(top,join(X_52,complement(complement(X_52)))))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
complement(meet(top,join(X_52,complement(complement(X_52))))) = complement(join(X_52,X_52)),
inference(resolve,[$cnf( $equal(meet(top,join(X_52,complement(complement(X_52)))),join(X_52,X_52)) )],[refute_0_758,refute_0_761]) ).
cnf(refute_0_763,plain,
( complement(X_52) != complement(meet(top,join(X_52,complement(complement(X_52)))))
| complement(meet(top,join(X_52,complement(complement(X_52))))) != complement(join(X_52,X_52))
| complement(X_52) = complement(join(X_52,X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_52),complement(join(X_52,X_52))) ),[0],$fot(complement(meet(top,join(X_52,complement(complement(X_52))))))]]) ).
cnf(refute_0_764,plain,
( complement(X_52) != complement(meet(top,join(X_52,complement(complement(X_52)))))
| complement(X_52) = complement(join(X_52,X_52)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,join(X_52,complement(complement(X_52))))),complement(join(X_52,X_52))) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
complement(X_52) = complement(join(X_52,X_52)),
inference(resolve,[$cnf( $equal(complement(X_52),complement(meet(top,join(X_52,complement(complement(X_52)))))) )],[refute_0_256,refute_0_764]) ).
cnf(refute_0_766,plain,
complement(X_118) = complement(join(X_118,X_118)),
inference(subst,[],[refute_0_765:[bind(X_52,$fot(X_118))]]) ).
cnf(refute_0_767,plain,
( complement(X_118) != complement(join(X_118,X_118))
| complement(join(X_118,X_118)) = complement(X_118) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_118))),bind(Y,$fot(complement(join(X_118,X_118))))]]) ).
cnf(refute_0_768,plain,
complement(join(X_118,X_118)) = complement(X_118),
inference(resolve,[$cnf( $equal(complement(X_118),complement(join(X_118,X_118))) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
( complement(join(X_118,X_118)) != complement(X_118)
| zero != meet(join(X_118,X_118),complement(join(X_118,X_118)))
| zero = meet(join(X_118,X_118),complement(X_118)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(X_118,X_118),complement(join(X_118,X_118)))) ),[1,1],$fot(complement(X_118))]]) ).
cnf(refute_0_770,plain,
( zero != meet(join(X_118,X_118),complement(join(X_118,X_118)))
| zero = meet(join(X_118,X_118),complement(X_118)) ),
inference(resolve,[$cnf( $equal(complement(join(X_118,X_118)),complement(X_118)) )],[refute_0_768,refute_0_769]) ).
cnf(refute_0_771,plain,
zero = meet(join(X_118,X_118),complement(X_118)),
inference(resolve,[$cnf( $equal(zero,meet(join(X_118,X_118),complement(join(X_118,X_118)))) )],[refute_0_85,refute_0_770]) ).
cnf(refute_0_772,plain,
meet(join(X_118,X_118),complement(X_118)) = meet(complement(X_118),join(X_118,X_118)),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(complement(X_118))),bind(X_7,$fot(join(X_118,X_118)))]]) ).
cnf(refute_0_773,plain,
( meet(join(X_118,X_118),complement(X_118)) != meet(complement(X_118),join(X_118,X_118))
| zero != meet(join(X_118,X_118),complement(X_118))
| zero = meet(complement(X_118),join(X_118,X_118)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(X_118,X_118),complement(X_118))) ),[1],$fot(meet(complement(X_118),join(X_118,X_118)))]]) ).
cnf(refute_0_774,plain,
( zero != meet(join(X_118,X_118),complement(X_118))
| zero = meet(complement(X_118),join(X_118,X_118)) ),
inference(resolve,[$cnf( $equal(meet(join(X_118,X_118),complement(X_118)),meet(complement(X_118),join(X_118,X_118))) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
zero = meet(complement(X_118),join(X_118,X_118)),
inference(resolve,[$cnf( $equal(zero,meet(join(X_118,X_118),complement(X_118))) )],[refute_0_771,refute_0_774]) ).
cnf(refute_0_776,plain,
zero = meet(complement(X_119),join(X_119,X_119)),
inference(subst,[],[refute_0_775:[bind(X_118,$fot(X_119))]]) ).
cnf(refute_0_777,plain,
( zero != meet(complement(X_119),join(X_119,X_119))
| meet(complement(X_119),join(X_119,X_119)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(complement(X_119),join(X_119,X_119))))]]) ).
cnf(refute_0_778,plain,
meet(complement(X_119),join(X_119,X_119)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(complement(X_119),join(X_119,X_119))) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
( join(X_119,X_119) != join(meet(complement(X_119),join(X_119,X_119)),complement(join(complement(join(X_119,X_119)),complement(X_119))))
| meet(complement(X_119),join(X_119,X_119)) != zero
| join(X_119,X_119) = join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_119,X_119),join(meet(complement(X_119),join(X_119,X_119)),complement(join(complement(join(X_119,X_119)),complement(X_119))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_780,plain,
( join(X_119,X_119) != join(meet(complement(X_119),join(X_119,X_119)),complement(join(complement(join(X_119,X_119)),complement(X_119))))
| join(X_119,X_119) = join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_119),join(X_119,X_119)),zero) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
join(X_119,X_119) = join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))),
inference(resolve,[$cnf( $equal(join(X_119,X_119),join(meet(complement(X_119),join(X_119,X_119)),complement(join(complement(join(X_119,X_119)),complement(X_119))))) )],[refute_0_84,refute_0_780]) ).
cnf(refute_0_782,plain,
complement(complement(X_119)) = X_119,
inference(subst,[],[refute_0_745:[bind(X_38,$fot(X_119))]]) ).
cnf(refute_0_783,plain,
( complement(X_52) != complement(join(X_52,X_52))
| complement(join(X_52,X_52)) = complement(X_52) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_52))),bind(Y,$fot(complement(join(X_52,X_52))))]]) ).
cnf(refute_0_784,plain,
complement(join(X_52,X_52)) = complement(X_52),
inference(resolve,[$cnf( $equal(complement(X_52),complement(join(X_52,X_52))) )],[refute_0_765,refute_0_783]) ).
cnf(refute_0_785,plain,
complement(join(X_119,X_119)) = complement(X_119),
inference(subst,[],[refute_0_784:[bind(X_52,$fot(X_119))]]) ).
cnf(refute_0_786,plain,
X_36 = join(meet(X_36,X_35),meet(X_36,complement(X_35))),
inference(subst,[],[refute_0_49:[bind(B,$fot(X_35)),bind(X_24,$fot(X_36))]]) ).
cnf(refute_0_787,plain,
meet(X_35,X_36) = meet(X_36,X_35),
inference(subst,[],[refute_0_77:[bind(X_6,$fot(X_35)),bind(X_7,$fot(X_36))]]) ).
cnf(refute_0_788,plain,
( meet(X_35,X_36) != meet(X_36,X_35)
| meet(X_36,X_35) = meet(X_35,X_36) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_35,X_36))),bind(Y,$fot(meet(X_36,X_35)))]]) ).
cnf(refute_0_789,plain,
meet(X_36,X_35) = meet(X_35,X_36),
inference(resolve,[$cnf( $equal(meet(X_35,X_36),meet(X_36,X_35)) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
( X_36 != join(meet(X_36,X_35),meet(X_36,complement(X_35)))
| meet(X_36,X_35) != meet(X_35,X_36)
| X_36 = join(meet(X_35,X_36),meet(X_36,complement(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(X_36,join(meet(X_36,X_35),meet(X_36,complement(X_35)))) ),[1,0],$fot(meet(X_35,X_36))]]) ).
cnf(refute_0_791,plain,
( X_36 != join(meet(X_36,X_35),meet(X_36,complement(X_35)))
| X_36 = join(meet(X_35,X_36),meet(X_36,complement(X_35))) ),
inference(resolve,[$cnf( $equal(meet(X_36,X_35),meet(X_35,X_36)) )],[refute_0_789,refute_0_790]) ).
cnf(refute_0_792,plain,
X_36 = join(meet(X_35,X_36),meet(X_36,complement(X_35))),
inference(resolve,[$cnf( $equal(X_36,join(meet(X_36,X_35),meet(X_36,complement(X_35)))) )],[refute_0_786,refute_0_791]) ).
cnf(refute_0_793,plain,
join(X_119,X_119) = join(meet(complement(X_119),join(X_119,X_119)),meet(join(X_119,X_119),complement(complement(X_119)))),
inference(subst,[],[refute_0_792:[bind(X_35,$fot(complement(X_119))),bind(X_36,$fot(join(X_119,X_119)))]]) ).
cnf(refute_0_794,plain,
( join(X_119,X_119) != join(meet(complement(X_119),join(X_119,X_119)),meet(join(X_119,X_119),complement(complement(X_119))))
| meet(complement(X_119),join(X_119,X_119)) != zero
| join(X_119,X_119) = join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_119,X_119),join(meet(complement(X_119),join(X_119,X_119)),meet(join(X_119,X_119),complement(complement(X_119))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_795,plain,
( join(X_119,X_119) != join(meet(complement(X_119),join(X_119,X_119)),meet(join(X_119,X_119),complement(complement(X_119))))
| join(X_119,X_119) = join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_119),join(X_119,X_119)),zero) )],[refute_0_778,refute_0_794]) ).
cnf(refute_0_796,plain,
join(X_119,X_119) = join(zero,meet(join(X_119,X_119),complement(complement(X_119)))),
inference(resolve,[$cnf( $equal(join(X_119,X_119),join(meet(complement(X_119),join(X_119,X_119)),meet(join(X_119,X_119),complement(complement(X_119))))) )],[refute_0_793,refute_0_795]) ).
cnf(refute_0_797,plain,
meet(complement(complement(X_119)),join(X_119,X_119)) = meet(complement(complement(X_119)),join(X_119,X_119)),
introduced(tautology,[refl,[$fot(meet(complement(complement(X_119)),join(X_119,X_119)))]]) ).
cnf(refute_0_798,plain,
( complement(complement(X_119)) != X_119
| meet(complement(complement(X_119)),join(X_119,X_119)) != meet(complement(complement(X_119)),join(X_119,X_119))
| meet(complement(complement(X_119)),join(X_119,X_119)) = meet(X_119,join(X_119,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(complement(X_119)),join(X_119,X_119)),meet(complement(complement(X_119)),join(X_119,X_119))) ),[1,0],$fot(X_119)]]) ).
cnf(refute_0_799,plain,
( complement(complement(X_119)) != X_119
| meet(complement(complement(X_119)),join(X_119,X_119)) = meet(X_119,join(X_119,X_119)) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_119)),join(X_119,X_119)),meet(complement(complement(X_119)),join(X_119,X_119))) )],[refute_0_797,refute_0_798]) ).
cnf(refute_0_800,plain,
meet(complement(complement(X_119)),join(X_119,X_119)) = meet(X_119,join(X_119,X_119)),
inference(resolve,[$cnf( $equal(complement(complement(X_119)),X_119) )],[refute_0_782,refute_0_799]) ).
cnf(refute_0_801,plain,
meet(join(X_119,X_119),complement(complement(X_119))) = meet(complement(complement(X_119)),join(X_119,X_119)),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(complement(complement(X_119)))),bind(X_7,$fot(join(X_119,X_119)))]]) ).
cnf(refute_0_802,plain,
X_24 = join(meet(X_24,join(zero,complement(complement(X_24)))),complement(join(complement(X_24),join(zero,complement(complement(X_24)))))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_24)),bind(B,$fot(join(zero,complement(complement(X_24)))))]]) ).
cnf(refute_0_803,plain,
top = join(complement(X_18),join(complement(complement(X_18)),meet(X_18,complement(X_18)))),
inference(subst,[],[refute_0_287:[bind(X_6,$fot(X_18)),bind(X_7,$fot(complement(X_18)))]]) ).
cnf(refute_0_804,plain,
zero = meet(X_18,complement(X_18)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_18))]]) ).
cnf(refute_0_805,plain,
( zero != meet(X_18,complement(X_18))
| meet(X_18,complement(X_18)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_18,complement(X_18))))]]) ).
cnf(refute_0_806,plain,
meet(X_18,complement(X_18)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_18,complement(X_18))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
( meet(X_18,complement(X_18)) != zero
| top != join(complement(X_18),join(complement(complement(X_18)),meet(X_18,complement(X_18))))
| top = join(complement(X_18),join(complement(complement(X_18)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_18),join(complement(complement(X_18)),meet(X_18,complement(X_18))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_808,plain,
( top != join(complement(X_18),join(complement(complement(X_18)),meet(X_18,complement(X_18))))
| top = join(complement(X_18),join(complement(complement(X_18)),zero)) ),
inference(resolve,[$cnf( $equal(meet(X_18,complement(X_18)),zero) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
top = join(complement(X_18),join(complement(complement(X_18)),zero)),
inference(resolve,[$cnf( $equal(top,join(complement(X_18),join(complement(complement(X_18)),meet(X_18,complement(X_18))))) )],[refute_0_803,refute_0_808]) ).
cnf(refute_0_810,plain,
join(complement(complement(X_18)),zero) = join(zero,complement(complement(X_18))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_18))))]]) ).
cnf(refute_0_811,plain,
join(complement(X_18),join(complement(complement(X_18)),zero)) = join(complement(X_18),join(complement(complement(X_18)),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_18),join(complement(complement(X_18)),zero)))]]) ).
cnf(refute_0_812,plain,
( join(complement(X_18),join(complement(complement(X_18)),zero)) != join(complement(X_18),join(complement(complement(X_18)),zero))
| join(complement(complement(X_18)),zero) != join(zero,complement(complement(X_18)))
| join(complement(X_18),join(complement(complement(X_18)),zero)) = join(complement(X_18),join(zero,complement(complement(X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_18),join(complement(complement(X_18)),zero)),join(complement(X_18),join(complement(complement(X_18)),zero))) ),[1,1],$fot(join(zero,complement(complement(X_18))))]]) ).
cnf(refute_0_813,plain,
( join(complement(complement(X_18)),zero) != join(zero,complement(complement(X_18)))
| join(complement(X_18),join(complement(complement(X_18)),zero)) = join(complement(X_18),join(zero,complement(complement(X_18)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),join(complement(complement(X_18)),zero)),join(complement(X_18),join(complement(complement(X_18)),zero))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
join(complement(X_18),join(complement(complement(X_18)),zero)) = join(complement(X_18),join(zero,complement(complement(X_18)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_18)),zero),join(zero,complement(complement(X_18)))) )],[refute_0_810,refute_0_813]) ).
cnf(refute_0_815,plain,
( join(complement(X_18),join(complement(complement(X_18)),zero)) != join(complement(X_18),join(zero,complement(complement(X_18))))
| top != join(complement(X_18),join(complement(complement(X_18)),zero))
| top = join(complement(X_18),join(zero,complement(complement(X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_18),join(complement(complement(X_18)),zero))) ),[1],$fot(join(complement(X_18),join(zero,complement(complement(X_18)))))]]) ).
cnf(refute_0_816,plain,
( top != join(complement(X_18),join(complement(complement(X_18)),zero))
| top = join(complement(X_18),join(zero,complement(complement(X_18)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),join(complement(complement(X_18)),zero)),join(complement(X_18),join(zero,complement(complement(X_18))))) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
top = join(complement(X_18),join(zero,complement(complement(X_18)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_18),join(complement(complement(X_18)),zero))) )],[refute_0_809,refute_0_816]) ).
cnf(refute_0_818,plain,
top = join(complement(X_24),join(zero,complement(complement(X_24)))),
inference(subst,[],[refute_0_817:[bind(X_18,$fot(X_24))]]) ).
cnf(refute_0_819,plain,
( top != join(complement(X_24),join(zero,complement(complement(X_24))))
| join(complement(X_24),join(zero,complement(complement(X_24)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_24),join(zero,complement(complement(X_24))))))]]) ).
cnf(refute_0_820,plain,
join(complement(X_24),join(zero,complement(complement(X_24)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_24),join(zero,complement(complement(X_24))))) )],[refute_0_818,refute_0_819]) ).
cnf(refute_0_821,plain,
( X_24 != join(meet(X_24,join(zero,complement(complement(X_24)))),complement(join(complement(X_24),join(zero,complement(complement(X_24))))))
| join(complement(X_24),join(zero,complement(complement(X_24)))) != top
| X_24 = join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_24,join(meet(X_24,join(zero,complement(complement(X_24)))),complement(join(complement(X_24),join(zero,complement(complement(X_24))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_822,plain,
( X_24 != join(meet(X_24,join(zero,complement(complement(X_24)))),complement(join(complement(X_24),join(zero,complement(complement(X_24))))))
| X_24 = join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),join(zero,complement(complement(X_24)))),top) )],[refute_0_820,refute_0_821]) ).
cnf(refute_0_823,plain,
X_24 = join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,join(zero,complement(complement(X_24)))),complement(join(complement(X_24),join(zero,complement(complement(X_24))))))) )],[refute_0_802,refute_0_822]) ).
cnf(refute_0_824,plain,
join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))) = join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))))]]) ).
cnf(refute_0_825,plain,
( complement(top) != zero
| join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))) != join(complement(top),meet(X_24,join(zero,complement(complement(X_24)))))
| join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))) = join(zero,meet(X_24,join(zero,complement(complement(X_24))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))),join(complement(top),meet(X_24,join(zero,complement(complement(X_24)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_826,plain,
( complement(top) != zero
| join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))) = join(zero,meet(X_24,join(zero,complement(complement(X_24))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))),join(complement(top),meet(X_24,join(zero,complement(complement(X_24)))))) )],[refute_0_824,refute_0_825]) ).
cnf(refute_0_827,plain,
join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))) = join(zero,meet(X_24,join(zero,complement(complement(X_24))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_826]) ).
cnf(refute_0_828,plain,
join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) = join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_24,join(zero,complement(complement(X_24))))))]]) ).
cnf(refute_0_829,plain,
( join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))) != join(zero,meet(X_24,join(zero,complement(complement(X_24)))))
| join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) != join(complement(top),meet(X_24,join(zero,complement(complement(X_24)))))
| join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) = join(zero,meet(X_24,join(zero,complement(complement(X_24))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))))),bind(Z,$fot(join(zero,meet(X_24,join(zero,complement(complement(X_24)))))))]]) ).
cnf(refute_0_830,plain,
( join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))) != join(zero,meet(X_24,join(zero,complement(complement(X_24)))))
| join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) = join(zero,meet(X_24,join(zero,complement(complement(X_24))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)),join(complement(top),meet(X_24,join(zero,complement(complement(X_24)))))) )],[refute_0_828,refute_0_829]) ).
cnf(refute_0_831,plain,
join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) = join(zero,meet(X_24,join(zero,complement(complement(X_24))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_24,join(zero,complement(complement(X_24))))),join(zero,meet(X_24,join(zero,complement(complement(X_24)))))) )],[refute_0_827,refute_0_830]) ).
cnf(refute_0_832,plain,
( X_24 != join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top))
| join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)) != join(zero,meet(X_24,join(zero,complement(complement(X_24)))))
| X_24 = join(zero,meet(X_24,join(zero,complement(complement(X_24))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(zero,meet(X_24,join(zero,complement(complement(X_24)))))) ),[0],$fot(join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)))]]) ).
cnf(refute_0_833,plain,
( X_24 != join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top))
| X_24 = join(zero,meet(X_24,join(zero,complement(complement(X_24))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top)),join(zero,meet(X_24,join(zero,complement(complement(X_24)))))) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
X_24 = join(zero,meet(X_24,join(zero,complement(complement(X_24))))),
inference(resolve,[$cnf( $equal(X_24,join(meet(X_24,join(zero,complement(complement(X_24)))),complement(top))) )],[refute_0_823,refute_0_833]) ).
cnf(refute_0_835,plain,
meet(X_24,join(zero,complement(complement(X_24)))) = meet(X_24,complement(meet(top,complement(X_24)))),
inference(subst,[],[refute_0_241:[bind(A,$fot(X_24)),bind(X_10,$fot(complement(X_24)))]]) ).
cnf(refute_0_836,plain,
join(zero,meet(X_24,join(zero,complement(complement(X_24))))) = join(zero,meet(X_24,join(zero,complement(complement(X_24))))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_24,join(zero,complement(complement(X_24))))))]]) ).
cnf(refute_0_837,plain,
( join(zero,meet(X_24,join(zero,complement(complement(X_24))))) != join(zero,meet(X_24,join(zero,complement(complement(X_24)))))
| meet(X_24,join(zero,complement(complement(X_24)))) != meet(X_24,complement(meet(top,complement(X_24))))
| join(zero,meet(X_24,join(zero,complement(complement(X_24))))) = join(zero,meet(X_24,complement(meet(top,complement(X_24))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_24,join(zero,complement(complement(X_24))))),join(zero,meet(X_24,join(zero,complement(complement(X_24)))))) ),[1,1],$fot(meet(X_24,complement(meet(top,complement(X_24)))))]]) ).
cnf(refute_0_838,plain,
( meet(X_24,join(zero,complement(complement(X_24)))) != meet(X_24,complement(meet(top,complement(X_24))))
| join(zero,meet(X_24,join(zero,complement(complement(X_24))))) = join(zero,meet(X_24,complement(meet(top,complement(X_24))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_24,join(zero,complement(complement(X_24))))),join(zero,meet(X_24,join(zero,complement(complement(X_24)))))) )],[refute_0_836,refute_0_837]) ).
cnf(refute_0_839,plain,
join(zero,meet(X_24,join(zero,complement(complement(X_24))))) = join(zero,meet(X_24,complement(meet(top,complement(X_24))))),
inference(resolve,[$cnf( $equal(meet(X_24,join(zero,complement(complement(X_24)))),meet(X_24,complement(meet(top,complement(X_24))))) )],[refute_0_835,refute_0_838]) ).
cnf(refute_0_840,plain,
( X_24 != join(zero,meet(X_24,join(zero,complement(complement(X_24)))))
| join(zero,meet(X_24,join(zero,complement(complement(X_24))))) != join(zero,meet(X_24,complement(meet(top,complement(X_24)))))
| X_24 = join(zero,meet(X_24,complement(meet(top,complement(X_24))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(zero,meet(X_24,complement(meet(top,complement(X_24)))))) ),[0],$fot(join(zero,meet(X_24,join(zero,complement(complement(X_24))))))]]) ).
cnf(refute_0_841,plain,
( X_24 != join(zero,meet(X_24,join(zero,complement(complement(X_24)))))
| X_24 = join(zero,meet(X_24,complement(meet(top,complement(X_24))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_24,join(zero,complement(complement(X_24))))),join(zero,meet(X_24,complement(meet(top,complement(X_24)))))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
X_24 = join(zero,meet(X_24,complement(meet(top,complement(X_24))))),
inference(resolve,[$cnf( $equal(X_24,join(zero,meet(X_24,join(zero,complement(complement(X_24)))))) )],[refute_0_834,refute_0_841]) ).
cnf(refute_0_843,plain,
meet(X_92,X_92) = join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(meet(X_92,X_92)))))),
inference(subst,[],[refute_0_842:[bind(X_24,$fot(meet(X_92,X_92)))]]) ).
cnf(refute_0_844,plain,
( complement(meet(X_92,X_92)) != complement(X_92)
| meet(X_92,X_92) != join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(meet(X_92,X_92))))))
| meet(X_92,X_92) = join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_92,X_92),join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(meet(X_92,X_92))))))) ),[1,1,1,0,1],$fot(complement(X_92))]]) ).
cnf(refute_0_845,plain,
( meet(X_92,X_92) != join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(meet(X_92,X_92))))))
| meet(X_92,X_92) = join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) ),
inference(resolve,[$cnf( $equal(complement(meet(X_92,X_92)),complement(X_92)) )],[refute_0_433,refute_0_844]) ).
cnf(refute_0_846,plain,
meet(X_92,X_92) = join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))),
inference(resolve,[$cnf( $equal(meet(X_92,X_92),join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(meet(X_92,X_92))))))) )],[refute_0_843,refute_0_845]) ).
cnf(refute_0_847,plain,
X_24 = join(meet(meet(X_24,X_24),X_24),complement(join(complement(X_24),meet(X_24,X_24)))),
inference(subst,[],[refute_0_83:[bind(X_25,$fot(meet(X_24,X_24)))]]) ).
cnf(refute_0_848,plain,
top = join(complement(X_24),meet(X_24,X_24)),
inference(subst,[],[refute_0_440:[bind(X_92,$fot(X_24))]]) ).
cnf(refute_0_849,plain,
( top != join(complement(X_24),meet(X_24,X_24))
| join(complement(X_24),meet(X_24,X_24)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_24),meet(X_24,X_24))))]]) ).
cnf(refute_0_850,plain,
join(complement(X_24),meet(X_24,X_24)) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_24),meet(X_24,X_24))) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
( X_24 != join(meet(meet(X_24,X_24),X_24),complement(join(complement(X_24),meet(X_24,X_24))))
| join(complement(X_24),meet(X_24,X_24)) != top
| X_24 = join(meet(meet(X_24,X_24),X_24),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_24,join(meet(meet(X_24,X_24),X_24),complement(join(complement(X_24),meet(X_24,X_24))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_852,plain,
( X_24 != join(meet(meet(X_24,X_24),X_24),complement(join(complement(X_24),meet(X_24,X_24))))
| X_24 = join(meet(meet(X_24,X_24),X_24),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),meet(X_24,X_24)),top) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
X_24 = join(meet(meet(X_24,X_24),X_24),complement(top)),
inference(resolve,[$cnf( $equal(X_24,join(meet(meet(X_24,X_24),X_24),complement(join(complement(X_24),meet(X_24,X_24))))) )],[refute_0_847,refute_0_852]) ).
cnf(refute_0_854,plain,
meet(meet(X_24,X_24),X_24) = meet(X_24,meet(X_24,X_24)),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(X_24)),bind(X_7,$fot(meet(X_24,X_24)))]]) ).
cnf(refute_0_855,plain,
join(zero,meet(meet(X_24,X_24),X_24)) = join(zero,meet(meet(X_24,X_24),X_24)),
introduced(tautology,[refl,[$fot(join(zero,meet(meet(X_24,X_24),X_24)))]]) ).
cnf(refute_0_856,plain,
( join(zero,meet(meet(X_24,X_24),X_24)) != join(zero,meet(meet(X_24,X_24),X_24))
| meet(meet(X_24,X_24),X_24) != meet(X_24,meet(X_24,X_24))
| join(zero,meet(meet(X_24,X_24),X_24)) = join(zero,meet(X_24,meet(X_24,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(meet(X_24,X_24),X_24)),join(zero,meet(meet(X_24,X_24),X_24))) ),[1,1],$fot(meet(X_24,meet(X_24,X_24)))]]) ).
cnf(refute_0_857,plain,
( meet(meet(X_24,X_24),X_24) != meet(X_24,meet(X_24,X_24))
| join(zero,meet(meet(X_24,X_24),X_24)) = join(zero,meet(X_24,meet(X_24,X_24))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(X_24,X_24),X_24)),join(zero,meet(meet(X_24,X_24),X_24))) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
join(zero,meet(meet(X_24,X_24),X_24)) = join(zero,meet(X_24,meet(X_24,X_24))),
inference(resolve,[$cnf( $equal(meet(meet(X_24,X_24),X_24),meet(X_24,meet(X_24,X_24))) )],[refute_0_854,refute_0_857]) ).
cnf(refute_0_859,plain,
join(complement(top),meet(meet(X_24,X_24),X_24)) = join(complement(top),meet(meet(X_24,X_24),X_24)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(meet(X_24,X_24),X_24)))]]) ).
cnf(refute_0_860,plain,
( complement(top) != zero
| join(complement(top),meet(meet(X_24,X_24),X_24)) != join(complement(top),meet(meet(X_24,X_24),X_24))
| join(complement(top),meet(meet(X_24,X_24),X_24)) = join(zero,meet(meet(X_24,X_24),X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(meet(X_24,X_24),X_24)),join(complement(top),meet(meet(X_24,X_24),X_24))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_861,plain,
( complement(top) != zero
| join(complement(top),meet(meet(X_24,X_24),X_24)) = join(zero,meet(meet(X_24,X_24),X_24)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(meet(X_24,X_24),X_24)),join(complement(top),meet(meet(X_24,X_24),X_24))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
join(complement(top),meet(meet(X_24,X_24),X_24)) = join(zero,meet(meet(X_24,X_24),X_24)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_137,refute_0_861]) ).
cnf(refute_0_863,plain,
( join(complement(top),meet(meet(X_24,X_24),X_24)) != join(zero,meet(meet(X_24,X_24),X_24))
| join(zero,meet(meet(X_24,X_24),X_24)) != join(zero,meet(X_24,meet(X_24,X_24)))
| join(complement(top),meet(meet(X_24,X_24),X_24)) = join(zero,meet(X_24,meet(X_24,X_24))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(top),meet(meet(X_24,X_24),X_24)))),bind(Y,$fot(join(zero,meet(meet(X_24,X_24),X_24)))),bind(Z,$fot(join(zero,meet(X_24,meet(X_24,X_24)))))]]) ).
cnf(refute_0_864,plain,
( join(zero,meet(meet(X_24,X_24),X_24)) != join(zero,meet(X_24,meet(X_24,X_24)))
| join(complement(top),meet(meet(X_24,X_24),X_24)) = join(zero,meet(X_24,meet(X_24,X_24))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(meet(X_24,X_24),X_24)),join(zero,meet(meet(X_24,X_24),X_24))) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
join(complement(top),meet(meet(X_24,X_24),X_24)) = join(zero,meet(X_24,meet(X_24,X_24))),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(X_24,X_24),X_24)),join(zero,meet(X_24,meet(X_24,X_24)))) )],[refute_0_858,refute_0_864]) ).
cnf(refute_0_866,plain,
join(meet(meet(X_24,X_24),X_24),complement(top)) = join(complement(top),meet(meet(X_24,X_24),X_24)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(meet(X_24,X_24),X_24)))]]) ).
cnf(refute_0_867,plain,
( join(complement(top),meet(meet(X_24,X_24),X_24)) != join(zero,meet(X_24,meet(X_24,X_24)))
| join(meet(meet(X_24,X_24),X_24),complement(top)) != join(complement(top),meet(meet(X_24,X_24),X_24))
| join(meet(meet(X_24,X_24),X_24),complement(top)) = join(zero,meet(X_24,meet(X_24,X_24))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(meet(X_24,X_24),X_24),complement(top)))),bind(Y,$fot(join(complement(top),meet(meet(X_24,X_24),X_24)))),bind(Z,$fot(join(zero,meet(X_24,meet(X_24,X_24)))))]]) ).
cnf(refute_0_868,plain,
( join(complement(top),meet(meet(X_24,X_24),X_24)) != join(zero,meet(X_24,meet(X_24,X_24)))
| join(meet(meet(X_24,X_24),X_24),complement(top)) = join(zero,meet(X_24,meet(X_24,X_24))) ),
inference(resolve,[$cnf( $equal(join(meet(meet(X_24,X_24),X_24),complement(top)),join(complement(top),meet(meet(X_24,X_24),X_24))) )],[refute_0_866,refute_0_867]) ).
cnf(refute_0_869,plain,
join(meet(meet(X_24,X_24),X_24),complement(top)) = join(zero,meet(X_24,meet(X_24,X_24))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(meet(X_24,X_24),X_24)),join(zero,meet(X_24,meet(X_24,X_24)))) )],[refute_0_865,refute_0_868]) ).
cnf(refute_0_870,plain,
( X_24 != join(meet(meet(X_24,X_24),X_24),complement(top))
| join(meet(meet(X_24,X_24),X_24),complement(top)) != join(zero,meet(X_24,meet(X_24,X_24)))
| X_24 = join(zero,meet(X_24,meet(X_24,X_24))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(zero,meet(X_24,meet(X_24,X_24)))) ),[0],$fot(join(meet(meet(X_24,X_24),X_24),complement(top)))]]) ).
cnf(refute_0_871,plain,
( X_24 != join(meet(meet(X_24,X_24),X_24),complement(top))
| X_24 = join(zero,meet(X_24,meet(X_24,X_24))) ),
inference(resolve,[$cnf( $equal(join(meet(meet(X_24,X_24),X_24),complement(top)),join(zero,meet(X_24,meet(X_24,X_24)))) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
X_24 = join(zero,meet(X_24,meet(X_24,X_24))),
inference(resolve,[$cnf( $equal(X_24,join(meet(meet(X_24,X_24),X_24),complement(top))) )],[refute_0_853,refute_0_871]) ).
cnf(refute_0_873,plain,
( X_24 != join(zero,meet(X_24,meet(X_24,X_24)))
| join(zero,meet(X_24,meet(X_24,X_24))) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(join(zero,meet(X_24,meet(X_24,X_24)))))]]) ).
cnf(refute_0_874,plain,
join(zero,meet(X_24,meet(X_24,X_24))) = X_24,
inference(resolve,[$cnf( $equal(X_24,join(zero,meet(X_24,meet(X_24,X_24)))) )],[refute_0_872,refute_0_873]) ).
cnf(refute_0_875,plain,
join(zero,meet(X_92,meet(X_92,X_92))) = X_92,
inference(subst,[],[refute_0_874:[bind(X_24,$fot(X_92))]]) ).
cnf(refute_0_876,plain,
meet(meet(X_92,X_92),X_92) = meet(X_92,meet(X_92,X_92)),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(X_92)),bind(X_7,$fot(meet(X_92,X_92)))]]) ).
cnf(refute_0_877,plain,
complement(complement(X_92)) = X_92,
inference(subst,[],[refute_0_745:[bind(X_38,$fot(X_92))]]) ).
cnf(refute_0_878,plain,
meet(top,complement(X_92)) = complement(X_92),
inference(subst,[],[refute_0_754:[bind(X_33,$fot(complement(X_92)))]]) ).
cnf(refute_0_879,plain,
complement(meet(top,complement(X_92))) = complement(meet(top,complement(X_92))),
introduced(tautology,[refl,[$fot(complement(meet(top,complement(X_92))))]]) ).
cnf(refute_0_880,plain,
( complement(meet(top,complement(X_92))) != complement(meet(top,complement(X_92)))
| meet(top,complement(X_92)) != complement(X_92)
| complement(meet(top,complement(X_92))) = complement(complement(X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,complement(X_92))),complement(meet(top,complement(X_92)))) ),[1,0],$fot(complement(X_92))]]) ).
cnf(refute_0_881,plain,
( meet(top,complement(X_92)) != complement(X_92)
| complement(meet(top,complement(X_92))) = complement(complement(X_92)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_92))),complement(meet(top,complement(X_92)))) )],[refute_0_879,refute_0_880]) ).
cnf(refute_0_882,plain,
complement(meet(top,complement(X_92))) = complement(complement(X_92)),
inference(resolve,[$cnf( $equal(meet(top,complement(X_92)),complement(X_92)) )],[refute_0_878,refute_0_881]) ).
cnf(refute_0_883,plain,
( complement(complement(X_92)) != X_92
| complement(meet(top,complement(X_92))) != complement(complement(X_92))
| complement(meet(top,complement(X_92))) = X_92 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(meet(top,complement(X_92))))),bind(Y,$fot(complement(complement(X_92)))),bind(Z,$fot(X_92))]]) ).
cnf(refute_0_884,plain,
( complement(complement(X_92)) != X_92
| complement(meet(top,complement(X_92))) = X_92 ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_92))),complement(complement(X_92))) )],[refute_0_882,refute_0_883]) ).
cnf(refute_0_885,plain,
complement(meet(top,complement(X_92))) = X_92,
inference(resolve,[$cnf( $equal(complement(complement(X_92)),X_92) )],[refute_0_877,refute_0_884]) ).
cnf(refute_0_886,plain,
meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) = meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))),
introduced(tautology,[refl,[$fot(meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))]]) ).
cnf(refute_0_887,plain,
( complement(meet(top,complement(X_92))) != X_92
| meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) != meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))
| meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) = meet(meet(X_92,X_92),X_92) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))),meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) ),[1,1],$fot(X_92)]]) ).
cnf(refute_0_888,plain,
( complement(meet(top,complement(X_92))) != X_92
| meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) = meet(meet(X_92,X_92),X_92) ),
inference(resolve,[$cnf( $equal(meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))),meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) )],[refute_0_886,refute_0_887]) ).
cnf(refute_0_889,plain,
meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) = meet(meet(X_92,X_92),X_92),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_92))),X_92) )],[refute_0_885,refute_0_888]) ).
cnf(refute_0_890,plain,
( meet(meet(X_92,X_92),X_92) != meet(X_92,meet(X_92,X_92))
| meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) != meet(meet(X_92,X_92),X_92)
| meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) = meet(X_92,meet(X_92,X_92)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))),bind(Y,$fot(meet(meet(X_92,X_92),X_92))),bind(Z,$fot(meet(X_92,meet(X_92,X_92))))]]) ).
cnf(refute_0_891,plain,
( meet(meet(X_92,X_92),X_92) != meet(X_92,meet(X_92,X_92))
| meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) = meet(X_92,meet(X_92,X_92)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))),meet(meet(X_92,X_92),X_92)) )],[refute_0_889,refute_0_890]) ).
cnf(refute_0_892,plain,
meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) = meet(X_92,meet(X_92,X_92)),
inference(resolve,[$cnf( $equal(meet(meet(X_92,X_92),X_92),meet(X_92,meet(X_92,X_92))) )],[refute_0_876,refute_0_891]) ).
cnf(refute_0_893,plain,
join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) = join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))),
introduced(tautology,[refl,[$fot(join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))))]]) ).
cnf(refute_0_894,plain,
( join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) != join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))
| meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) != meet(X_92,meet(X_92,X_92))
| join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) = join(zero,meet(X_92,meet(X_92,X_92))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))),join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))) ),[1,1],$fot(meet(X_92,meet(X_92,X_92)))]]) ).
cnf(refute_0_895,plain,
( meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))) != meet(X_92,meet(X_92,X_92))
| join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) = join(zero,meet(X_92,meet(X_92,X_92))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))),join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) = join(zero,meet(X_92,meet(X_92,X_92))),
inference(resolve,[$cnf( $equal(meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))),meet(X_92,meet(X_92,X_92))) )],[refute_0_892,refute_0_895]) ).
cnf(refute_0_897,plain,
( join(zero,meet(X_92,meet(X_92,X_92))) != X_92
| join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) != join(zero,meet(X_92,meet(X_92,X_92)))
| join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) = X_92 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))))),bind(Y,$fot(join(zero,meet(X_92,meet(X_92,X_92))))),bind(Z,$fot(X_92))]]) ).
cnf(refute_0_898,plain,
( join(zero,meet(X_92,meet(X_92,X_92))) != X_92
| join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) = X_92 ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))),join(zero,meet(X_92,meet(X_92,X_92)))) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) = X_92,
inference(resolve,[$cnf( $equal(join(zero,meet(X_92,meet(X_92,X_92))),X_92) )],[refute_0_875,refute_0_898]) ).
cnf(refute_0_900,plain,
( join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))) != X_92
| meet(X_92,X_92) != join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))
| meet(X_92,X_92) = X_92 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_92,X_92),join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))) ),[1],$fot(X_92)]]) ).
cnf(refute_0_901,plain,
( meet(X_92,X_92) != join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))
| meet(X_92,X_92) = X_92 ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92))))),X_92) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
meet(X_92,X_92) = X_92,
inference(resolve,[$cnf( $equal(meet(X_92,X_92),join(zero,meet(meet(X_92,X_92),complement(meet(top,complement(X_92)))))) )],[refute_0_846,refute_0_901]) ).
cnf(refute_0_903,plain,
meet(X_24,X_24) = X_24,
inference(subst,[],[refute_0_902:[bind(X_92,$fot(X_24))]]) ).
cnf(refute_0_904,plain,
join(zero,meet(X_24,X_24)) = join(zero,meet(X_24,X_24)),
introduced(tautology,[refl,[$fot(join(zero,meet(X_24,X_24)))]]) ).
cnf(refute_0_905,plain,
( join(zero,meet(X_24,X_24)) != join(zero,meet(X_24,X_24))
| meet(X_24,X_24) != X_24
| join(zero,meet(X_24,X_24)) = join(zero,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_24,X_24)),join(zero,meet(X_24,X_24))) ),[1,1],$fot(X_24)]]) ).
cnf(refute_0_906,plain,
( meet(X_24,X_24) != X_24
| join(zero,meet(X_24,X_24)) = join(zero,X_24) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_24,X_24)),join(zero,meet(X_24,X_24))) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
join(zero,meet(X_24,X_24)) = join(zero,X_24),
inference(resolve,[$cnf( $equal(meet(X_24,X_24),X_24) )],[refute_0_903,refute_0_906]) ).
cnf(refute_0_908,plain,
( X_24 != join(zero,meet(X_24,X_24))
| join(zero,meet(X_24,X_24)) != join(zero,X_24)
| X_24 = join(zero,X_24) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,join(zero,X_24)) ),[0],$fot(join(zero,meet(X_24,X_24)))]]) ).
cnf(refute_0_909,plain,
( X_24 != join(zero,meet(X_24,X_24))
| X_24 = join(zero,X_24) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_24,X_24)),join(zero,X_24)) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
X_24 = join(zero,X_24),
inference(resolve,[$cnf( $equal(X_24,join(zero,meet(X_24,X_24))) )],[refute_0_183,refute_0_909]) ).
cnf(refute_0_911,plain,
( X_24 != join(zero,X_24)
| join(zero,X_24) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(join(zero,X_24)))]]) ).
cnf(refute_0_912,plain,
join(zero,X_24) = X_24,
inference(resolve,[$cnf( $equal(X_24,join(zero,X_24)) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) = meet(join(X_119,X_119),complement(complement(X_119))),
inference(subst,[],[refute_0_912:[bind(X_24,$fot(meet(join(X_119,X_119),complement(complement(X_119)))))]]) ).
cnf(refute_0_914,plain,
( join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) != meet(join(X_119,X_119),complement(complement(X_119)))
| meet(join(X_119,X_119),complement(complement(X_119))) != meet(complement(complement(X_119)),join(X_119,X_119))
| join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) = meet(complement(complement(X_119)),join(X_119,X_119)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,meet(join(X_119,X_119),complement(complement(X_119)))))),bind(Y,$fot(meet(join(X_119,X_119),complement(complement(X_119))))),bind(Z,$fot(meet(complement(complement(X_119)),join(X_119,X_119))))]]) ).
cnf(refute_0_915,plain,
( meet(join(X_119,X_119),complement(complement(X_119))) != meet(complement(complement(X_119)),join(X_119,X_119))
| join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) = meet(complement(complement(X_119)),join(X_119,X_119)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_119,X_119),complement(complement(X_119)))),meet(join(X_119,X_119),complement(complement(X_119)))) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) = meet(complement(complement(X_119)),join(X_119,X_119)),
inference(resolve,[$cnf( $equal(meet(join(X_119,X_119),complement(complement(X_119))),meet(complement(complement(X_119)),join(X_119,X_119))) )],[refute_0_801,refute_0_915]) ).
cnf(refute_0_917,plain,
( join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) != meet(complement(complement(X_119)),join(X_119,X_119))
| meet(complement(complement(X_119)),join(X_119,X_119)) != meet(X_119,join(X_119,X_119))
| join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) = meet(X_119,join(X_119,X_119)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,meet(join(X_119,X_119),complement(complement(X_119)))))),bind(Y,$fot(meet(complement(complement(X_119)),join(X_119,X_119)))),bind(Z,$fot(meet(X_119,join(X_119,X_119))))]]) ).
cnf(refute_0_918,plain,
( meet(complement(complement(X_119)),join(X_119,X_119)) != meet(X_119,join(X_119,X_119))
| join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) = meet(X_119,join(X_119,X_119)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_119,X_119),complement(complement(X_119)))),meet(complement(complement(X_119)),join(X_119,X_119))) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) = meet(X_119,join(X_119,X_119)),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_119)),join(X_119,X_119)),meet(X_119,join(X_119,X_119))) )],[refute_0_800,refute_0_918]) ).
cnf(refute_0_920,plain,
( join(X_119,X_119) != join(zero,meet(join(X_119,X_119),complement(complement(X_119))))
| join(zero,meet(join(X_119,X_119),complement(complement(X_119)))) != meet(X_119,join(X_119,X_119))
| join(X_119,X_119) = meet(X_119,join(X_119,X_119)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_119,X_119),meet(X_119,join(X_119,X_119))) ),[0],$fot(join(zero,meet(join(X_119,X_119),complement(complement(X_119)))))]]) ).
cnf(refute_0_921,plain,
( join(X_119,X_119) != join(zero,meet(join(X_119,X_119),complement(complement(X_119))))
| join(X_119,X_119) = meet(X_119,join(X_119,X_119)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_119,X_119),complement(complement(X_119)))),meet(X_119,join(X_119,X_119))) )],[refute_0_919,refute_0_920]) ).
cnf(refute_0_922,plain,
join(X_119,X_119) = meet(X_119,join(X_119,X_119)),
inference(resolve,[$cnf( $equal(join(X_119,X_119),join(zero,meet(join(X_119,X_119),complement(complement(X_119))))) )],[refute_0_796,refute_0_921]) ).
cnf(refute_0_923,plain,
( join(X_119,X_119) != meet(X_119,join(X_119,X_119))
| meet(X_119,join(X_119,X_119)) = join(X_119,X_119) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_119,X_119))),bind(Y,$fot(meet(X_119,join(X_119,X_119))))]]) ).
cnf(refute_0_924,plain,
meet(X_119,join(X_119,X_119)) = join(X_119,X_119),
inference(resolve,[$cnf( $equal(join(X_119,X_119),meet(X_119,join(X_119,X_119))) )],[refute_0_922,refute_0_923]) ).
cnf(refute_0_925,plain,
meet(join(X_119,X_119),X_119) = meet(X_119,join(X_119,X_119)),
inference(subst,[],[refute_0_160:[bind(X_6,$fot(X_119)),bind(X_7,$fot(join(X_119,X_119)))]]) ).
cnf(refute_0_926,plain,
( meet(X_119,join(X_119,X_119)) != join(X_119,X_119)
| meet(join(X_119,X_119),X_119) != meet(X_119,join(X_119,X_119))
| meet(join(X_119,X_119),X_119) = join(X_119,X_119) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(join(X_119,X_119),X_119))),bind(Y,$fot(meet(X_119,join(X_119,X_119)))),bind(Z,$fot(join(X_119,X_119)))]]) ).
cnf(refute_0_927,plain,
( meet(X_119,join(X_119,X_119)) != join(X_119,X_119)
| meet(join(X_119,X_119),X_119) = join(X_119,X_119) ),
inference(resolve,[$cnf( $equal(meet(join(X_119,X_119),X_119),meet(X_119,join(X_119,X_119))) )],[refute_0_925,refute_0_926]) ).
cnf(refute_0_928,plain,
meet(join(X_119,X_119),X_119) = join(X_119,X_119),
inference(resolve,[$cnf( $equal(meet(X_119,join(X_119,X_119)),join(X_119,X_119)) )],[refute_0_924,refute_0_927]) ).
cnf(refute_0_929,plain,
complement(meet(join(X_119,X_119),X_119)) = complement(meet(join(X_119,X_119),X_119)),
introduced(tautology,[refl,[$fot(complement(meet(join(X_119,X_119),X_119)))]]) ).
cnf(refute_0_930,plain,
( complement(meet(join(X_119,X_119),X_119)) != complement(meet(join(X_119,X_119),X_119))
| meet(join(X_119,X_119),X_119) != join(X_119,X_119)
| complement(meet(join(X_119,X_119),X_119)) = complement(join(X_119,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(join(X_119,X_119),X_119)),complement(meet(join(X_119,X_119),X_119))) ),[1,0],$fot(join(X_119,X_119))]]) ).
cnf(refute_0_931,plain,
( meet(join(X_119,X_119),X_119) != join(X_119,X_119)
| complement(meet(join(X_119,X_119),X_119)) = complement(join(X_119,X_119)) ),
inference(resolve,[$cnf( $equal(complement(meet(join(X_119,X_119),X_119)),complement(meet(join(X_119,X_119),X_119))) )],[refute_0_929,refute_0_930]) ).
cnf(refute_0_932,plain,
complement(meet(join(X_119,X_119),X_119)) = complement(join(X_119,X_119)),
inference(resolve,[$cnf( $equal(meet(join(X_119,X_119),X_119),join(X_119,X_119)) )],[refute_0_928,refute_0_931]) ).
cnf(refute_0_933,plain,
( complement(join(X_119,X_119)) != complement(X_119)
| complement(meet(join(X_119,X_119),X_119)) != complement(join(X_119,X_119))
| complement(meet(join(X_119,X_119),X_119)) = complement(X_119) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(meet(join(X_119,X_119),X_119)))),bind(Y,$fot(complement(join(X_119,X_119)))),bind(Z,$fot(complement(X_119)))]]) ).
cnf(refute_0_934,plain,
( complement(join(X_119,X_119)) != complement(X_119)
| complement(meet(join(X_119,X_119),X_119)) = complement(X_119) ),
inference(resolve,[$cnf( $equal(complement(meet(join(X_119,X_119),X_119)),complement(join(X_119,X_119))) )],[refute_0_932,refute_0_933]) ).
cnf(refute_0_935,plain,
complement(meet(join(X_119,X_119),X_119)) = complement(X_119),
inference(resolve,[$cnf( $equal(complement(join(X_119,X_119)),complement(X_119)) )],[refute_0_785,refute_0_934]) ).
cnf(refute_0_936,plain,
join(complement(join(X_119,X_119)),complement(X_119)) = complement(meet(join(X_119,X_119),X_119)),
inference(subst,[],[refute_0_227:[bind(A,$fot(join(X_119,X_119))),bind(B,$fot(X_119))]]) ).
cnf(refute_0_937,plain,
( complement(meet(join(X_119,X_119),X_119)) != complement(X_119)
| join(complement(join(X_119,X_119)),complement(X_119)) != complement(meet(join(X_119,X_119),X_119))
| join(complement(join(X_119,X_119)),complement(X_119)) = complement(X_119) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(X_119,X_119)),complement(X_119)))),bind(Y,$fot(complement(meet(join(X_119,X_119),X_119)))),bind(Z,$fot(complement(X_119)))]]) ).
cnf(refute_0_938,plain,
( complement(meet(join(X_119,X_119),X_119)) != complement(X_119)
| join(complement(join(X_119,X_119)),complement(X_119)) = complement(X_119) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_119,X_119)),complement(X_119)),complement(meet(join(X_119,X_119),X_119))) )],[refute_0_936,refute_0_937]) ).
cnf(refute_0_939,plain,
join(complement(join(X_119,X_119)),complement(X_119)) = complement(X_119),
inference(resolve,[$cnf( $equal(complement(meet(join(X_119,X_119),X_119)),complement(X_119)) )],[refute_0_935,refute_0_938]) ).
cnf(refute_0_940,plain,
complement(join(complement(join(X_119,X_119)),complement(X_119))) = complement(join(complement(join(X_119,X_119)),complement(X_119))),
introduced(tautology,[refl,[$fot(complement(join(complement(join(X_119,X_119)),complement(X_119))))]]) ).
cnf(refute_0_941,plain,
( complement(join(complement(join(X_119,X_119)),complement(X_119))) != complement(join(complement(join(X_119,X_119)),complement(X_119)))
| join(complement(join(X_119,X_119)),complement(X_119)) != complement(X_119)
| complement(join(complement(join(X_119,X_119)),complement(X_119))) = complement(complement(X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(join(X_119,X_119)),complement(X_119))),complement(join(complement(join(X_119,X_119)),complement(X_119)))) ),[1,0],$fot(complement(X_119))]]) ).
cnf(refute_0_942,plain,
( join(complement(join(X_119,X_119)),complement(X_119)) != complement(X_119)
| complement(join(complement(join(X_119,X_119)),complement(X_119))) = complement(complement(X_119)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(join(X_119,X_119)),complement(X_119))),complement(join(complement(join(X_119,X_119)),complement(X_119)))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
complement(join(complement(join(X_119,X_119)),complement(X_119))) = complement(complement(X_119)),
inference(resolve,[$cnf( $equal(join(complement(join(X_119,X_119)),complement(X_119)),complement(X_119)) )],[refute_0_939,refute_0_942]) ).
cnf(refute_0_944,plain,
( complement(complement(X_119)) != X_119
| complement(join(complement(join(X_119,X_119)),complement(X_119))) != complement(complement(X_119))
| complement(join(complement(join(X_119,X_119)),complement(X_119))) = X_119 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(join(complement(join(X_119,X_119)),complement(X_119))))),bind(Y,$fot(complement(complement(X_119)))),bind(Z,$fot(X_119))]]) ).
cnf(refute_0_945,plain,
( complement(complement(X_119)) != X_119
| complement(join(complement(join(X_119,X_119)),complement(X_119))) = X_119 ),
inference(resolve,[$cnf( $equal(complement(join(complement(join(X_119,X_119)),complement(X_119))),complement(complement(X_119))) )],[refute_0_943,refute_0_944]) ).
cnf(refute_0_946,plain,
complement(join(complement(join(X_119,X_119)),complement(X_119))) = X_119,
inference(resolve,[$cnf( $equal(complement(complement(X_119)),X_119) )],[refute_0_782,refute_0_945]) ).
cnf(refute_0_947,plain,
join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) = complement(join(complement(join(X_119,X_119)),complement(X_119))),
inference(subst,[],[refute_0_912:[bind(X_24,$fot(complement(join(complement(join(X_119,X_119)),complement(X_119)))))]]) ).
cnf(refute_0_948,plain,
( complement(join(complement(join(X_119,X_119)),complement(X_119))) != X_119
| join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) != complement(join(complement(join(X_119,X_119)),complement(X_119)))
| join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) = X_119 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))))),bind(Y,$fot(complement(join(complement(join(X_119,X_119)),complement(X_119))))),bind(Z,$fot(X_119))]]) ).
cnf(refute_0_949,plain,
( complement(join(complement(join(X_119,X_119)),complement(X_119))) != X_119
| join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) = X_119 ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))),complement(join(complement(join(X_119,X_119)),complement(X_119)))) )],[refute_0_947,refute_0_948]) ).
cnf(refute_0_950,plain,
join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) = X_119,
inference(resolve,[$cnf( $equal(complement(join(complement(join(X_119,X_119)),complement(X_119))),X_119) )],[refute_0_946,refute_0_949]) ).
cnf(refute_0_951,plain,
( join(X_119,X_119) != join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119))))
| join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))) != X_119
| join(X_119,X_119) = X_119 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_119,X_119),X_119) ),[0],$fot(join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))))]]) ).
cnf(refute_0_952,plain,
( join(X_119,X_119) != join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119))))
| join(X_119,X_119) = X_119 ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119)))),X_119) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
join(X_119,X_119) = X_119,
inference(resolve,[$cnf( $equal(join(X_119,X_119),join(zero,complement(join(complement(join(X_119,X_119)),complement(X_119))))) )],[refute_0_781,refute_0_952]) ).
cnf(refute_0_954,plain,
join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360))) = meet(X_361,complement(X_360)),
inference(subst,[],[refute_0_953:[bind(X_119,$fot(meet(X_361,complement(X_360))))]]) ).
cnf(refute_0_955,plain,
( join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360)))) != join(X_361,meet(X_361,complement(X_360)))
| join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360))) != meet(X_361,complement(X_360))
| join(meet(X_361,X_360),meet(X_361,complement(X_360))) = join(X_361,meet(X_361,complement(X_360))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360)))),join(X_361,meet(X_361,complement(X_360)))) ),[0,1],$fot(meet(X_361,complement(X_360)))]]) ).
cnf(refute_0_956,plain,
( join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360)))) != join(X_361,meet(X_361,complement(X_360)))
| join(meet(X_361,X_360),meet(X_361,complement(X_360))) = join(X_361,meet(X_361,complement(X_360))) ),
inference(resolve,[$cnf( $equal(join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360))),meet(X_361,complement(X_360))) )],[refute_0_954,refute_0_955]) ).
cnf(refute_0_957,plain,
join(meet(X_361,X_360),meet(X_361,complement(X_360))) = join(X_361,meet(X_361,complement(X_360))),
inference(resolve,[$cnf( $equal(join(meet(X_361,X_360),join(meet(X_361,complement(X_360)),meet(X_361,complement(X_360)))),join(X_361,meet(X_361,complement(X_360)))) )],[refute_0_65,refute_0_956]) ).
cnf(refute_0_958,plain,
join(meet(X_361,X_360),meet(X_361,complement(X_360))) = X_361,
inference(subst,[],[refute_0_51:[bind(B,$fot(X_360)),bind(X_24,$fot(X_361))]]) ).
cnf(refute_0_959,plain,
( join(meet(X_361,X_360),meet(X_361,complement(X_360))) != X_361
| join(meet(X_361,X_360),meet(X_361,complement(X_360))) != join(X_361,meet(X_361,complement(X_360)))
| X_361 = join(X_361,meet(X_361,complement(X_360))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_361,X_360),meet(X_361,complement(X_360))),join(X_361,meet(X_361,complement(X_360)))) ),[0],$fot(X_361)]]) ).
cnf(refute_0_960,plain,
( join(meet(X_361,X_360),meet(X_361,complement(X_360))) != join(X_361,meet(X_361,complement(X_360)))
| X_361 = join(X_361,meet(X_361,complement(X_360))) ),
inference(resolve,[$cnf( $equal(join(meet(X_361,X_360),meet(X_361,complement(X_360))),X_361) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
X_361 = join(X_361,meet(X_361,complement(X_360))),
inference(resolve,[$cnf( $equal(join(meet(X_361,X_360),meet(X_361,complement(X_360))),join(X_361,meet(X_361,complement(X_360)))) )],[refute_0_957,refute_0_960]) ).
cnf(refute_0_962,plain,
( X_361 != join(X_361,meet(X_361,complement(X_360)))
| join(X_361,meet(X_361,complement(X_360))) = X_361 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_361)),bind(Y,$fot(join(X_361,meet(X_361,complement(X_360)))))]]) ).
cnf(refute_0_963,plain,
join(X_361,meet(X_361,complement(X_360))) = X_361,
inference(resolve,[$cnf( $equal(X_361,join(X_361,meet(X_361,complement(X_360)))) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
join(X_361,meet(X_361,complement(complement(X_360)))) = X_361,
inference(subst,[],[refute_0_963:[bind(X_360,$fot(complement(X_360)))]]) ).
cnf(refute_0_965,plain,
( join(X_361,meet(X_361,X_360)) != join(X_361,meet(X_361,complement(complement(X_360))))
| join(X_361,meet(X_361,complement(complement(X_360)))) != X_361
| join(X_361,meet(X_361,X_360)) = X_361 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_361,meet(X_361,X_360)),X_361) ),[0],$fot(join(X_361,meet(X_361,complement(complement(X_360)))))]]) ).
cnf(refute_0_966,plain,
( join(X_361,meet(X_361,X_360)) != join(X_361,meet(X_361,complement(complement(X_360))))
| join(X_361,meet(X_361,X_360)) = X_361 ),
inference(resolve,[$cnf( $equal(join(X_361,meet(X_361,complement(complement(X_360)))),X_361) )],[refute_0_964,refute_0_965]) ).
cnf(refute_0_967,plain,
( join(meet(X_361,X_360),X_361) != join(X_361,meet(X_361,complement(complement(X_360))))
| join(X_361,meet(X_361,X_360)) = X_361 ),
inference(resolve,[$cnf( $equal(join(X_361,meet(X_361,X_360)),join(X_361,meet(X_361,complement(complement(X_360))))) )],[refute_0_64,refute_0_966]) ).
cnf(refute_0_968,plain,
join(X_361,meet(X_361,X_360)) = X_361,
inference(resolve,[$cnf( $equal(join(meet(X_361,X_360),X_361),join(X_361,meet(X_361,complement(complement(X_360))))) )],[refute_0_61,refute_0_967]) ).
cnf(refute_0_969,plain,
join(sk1,meet(sk1,converse(sk2))) = sk1,
inference(subst,[],[refute_0_968:[bind(X_360,$fot(converse(sk2))),bind(X_361,$fot(sk1))]]) ).
cnf(refute_0_970,plain,
composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),
introduced(tautology,[refl,[$fot(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)))]]) ).
cnf(refute_0_971,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(sk1,meet(sk1,converse(sk2))) != sk1
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) ),[1,0],$fot(sk1)]]) ).
cnf(refute_0_972,plain,
( join(sk1,meet(sk1,converse(sk2))) != sk1
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(sk1,meet(sk1,converse(sk2))),sk1) )],[refute_0_969,refute_0_972]) ).
cnf(refute_0_974,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| composition(sk1,meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) ),[0],$fot(composition(sk1,meet(sk2,sk3)))]]) ).
cnf(refute_0_975,plain,
( composition(sk1,meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) )],[refute_0_973,refute_0_974]) ).
cnf(refute_0_976,plain,
composition(sk1,meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) )],[refute_0_975,refute_0_20]) ).
cnf(refute_0_977,plain,
composition(sk1,meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)),
introduced(tautology,[refl,[$fot(composition(sk1,meet(sk2,sk3)))]]) ).
cnf(refute_0_978,plain,
$false,
inference(resolve,[$cnf( $equal(composition(sk1,meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) )],[refute_0_977,refute_0_976]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : REL023-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 13:28:31 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.23/5.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.23/5.44
% 5.23/5.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.34/5.55
%------------------------------------------------------------------------------