TSTP Solution File: REL004-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL004-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 19:42:58 EDT 2022
% Result : Unsatisfiable 1.54s 1.71s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 163
% Syntax : Number of clauses : 726 ( 373 unt; 0 nHn; 417 RR)
% Number of literals : 1231 (1230 equ; 507 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 816 ( 20 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(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,
converse(complement(sk1)) != complement(converse(sk1)) ).
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( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_6,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_7,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_7]) ).
cnf(refute_0_9,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_10,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_11,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_10]) ).
cnf(refute_0_12,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_13,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_14,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_17:[bind(X,$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_19,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_9,refute_0_19]) ).
cnf(refute_0_21,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_22,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_8,refute_0_22]) ).
cnf(refute_0_24,plain,
X_52 = join(meet(X_52,X_53),complement(join(complement(X_52),X_53))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_52)),bind(B,$fot(X_53))]]) ).
cnf(refute_0_25,plain,
meet(X_6,X_7) = complement(join(complement(X_6),complement(X_7))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_26,plain,
join(complement(X_7),complement(X_6)) = join(complement(X_6),complement(X_7)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_7))),bind(B,$fot(complement(X_6)))]]) ).
cnf(refute_0_27,plain,
( join(complement(X_7),complement(X_6)) != join(complement(X_6),complement(X_7))
| join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_7),complement(X_6)))),bind(Y,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_28,plain,
join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)),
inference(resolve,[$cnf( $equal(join(complement(X_7),complement(X_6)),join(complement(X_6),complement(X_7))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( join(complement(X_6),complement(X_7)) != join(complement(X_7),complement(X_6))
| meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))) ),
introduced(tautology,[equality,[$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_30,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( $equal(join(complement(X_6),complement(X_7)),join(complement(X_7),complement(X_6))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
complement(join(complement(X_7),complement(X_6))) = meet(X_7,X_6),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_7)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_33,plain,
( complement(join(complement(X_7),complement(X_6))) != meet(X_7,X_6)
| meet(X_6,X_7) != complement(join(complement(X_7),complement(X_6)))
| meet(X_6,X_7) = meet(X_7,X_6) ),
introduced(tautology,[equality,[$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_34,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( $equal(complement(join(complement(X_7),complement(X_6))),meet(X_7,X_6)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
meet(X_6,X_7) = meet(X_7,X_6),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_7),complement(X_6)))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
meet(X_53,X_52) = meet(X_52,X_53),
inference(subst,[],[refute_0_35:[bind(X_6,$fot(X_53)),bind(X_7,$fot(X_52))]]) ).
cnf(refute_0_37,plain,
( meet(X_53,X_52) != meet(X_52,X_53)
| meet(X_52,X_53) = meet(X_53,X_52) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_53,X_52))),bind(Y,$fot(meet(X_52,X_53)))]]) ).
cnf(refute_0_38,plain,
meet(X_52,X_53) = meet(X_53,X_52),
inference(resolve,[$cnf( $equal(meet(X_53,X_52),meet(X_52,X_53)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( X_52 != join(meet(X_52,X_53),complement(join(complement(X_52),X_53)))
| meet(X_52,X_53) != meet(X_53,X_52)
| X_52 = join(meet(X_53,X_52),complement(join(complement(X_52),X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(X_52,join(meet(X_52,X_53),complement(join(complement(X_52),X_53)))) ),[1,0],$fot(meet(X_53,X_52))]]) ).
cnf(refute_0_40,plain,
( X_52 != join(meet(X_52,X_53),complement(join(complement(X_52),X_53)))
| X_52 = join(meet(X_53,X_52),complement(join(complement(X_52),X_53))) ),
inference(resolve,[$cnf( $equal(meet(X_52,X_53),meet(X_53,X_52)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
X_52 = join(meet(X_53,X_52),complement(join(complement(X_52),X_53))),
inference(resolve,[$cnf( $equal(X_52,join(meet(X_52,X_53),complement(join(complement(X_52),X_53)))) )],[refute_0_24,refute_0_40]) ).
cnf(refute_0_42,plain,
X_52 = join(meet(join(complement(complement(X_52)),X_83),X_52),complement(join(complement(X_52),join(complement(complement(X_52)),X_83)))),
inference(subst,[],[refute_0_41:[bind(X_53,$fot(join(complement(complement(X_52)),X_83)))]]) ).
cnf(refute_0_43,plain,
join(X_29,join(complement(X_29),X_31)) = join(join(X_29,complement(X_29)),X_31),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_29)),bind(B,$fot(complement(X_29))),bind(C,$fot(X_31))]]) ).
cnf(refute_0_44,plain,
top = join(X_29,complement(X_29)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_29))]]) ).
cnf(refute_0_45,plain,
( top != join(X_29,complement(X_29))
| join(X_29,complement(X_29)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_29,complement(X_29))))]]) ).
cnf(refute_0_46,plain,
join(X_29,complement(X_29)) = top,
inference(resolve,[$cnf( $equal(top,join(X_29,complement(X_29))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( join(X_29,complement(X_29)) != top
| join(X_29,join(complement(X_29),X_31)) != join(join(X_29,complement(X_29)),X_31)
| join(X_29,join(complement(X_29),X_31)) = join(top,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_29,join(complement(X_29),X_31)),join(join(X_29,complement(X_29)),X_31)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_48,plain,
( join(X_29,join(complement(X_29),X_31)) != join(join(X_29,complement(X_29)),X_31)
| join(X_29,join(complement(X_29),X_31)) = join(top,X_31) ),
inference(resolve,[$cnf( $equal(join(X_29,complement(X_29)),top) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
join(X_29,join(complement(X_29),X_31)) = join(top,X_31),
inference(resolve,[$cnf( $equal(join(X_29,join(complement(X_29),X_31)),join(join(X_29,complement(X_29)),X_31)) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
join(X_29,join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))) = join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_29)),bind(B,$fot(meet(top,join(zero,zero)))),bind(C,$fot(join(zero,complement(meet(top,join(zero,zero))))))]]) ).
cnf(refute_0_51,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,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_52,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(complement(join(complement(X_6),complement(X_7)))))]]) ).
cnf(refute_0_53,plain,
complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_25,refute_0_52]) ).
cnf(refute_0_54,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| top != join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
introduced(tautology,[equality,[$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_55,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( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_51,refute_0_55]) ).
cnf(refute_0_57,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_58,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_57]) ).
cnf(refute_0_59,plain,
join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))),
inference(subst,[],[refute_0_58:[bind(A,$fot(complement(X_6))),bind(B,$fot(complement(X_7))),bind(C,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_60,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_61,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( $equal(join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),join(complement(X_6),join(complement(X_7),meet(X_6,X_7)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
top = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
top = join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),meet(join(zero,meet(top,top)),meet(top,join(zero,zero))))),
inference(subst,[],[refute_0_62:[bind(X_6,$fot(join(zero,meet(top,top)))),bind(X_7,$fot(meet(top,join(zero,zero))))]]) ).
cnf(refute_0_64,plain,
zero = meet(join(zero,meet(top,top)),complement(join(zero,meet(top,top)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(zero,meet(top,top))))]]) ).
cnf(refute_0_65,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_66,plain,
zero = meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_67,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_68,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( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_53,refute_0_67]) ).
cnf(refute_0_69,plain,
zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_66,refute_0_68]) ).
cnf(refute_0_70,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_71,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_70]) ).
cnf(refute_0_72,plain,
join(meet(X_6,X_7),complement(meet(X_6,X_7))) = top,
inference(subst,[],[refute_0_71:[bind(A,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_73,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,[$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))]]) ).
cnf(refute_0_74,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
introduced(tautology,[equality,[$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_75,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( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_6,X_7),complement(meet(X_6,X_7))),top) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
meet(join(complement(X_6),complement(X_7)),B) = complement(join(complement(join(complement(X_6),complement(X_7))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_78,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_79,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( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_53,refute_0_78]) ).
cnf(refute_0_80,plain,
meet(join(complement(X_6),complement(X_7)),B) = complement(join(meet(X_6,X_7),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))) )],[refute_0_77,refute_0_79]) ).
cnf(refute_0_81,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
inference(subst,[],[refute_0_80:[bind(B,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_82,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_17:[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,$fot(complement(top)))]]) ).
cnf(refute_0_83,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(top)) )],[refute_0_76,refute_0_83]) ).
cnf(refute_0_85,plain,
( meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(top)
| zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_86,plain,
( zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(top)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_69,refute_0_86]) ).
cnf(refute_0_88,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_89,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( complement(top) != zero
| meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_91,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_65,refute_0_91]) ).
cnf(refute_0_93,plain,
meet(top,join(zero,zero)) = complement(join(zero,complement(join(zero,zero)))),
inference(subst,[],[refute_0_92:[bind(B,$fot(join(zero,zero)))]]) ).
cnf(refute_0_94,plain,
meet(top,top) = complement(join(zero,complement(top))),
inference(subst,[],[refute_0_92:[bind(B,$fot(top))]]) ).
cnf(refute_0_95,plain,
( complement(top) != zero
| meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_96,plain,
( meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_95]) ).
cnf(refute_0_97,plain,
meet(top,top) = complement(join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) )],[refute_0_94,refute_0_96]) ).
cnf(refute_0_98,plain,
( meet(top,top) != complement(join(zero,zero))
| complement(join(zero,zero)) = meet(top,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,top))),bind(Y,$fot(complement(join(zero,zero))))]]) ).
cnf(refute_0_99,plain,
complement(join(zero,zero)) = meet(top,top),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( complement(join(zero,zero)) != meet(top,top)
| meet(top,join(zero,zero)) != complement(join(zero,complement(join(zero,zero))))
| meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,complement(join(zero,zero))))) ),[1,0,1],$fot(meet(top,top))]]) ).
cnf(refute_0_101,plain,
( meet(top,join(zero,zero)) != complement(join(zero,complement(join(zero,zero))))
| meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,complement(join(zero,zero))))) )],[refute_0_93,refute_0_101]) ).
cnf(refute_0_103,plain,
( meet(top,join(zero,zero)) != complement(join(zero,meet(top,top)))
| complement(join(zero,meet(top,top))) = meet(top,join(zero,zero)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,join(zero,zero)))),bind(Y,$fot(complement(join(zero,meet(top,top)))))]]) ).
cnf(refute_0_104,plain,
complement(join(zero,meet(top,top))) = meet(top,join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,meet(top,top)))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( complement(join(zero,meet(top,top))) != meet(top,join(zero,zero))
| zero != meet(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))
| zero = meet(join(zero,meet(top,top)),meet(top,join(zero,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))) ),[1,1],$fot(meet(top,join(zero,zero)))]]) ).
cnf(refute_0_106,plain,
( zero != meet(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))
| zero = meet(join(zero,meet(top,top)),meet(top,join(zero,zero))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,top))),meet(top,join(zero,zero))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
zero = meet(join(zero,meet(top,top)),meet(top,join(zero,zero))),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))) )],[refute_0_64,refute_0_106]) ).
cnf(refute_0_108,plain,
( zero != meet(join(zero,meet(top,top)),meet(top,join(zero,zero)))
| meet(join(zero,meet(top,top)),meet(top,join(zero,zero))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(join(zero,meet(top,top)),meet(top,join(zero,zero)))))]]) ).
cnf(refute_0_109,plain,
meet(join(zero,meet(top,top)),meet(top,join(zero,zero))) = zero,
inference(resolve,[$cnf( $equal(zero,meet(join(zero,meet(top,top)),meet(top,join(zero,zero)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( meet(join(zero,meet(top,top)),meet(top,join(zero,zero))) != zero
| top != join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),meet(join(zero,meet(top,top)),meet(top,join(zero,zero)))))
| top = join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),meet(join(zero,meet(top,top)),meet(top,join(zero,zero)))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_111,plain,
( top != join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),meet(join(zero,meet(top,top)),meet(top,join(zero,zero)))))
| top = join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) ),
inference(resolve,[$cnf( $equal(meet(join(zero,meet(top,top)),meet(top,join(zero,zero))),zero) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
top = join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)),
inference(resolve,[$cnf( $equal(top,join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),meet(join(zero,meet(top,top)),meet(top,join(zero,zero)))))) )],[refute_0_63,refute_0_111]) ).
cnf(refute_0_113,plain,
join(complement(meet(top,join(zero,zero))),zero) = join(zero,complement(meet(top,join(zero,zero)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(meet(top,join(zero,zero)))))]]) ).
cnf(refute_0_114,plain,
join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)),
introduced(tautology,[refl,[$fot(join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)))]]) ).
cnf(refute_0_115,plain,
( join(complement(meet(top,join(zero,zero))),zero) != join(zero,complement(meet(top,join(zero,zero))))
| join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) != join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero))
| join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)),join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero))) ),[1,1],$fot(join(zero,complement(meet(top,join(zero,zero)))))]]) ).
cnf(refute_0_116,plain,
( join(complement(meet(top,join(zero,zero))),zero) != join(zero,complement(meet(top,join(zero,zero))))
| join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)),join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))),
inference(resolve,[$cnf( $equal(join(complement(meet(top,join(zero,zero))),zero),join(zero,complement(meet(top,join(zero,zero))))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) = join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)),
introduced(tautology,[refl,[$fot(join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)))]]) ).
cnf(refute_0_119,plain,
( complement(join(zero,meet(top,top))) != meet(top,join(zero,zero))
| join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) != join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero))
| join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)),join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero))) ),[1,0],$fot(meet(top,join(zero,zero)))]]) ).
cnf(refute_0_120,plain,
( complement(join(zero,meet(top,top))) != meet(top,join(zero,zero))
| join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) ),
inference(resolve,[$cnf( $equal(join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)),join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,top))),meet(top,join(zero,zero))) )],[refute_0_104,refute_0_120]) ).
cnf(refute_0_122,plain,
( join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) != join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero))
| join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) != join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))
| join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)))),bind(Y,$fot(join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)))),bind(Z,$fot(join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))))]]) ).
cnf(refute_0_123,plain,
( join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)) != join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))
| join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) ),
inference(resolve,[$cnf( $equal(join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)),join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),zero)),join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))) )],[refute_0_117,refute_0_123]) ).
cnf(refute_0_125,plain,
( join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)) != join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))
| top != join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero))
| top = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero))) ),[1],$fot(join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))))]]) ).
cnf(refute_0_126,plain,
( top != join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero))
| top = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) ),
inference(resolve,[$cnf( $equal(join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero)),join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
top = join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))),
inference(resolve,[$cnf( $equal(top,join(complement(join(zero,meet(top,top))),join(complement(meet(top,join(zero,zero))),zero))) )],[refute_0_112,refute_0_126]) ).
cnf(refute_0_128,plain,
( top != join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))
| join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))))]]) ).
cnf(refute_0_129,plain,
join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) = top,
inference(resolve,[$cnf( $equal(top,join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( join(X_29,join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))) != join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero)))))
| join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))) != top
| join(X_29,top) = join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_29,join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))),join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero)))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_131,plain,
( join(X_29,join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))) != join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero)))))
| join(X_29,top) = join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero))))),top) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
join(X_29,top) = join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))),
inference(resolve,[$cnf( $equal(join(X_29,join(meet(top,join(zero,zero)),join(zero,complement(meet(top,join(zero,zero)))))),join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero)))))) )],[refute_0_50,refute_0_131]) ).
cnf(refute_0_133,plain,
join(A,join(X_29,X_30)) = join(join(X_29,X_30),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_29,X_30)))]]) ).
cnf(refute_0_134,plain,
join(X_29,join(X_30,A)) = join(join(X_29,X_30),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_29)),bind(B,$fot(X_30)),bind(C,$fot(A))]]) ).
cnf(refute_0_135,plain,
( join(X_29,join(X_30,A)) != join(join(X_29,X_30),A)
| join(join(X_29,X_30),A) = join(X_29,join(X_30,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_29,join(X_30,A)))),bind(Y,$fot(join(join(X_29,X_30),A)))]]) ).
cnf(refute_0_136,plain,
join(join(X_29,X_30),A) = join(X_29,join(X_30,A)),
inference(resolve,[$cnf( $equal(join(X_29,join(X_30,A)),join(join(X_29,X_30),A)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
( join(A,join(X_29,X_30)) != join(join(X_29,X_30),A)
| join(join(X_29,X_30),A) != join(X_29,join(X_30,A))
| join(A,join(X_29,X_30)) = join(X_29,join(X_30,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_29,X_30)),join(X_29,join(X_30,A))) ),[0],$fot(join(join(X_29,X_30),A))]]) ).
cnf(refute_0_138,plain,
( join(A,join(X_29,X_30)) != join(join(X_29,X_30),A)
| join(A,join(X_29,X_30)) = join(X_29,join(X_30,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_29,X_30),A),join(X_29,join(X_30,A))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
join(A,join(X_29,X_30)) = join(X_29,join(X_30,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_29,X_30)),join(join(X_29,X_30),A)) )],[refute_0_133,refute_0_138]) ).
cnf(refute_0_140,plain,
( join(A,join(X_29,X_30)) != join(X_29,join(X_30,A))
| join(X_29,join(X_30,A)) = join(A,join(X_29,X_30)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(X_29,X_30)))),bind(Y,$fot(join(X_29,join(X_30,A))))]]) ).
cnf(refute_0_141,plain,
join(X_29,join(X_30,A)) = join(A,join(X_29,X_30)),
inference(resolve,[$cnf( $equal(join(A,join(X_29,X_30)),join(X_29,join(X_30,A))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))) = join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)),
inference(subst,[],[refute_0_141:[bind(A,$fot(meet(top,join(zero,zero)))),bind(X_29,$fot(complement(meet(top,join(zero,zero))))),bind(X_30,$fot(X_29))]]) ).
cnf(refute_0_143,plain,
join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) = join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))),
introduced(tautology,[refl,[$fot(join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))))]]) ).
cnf(refute_0_144,plain,
( join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))) != join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))
| join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) != join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))
| join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))),join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))) ),[1,1],$fot(join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))]]) ).
cnf(refute_0_145,plain,
( join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))) != join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))
| join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))),join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),
inference(resolve,[$cnf( $equal(join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))),join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero)) = join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))),
inference(subst,[],[refute_0_141:[bind(A,$fot(zero)),bind(X_29,$fot(complement(meet(top,join(zero,zero))))),bind(X_30,$fot(join(X_29,meet(top,join(zero,zero)))))]]) ).
cnf(refute_0_148,plain,
join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) = join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero)),
inference(subst,[],[refute_0_141:[bind(A,$fot(complement(meet(top,join(zero,zero))))),bind(X_29,$fot(join(X_29,meet(top,join(zero,zero))))),bind(X_30,$fot(zero))]]) ).
cnf(refute_0_149,plain,
( join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero)) != join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))
| join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) != join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero))
| join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) = join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))))),bind(Y,$fot(join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero)))),bind(Z,$fot(join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))))]]) ).
cnf(refute_0_150,plain,
( join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero)) != join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))
| join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) = join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) ),
inference(resolve,[$cnf( $equal(join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))),join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) = join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))),
inference(resolve,[$cnf( $equal(join(complement(meet(top,join(zero,zero))),join(join(X_29,meet(top,join(zero,zero))),zero)),join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) != join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))
| join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) != join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))
| join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))))),bind(Y,$fot(join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))))),bind(Z,$fot(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))))]]) ).
cnf(refute_0_153,plain,
( join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))) != join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))
| join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) ),
inference(resolve,[$cnf( $equal(join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))),join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero)))))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),
inference(resolve,[$cnf( $equal(join(zero,join(complement(meet(top,join(zero,zero))),join(X_29,meet(top,join(zero,zero))))),join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))) )],[refute_0_146,refute_0_153]) ).
cnf(refute_0_155,plain,
( join(X_29,top) != join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero)))))
| join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))) != join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))
| join(X_29,top) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_29,top),join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))) ),[0],$fot(join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))))]]) ).
cnf(refute_0_156,plain,
( join(X_29,top) != join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero)))))
| join(X_29,top) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) ),
inference(resolve,[$cnf( $equal(join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero))))),join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
join(X_29,top) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),
inference(resolve,[$cnf( $equal(join(X_29,top),join(join(X_29,meet(top,join(zero,zero))),join(zero,complement(meet(top,join(zero,zero)))))) )],[refute_0_132,refute_0_156]) ).
cnf(refute_0_158,plain,
join(top,join(zero,X_31)) = join(join(top,zero),X_31),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(zero)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_159,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_160,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_161,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_160]) ).
cnf(refute_0_162,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_159,refute_0_161]) ).
cnf(refute_0_163,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_164,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( join(top,join(zero,X_31)) != join(join(top,zero),X_31)
| join(top,zero) != top
| join(top,join(zero,X_31)) = join(top,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,X_31)),join(join(top,zero),X_31)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_166,plain,
( join(top,join(zero,X_31)) != join(join(top,zero),X_31)
| join(top,join(zero,X_31)) = join(top,X_31) ),
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
join(top,join(zero,X_31)) = join(top,X_31),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_31)),join(join(top,zero),X_31)) )],[refute_0_158,refute_0_166]) ).
cnf(refute_0_168,plain,
join(top,join(zero,X_29)) = join(top,X_29),
inference(subst,[],[refute_0_167:[bind(X_31,$fot(X_29))]]) ).
cnf(refute_0_169,plain,
join(X_29,join(X_30,X_31)) = join(join(X_29,X_30),X_31),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_29)),bind(B,$fot(X_30)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_170,plain,
join(X_30,X_29) = join(X_29,X_30),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_30)),bind(B,$fot(X_29))]]) ).
cnf(refute_0_171,plain,
( join(X_30,X_29) != join(X_29,X_30)
| join(X_29,X_30) = join(X_30,X_29) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_30,X_29))),bind(Y,$fot(join(X_29,X_30)))]]) ).
cnf(refute_0_172,plain,
join(X_29,X_30) = join(X_30,X_29),
inference(resolve,[$cnf( $equal(join(X_30,X_29),join(X_29,X_30)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( join(X_29,X_30) != join(X_30,X_29)
| join(X_29,join(X_30,X_31)) != join(join(X_29,X_30),X_31)
| join(X_29,join(X_30,X_31)) = join(join(X_30,X_29),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_29,join(X_30,X_31)),join(join(X_29,X_30),X_31)) ),[1,0],$fot(join(X_30,X_29))]]) ).
cnf(refute_0_174,plain,
( join(X_29,join(X_30,X_31)) != join(join(X_29,X_30),X_31)
| join(X_29,join(X_30,X_31)) = join(join(X_30,X_29),X_31) ),
inference(resolve,[$cnf( $equal(join(X_29,X_30),join(X_30,X_29)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
join(X_29,join(X_30,X_31)) = join(join(X_30,X_29),X_31),
inference(resolve,[$cnf( $equal(join(X_29,join(X_30,X_31)),join(join(X_29,X_30),X_31)) )],[refute_0_169,refute_0_174]) ).
cnf(refute_0_176,plain,
join(join(X_30,X_29),X_31) = join(X_30,join(X_29,X_31)),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_30)),bind(B,$fot(X_29)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_177,plain,
( join(X_29,join(X_30,X_31)) != join(join(X_30,X_29),X_31)
| join(join(X_30,X_29),X_31) != join(X_30,join(X_29,X_31))
| join(X_29,join(X_30,X_31)) = join(X_30,join(X_29,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_29,join(X_30,X_31)),join(X_30,join(X_29,X_31))) ),[0],$fot(join(join(X_30,X_29),X_31))]]) ).
cnf(refute_0_178,plain,
( join(X_29,join(X_30,X_31)) != join(join(X_30,X_29),X_31)
| join(X_29,join(X_30,X_31)) = join(X_30,join(X_29,X_31)) ),
inference(resolve,[$cnf( $equal(join(join(X_30,X_29),X_31),join(X_30,join(X_29,X_31))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
join(X_29,join(X_30,X_31)) = join(X_30,join(X_29,X_31)),
inference(resolve,[$cnf( $equal(join(X_29,join(X_30,X_31)),join(join(X_30,X_29),X_31)) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
( join(X_29,join(X_30,X_31)) != join(X_30,join(X_29,X_31))
| join(X_30,join(X_29,X_31)) = join(X_29,join(X_30,X_31)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_29,join(X_30,X_31)))),bind(Y,$fot(join(X_30,join(X_29,X_31))))]]) ).
cnf(refute_0_181,plain,
join(X_30,join(X_29,X_31)) = join(X_29,join(X_30,X_31)),
inference(resolve,[$cnf( $equal(join(X_29,join(X_30,X_31)),join(X_30,join(X_29,X_31))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
join(zero,join(top,X_29)) = join(top,join(zero,X_29)),
inference(subst,[],[refute_0_181:[bind(X_29,$fot(top)),bind(X_30,$fot(zero)),bind(X_31,$fot(X_29))]]) ).
cnf(refute_0_183,plain,
( join(top,join(zero,X_29)) != join(top,X_29)
| join(zero,join(top,X_29)) != join(top,join(zero,X_29))
| join(zero,join(top,X_29)) = join(top,X_29) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,join(top,X_29)))),bind(Y,$fot(join(top,join(zero,X_29)))),bind(Z,$fot(join(top,X_29)))]]) ).
cnf(refute_0_184,plain,
( join(top,join(zero,X_29)) != join(top,X_29)
| join(zero,join(top,X_29)) = join(top,X_29) ),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_29)),join(top,join(zero,X_29))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
join(zero,join(top,X_29)) = join(top,X_29),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_29)),join(top,X_29)) )],[refute_0_168,refute_0_184]) ).
cnf(refute_0_186,plain,
join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)) = join(top,X_29),
inference(subst,[],[refute_0_49:[bind(X_29,$fot(meet(top,join(zero,zero)))),bind(X_31,$fot(X_29))]]) ).
cnf(refute_0_187,plain,
join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) = join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),
introduced(tautology,[refl,[$fot(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))))]]) ).
cnf(refute_0_188,plain,
( join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)) != join(top,X_29)
| join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) != join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))
| join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) = join(zero,join(top,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))) ),[1,1],$fot(join(top,X_29))]]) ).
cnf(refute_0_189,plain,
( join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)) != join(top,X_29)
| join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) = join(zero,join(top,X_29)) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) = join(zero,join(top,X_29)),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)),join(top,X_29)) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
( join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) != join(zero,join(top,X_29))
| join(zero,join(top,X_29)) != join(top,X_29)
| join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) = join(top,X_29) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))))),bind(Y,$fot(join(zero,join(top,X_29)))),bind(Z,$fot(join(top,X_29)))]]) ).
cnf(refute_0_192,plain,
( join(zero,join(top,X_29)) != join(top,X_29)
| join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) = join(top,X_29) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),join(zero,join(top,X_29))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) = join(top,X_29),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_29)),join(top,X_29)) )],[refute_0_185,refute_0_192]) ).
cnf(refute_0_194,plain,
( join(X_29,top) != join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))
| join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))) != join(top,X_29)
| join(X_29,top) = join(top,X_29) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_29,top),join(top,X_29)) ),[0],$fot(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))))]]) ).
cnf(refute_0_195,plain,
( join(X_29,top) != join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))
| join(X_29,top) = join(top,X_29) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29))),join(top,X_29)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
join(X_29,top) = join(top,X_29),
inference(resolve,[$cnf( $equal(join(X_29,top),join(zero,join(meet(top,join(zero,zero)),join(complement(meet(top,join(zero,zero))),X_29)))) )],[refute_0_157,refute_0_195]) ).
cnf(refute_0_197,plain,
join(X_46,join(complement(X_46),complement(complement(X_46)))) = join(top,complement(complement(X_46))),
inference(subst,[],[refute_0_49:[bind(X_29,$fot(X_46)),bind(X_31,$fot(complement(complement(X_46))))]]) ).
cnf(refute_0_198,plain,
top = join(complement(X_46),complement(complement(X_46))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_46)))]]) ).
cnf(refute_0_199,plain,
( top != join(complement(X_46),complement(complement(X_46)))
| join(complement(X_46),complement(complement(X_46))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_46),complement(complement(X_46)))))]]) ).
cnf(refute_0_200,plain,
join(complement(X_46),complement(complement(X_46))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_46),complement(complement(X_46)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
( join(X_46,join(complement(X_46),complement(complement(X_46)))) != join(top,complement(complement(X_46)))
| join(complement(X_46),complement(complement(X_46))) != top
| join(X_46,top) = join(top,complement(complement(X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,join(complement(X_46),complement(complement(X_46)))),join(top,complement(complement(X_46)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_202,plain,
( join(X_46,join(complement(X_46),complement(complement(X_46)))) != join(top,complement(complement(X_46)))
| join(X_46,top) = join(top,complement(complement(X_46))) ),
inference(resolve,[$cnf( $equal(join(complement(X_46),complement(complement(X_46))),top) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
join(X_46,top) = join(top,complement(complement(X_46))),
inference(resolve,[$cnf( $equal(join(X_46,join(complement(X_46),complement(complement(X_46)))),join(top,complement(complement(X_46)))) )],[refute_0_197,refute_0_202]) ).
cnf(refute_0_204,plain,
join(X_46,join(complement(X_46),complement(X_46))) = join(top,complement(X_46)),
inference(subst,[],[refute_0_49:[bind(X_29,$fot(X_46)),bind(X_31,$fot(complement(X_46)))]]) ).
cnf(refute_0_205,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_206,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$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_207,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_207]) ).
cnf(refute_0_209,plain,
join(complement(X_40),composition(converse(one),complement(composition(one,X_40)))) = complement(X_40),
inference(subst,[],[refute_0_208:[bind(A,$fot(one)),bind(B,$fot(X_40))]]) ).
cnf(refute_0_210,plain,
converse(composition(converse(A),X_19)) = composition(converse(X_19),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_19))]]) ).
cnf(refute_0_211,plain,
( converse(composition(converse(A),X_19)) != composition(converse(X_19),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_19)) = composition(converse(X_19),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_19)),composition(converse(X_19),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_212,plain,
( converse(composition(converse(A),X_19)) != composition(converse(X_19),converse(converse(A)))
| converse(composition(converse(A),X_19)) = composition(converse(X_19),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_211]) ).
cnf(refute_0_213,plain,
converse(composition(converse(A),X_19)) = composition(converse(X_19),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_19)),composition(converse(X_19),converse(converse(A)))) )],[refute_0_210,refute_0_212]) ).
cnf(refute_0_214,plain,
converse(composition(converse(X_20),one)) = composition(converse(one),X_20),
inference(subst,[],[refute_0_213:[bind(A,$fot(X_20)),bind(X_19,$fot(one))]]) ).
cnf(refute_0_215,plain,
composition(converse(X_20),one) = converse(X_20),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_20)))]]) ).
cnf(refute_0_216,plain,
( composition(converse(X_20),one) != converse(X_20)
| converse(composition(converse(X_20),one)) != composition(converse(one),X_20)
| converse(converse(X_20)) = composition(converse(one),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_20),one)),composition(converse(one),X_20)) ),[0,0],$fot(converse(X_20))]]) ).
cnf(refute_0_217,plain,
( converse(composition(converse(X_20),one)) != composition(converse(one),X_20)
| converse(converse(X_20)) = composition(converse(one),X_20) ),
inference(resolve,[$cnf( $equal(composition(converse(X_20),one),converse(X_20)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
converse(converse(X_20)) = composition(converse(one),X_20),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_20),one)),composition(converse(one),X_20)) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
converse(converse(X_20)) = X_20,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_220,plain,
( converse(converse(X_20)) != X_20
| converse(converse(X_20)) != composition(converse(one),X_20)
| X_20 = composition(converse(one),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_20)),composition(converse(one),X_20)) ),[0],$fot(X_20)]]) ).
cnf(refute_0_221,plain,
( converse(converse(X_20)) != composition(converse(one),X_20)
| X_20 = composition(converse(one),X_20) ),
inference(resolve,[$cnf( $equal(converse(converse(X_20)),X_20) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
X_20 = composition(converse(one),X_20),
inference(resolve,[$cnf( $equal(converse(converse(X_20)),composition(converse(one),X_20)) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_224,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_222:[bind(X_20,$fot(one))]]) ).
cnf(refute_0_225,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_226,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_228,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_223,refute_0_228]) ).
cnf(refute_0_230,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_231,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
composition(converse(one),X_20) = composition(converse(one),X_20),
introduced(tautology,[refl,[$fot(composition(converse(one),X_20))]]) ).
cnf(refute_0_233,plain,
( composition(converse(one),X_20) != composition(converse(one),X_20)
| converse(one) != one
| composition(converse(one),X_20) = composition(one,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_20),composition(converse(one),X_20)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_234,plain,
( converse(one) != one
| composition(converse(one),X_20) = composition(one,X_20) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_20),composition(converse(one),X_20)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
composition(converse(one),X_20) = composition(one,X_20),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
( X_20 != composition(converse(one),X_20)
| composition(converse(one),X_20) != composition(one,X_20)
| X_20 = composition(one,X_20) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_20,composition(one,X_20)) ),[0],$fot(composition(converse(one),X_20))]]) ).
cnf(refute_0_237,plain,
( X_20 != composition(converse(one),X_20)
| X_20 = composition(one,X_20) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_20),composition(one,X_20)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
X_20 = composition(one,X_20),
inference(resolve,[$cnf( $equal(X_20,composition(converse(one),X_20)) )],[refute_0_222,refute_0_237]) ).
cnf(refute_0_239,plain,
X_40 = composition(one,X_40),
inference(subst,[],[refute_0_238:[bind(X_20,$fot(X_40))]]) ).
cnf(refute_0_240,plain,
( X_40 != composition(one,X_40)
| composition(one,X_40) = X_40 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_40)),bind(Y,$fot(composition(one,X_40)))]]) ).
cnf(refute_0_241,plain,
composition(one,X_40) = X_40,
inference(resolve,[$cnf( $equal(X_40,composition(one,X_40)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( composition(one,X_40) != X_40
| join(complement(X_40),composition(converse(one),complement(composition(one,X_40)))) != complement(X_40)
| join(complement(X_40),composition(converse(one),complement(X_40))) = complement(X_40) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_40),composition(converse(one),complement(composition(one,X_40)))),complement(X_40)) ),[0,1,1,0],$fot(X_40)]]) ).
cnf(refute_0_243,plain,
( join(complement(X_40),composition(converse(one),complement(composition(one,X_40)))) != complement(X_40)
| join(complement(X_40),composition(converse(one),complement(X_40))) = complement(X_40) ),
inference(resolve,[$cnf( $equal(composition(one,X_40),X_40) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
join(complement(X_40),composition(converse(one),complement(X_40))) = complement(X_40),
inference(resolve,[$cnf( $equal(join(complement(X_40),composition(converse(one),complement(composition(one,X_40)))),complement(X_40)) )],[refute_0_209,refute_0_243]) ).
cnf(refute_0_245,plain,
( X_20 != composition(one,X_20)
| composition(one,X_20) = X_20 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_20)),bind(Y,$fot(composition(one,X_20)))]]) ).
cnf(refute_0_246,plain,
composition(one,X_20) = X_20,
inference(resolve,[$cnf( $equal(X_20,composition(one,X_20)) )],[refute_0_238,refute_0_245]) ).
cnf(refute_0_247,plain,
composition(one,complement(X_40)) = complement(X_40),
inference(subst,[],[refute_0_246:[bind(X_20,$fot(complement(X_40)))]]) ).
cnf(refute_0_248,plain,
composition(converse(one),complement(X_40)) = composition(converse(one),complement(X_40)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_40)))]]) ).
cnf(refute_0_249,plain,
( composition(converse(one),complement(X_40)) != composition(converse(one),complement(X_40))
| converse(one) != one
| composition(converse(one),complement(X_40)) = composition(one,complement(X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_40)),composition(converse(one),complement(X_40))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_250,plain,
( converse(one) != one
| composition(converse(one),complement(X_40)) = composition(one,complement(X_40)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_40)),composition(converse(one),complement(X_40))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
composition(converse(one),complement(X_40)) = composition(one,complement(X_40)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_231,refute_0_250]) ).
cnf(refute_0_252,plain,
( composition(converse(one),complement(X_40)) != composition(one,complement(X_40))
| composition(one,complement(X_40)) != complement(X_40)
| composition(converse(one),complement(X_40)) = complement(X_40) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(composition(converse(one),complement(X_40)))),bind(Y,$fot(composition(one,complement(X_40)))),bind(Z,$fot(complement(X_40)))]]) ).
cnf(refute_0_253,plain,
( composition(one,complement(X_40)) != complement(X_40)
| composition(converse(one),complement(X_40)) = complement(X_40) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_40)),composition(one,complement(X_40))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
composition(converse(one),complement(X_40)) = complement(X_40),
inference(resolve,[$cnf( $equal(composition(one,complement(X_40)),complement(X_40)) )],[refute_0_247,refute_0_253]) ).
cnf(refute_0_255,plain,
join(complement(X_40),composition(converse(one),complement(X_40))) = join(complement(X_40),composition(converse(one),complement(X_40))),
introduced(tautology,[refl,[$fot(join(complement(X_40),composition(converse(one),complement(X_40))))]]) ).
cnf(refute_0_256,plain,
( composition(converse(one),complement(X_40)) != complement(X_40)
| join(complement(X_40),composition(converse(one),complement(X_40))) != join(complement(X_40),composition(converse(one),complement(X_40)))
| join(complement(X_40),composition(converse(one),complement(X_40))) = join(complement(X_40),complement(X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_40),composition(converse(one),complement(X_40))),join(complement(X_40),composition(converse(one),complement(X_40)))) ),[1,1],$fot(complement(X_40))]]) ).
cnf(refute_0_257,plain,
( composition(converse(one),complement(X_40)) != complement(X_40)
| join(complement(X_40),composition(converse(one),complement(X_40))) = join(complement(X_40),complement(X_40)) ),
inference(resolve,[$cnf( $equal(join(complement(X_40),composition(converse(one),complement(X_40))),join(complement(X_40),composition(converse(one),complement(X_40)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
join(complement(X_40),composition(converse(one),complement(X_40))) = join(complement(X_40),complement(X_40)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_40)),complement(X_40)) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
( join(complement(X_40),composition(converse(one),complement(X_40))) != complement(X_40)
| join(complement(X_40),composition(converse(one),complement(X_40))) != join(complement(X_40),complement(X_40))
| join(complement(X_40),complement(X_40)) = complement(X_40) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_40),composition(converse(one),complement(X_40))),complement(X_40)) ),[0],$fot(join(complement(X_40),complement(X_40)))]]) ).
cnf(refute_0_260,plain,
( join(complement(X_40),composition(converse(one),complement(X_40))) != complement(X_40)
| join(complement(X_40),complement(X_40)) = complement(X_40) ),
inference(resolve,[$cnf( $equal(join(complement(X_40),composition(converse(one),complement(X_40))),join(complement(X_40),complement(X_40))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
join(complement(X_40),complement(X_40)) = complement(X_40),
inference(resolve,[$cnf( $equal(join(complement(X_40),composition(converse(one),complement(X_40))),complement(X_40)) )],[refute_0_244,refute_0_260]) ).
cnf(refute_0_262,plain,
join(complement(X_46),complement(X_46)) = complement(X_46),
inference(subst,[],[refute_0_261:[bind(X_40,$fot(X_46))]]) ).
cnf(refute_0_263,plain,
( join(X_46,join(complement(X_46),complement(X_46))) != join(top,complement(X_46))
| join(complement(X_46),complement(X_46)) != complement(X_46)
| join(X_46,complement(X_46)) = join(top,complement(X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,join(complement(X_46),complement(X_46))),join(top,complement(X_46))) ),[0,1],$fot(complement(X_46))]]) ).
cnf(refute_0_264,plain,
( join(X_46,join(complement(X_46),complement(X_46))) != join(top,complement(X_46))
| join(X_46,complement(X_46)) = join(top,complement(X_46)) ),
inference(resolve,[$cnf( $equal(join(complement(X_46),complement(X_46)),complement(X_46)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
join(X_46,complement(X_46)) = join(top,complement(X_46)),
inference(resolve,[$cnf( $equal(join(X_46,join(complement(X_46),complement(X_46))),join(top,complement(X_46))) )],[refute_0_204,refute_0_264]) ).
cnf(refute_0_266,plain,
join(X_46,complement(X_46)) = top,
inference(subst,[],[refute_0_71:[bind(A,$fot(X_46))]]) ).
cnf(refute_0_267,plain,
( join(X_46,complement(X_46)) != join(top,complement(X_46))
| join(X_46,complement(X_46)) != top
| top = join(top,complement(X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,complement(X_46)),join(top,complement(X_46))) ),[0],$fot(top)]]) ).
cnf(refute_0_268,plain,
( join(X_46,complement(X_46)) != join(top,complement(X_46))
| top = join(top,complement(X_46)) ),
inference(resolve,[$cnf( $equal(join(X_46,complement(X_46)),top) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
top = join(top,complement(X_46)),
inference(resolve,[$cnf( $equal(join(X_46,complement(X_46)),join(top,complement(X_46))) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
( top != join(top,complement(X_46))
| join(top,complement(X_46)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_46))))]]) ).
cnf(refute_0_271,plain,
join(top,complement(X_46)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_46))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
join(top,complement(complement(X_46))) = top,
inference(subst,[],[refute_0_271:[bind(X_46,$fot(complement(X_46)))]]) ).
cnf(refute_0_273,plain,
( join(X_46,top) != join(top,complement(complement(X_46)))
| join(top,complement(complement(X_46))) != top
| join(X_46,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_46,top),top) ),[0],$fot(join(top,complement(complement(X_46))))]]) ).
cnf(refute_0_274,plain,
( join(X_46,top) != join(top,complement(complement(X_46)))
| join(X_46,top) = top ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(X_46))),top) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
join(X_46,top) = top,
inference(resolve,[$cnf( $equal(join(X_46,top),join(top,complement(complement(X_46)))) )],[refute_0_203,refute_0_274]) ).
cnf(refute_0_276,plain,
join(X_29,top) = top,
inference(subst,[],[refute_0_275:[bind(X_46,$fot(X_29))]]) ).
cnf(refute_0_277,plain,
( join(X_29,top) != join(top,X_29)
| join(X_29,top) != top
| top = join(top,X_29) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_29,top),join(top,X_29)) ),[0],$fot(top)]]) ).
cnf(refute_0_278,plain,
( join(X_29,top) != join(top,X_29)
| top = join(top,X_29) ),
inference(resolve,[$cnf( $equal(join(X_29,top),top) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
top = join(top,X_29),
inference(resolve,[$cnf( $equal(join(X_29,top),join(top,X_29)) )],[refute_0_196,refute_0_278]) ).
cnf(refute_0_280,plain,
( top != join(top,X_29)
| join(top,X_29) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_29)))]]) ).
cnf(refute_0_281,plain,
join(top,X_29) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_29)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
join(top,X_31) = top,
inference(subst,[],[refute_0_281:[bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_283,plain,
( join(X_29,join(complement(X_29),X_31)) != join(top,X_31)
| join(top,X_31) != top
| join(X_29,join(complement(X_29),X_31)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_29,join(complement(X_29),X_31)),top) ),[0],$fot(join(top,X_31))]]) ).
cnf(refute_0_284,plain,
( join(X_29,join(complement(X_29),X_31)) != join(top,X_31)
| join(X_29,join(complement(X_29),X_31)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_31),top) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
join(X_29,join(complement(X_29),X_31)) = top,
inference(resolve,[$cnf( $equal(join(X_29,join(complement(X_29),X_31)),join(top,X_31)) )],[refute_0_49,refute_0_284]) ).
cnf(refute_0_286,plain,
join(complement(X_52),join(complement(complement(X_52)),X_83)) = top,
inference(subst,[],[refute_0_285:[bind(X_29,$fot(complement(X_52))),bind(X_31,$fot(X_83))]]) ).
cnf(refute_0_287,plain,
( X_52 != join(meet(join(complement(complement(X_52)),X_83),X_52),complement(join(complement(X_52),join(complement(complement(X_52)),X_83))))
| join(complement(X_52),join(complement(complement(X_52)),X_83)) != top
| X_52 = join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_52,join(meet(join(complement(complement(X_52)),X_83),X_52),complement(join(complement(X_52),join(complement(complement(X_52)),X_83))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_288,plain,
( X_52 != join(meet(join(complement(complement(X_52)),X_83),X_52),complement(join(complement(X_52),join(complement(complement(X_52)),X_83))))
| X_52 = join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_52),join(complement(complement(X_52)),X_83)),top) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
X_52 = join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)),
inference(resolve,[$cnf( $equal(X_52,join(meet(join(complement(complement(X_52)),X_83),X_52),complement(join(complement(X_52),join(complement(complement(X_52)),X_83))))) )],[refute_0_42,refute_0_288]) ).
cnf(refute_0_290,plain,
X_52 = join(meet(X_52,complement(complement(X_52))),complement(join(complement(X_52),complement(complement(X_52))))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_52)),bind(B,$fot(complement(complement(X_52))))]]) ).
cnf(refute_0_291,plain,
top = join(complement(X_52),complement(complement(X_52))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_52)))]]) ).
cnf(refute_0_292,plain,
( top != join(complement(X_52),complement(complement(X_52)))
| join(complement(X_52),complement(complement(X_52))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_52),complement(complement(X_52)))))]]) ).
cnf(refute_0_293,plain,
join(complement(X_52),complement(complement(X_52))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_52),complement(complement(X_52)))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
( X_52 != join(meet(X_52,complement(complement(X_52))),complement(join(complement(X_52),complement(complement(X_52)))))
| join(complement(X_52),complement(complement(X_52))) != top
| X_52 = join(meet(X_52,complement(complement(X_52))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_52,join(meet(X_52,complement(complement(X_52))),complement(join(complement(X_52),complement(complement(X_52)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_295,plain,
( X_52 != join(meet(X_52,complement(complement(X_52))),complement(join(complement(X_52),complement(complement(X_52)))))
| X_52 = join(meet(X_52,complement(complement(X_52))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_52),complement(complement(X_52))),top) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
X_52 = join(meet(X_52,complement(complement(X_52))),complement(top)),
inference(resolve,[$cnf( $equal(X_52,join(meet(X_52,complement(complement(X_52))),complement(join(complement(X_52),complement(complement(X_52)))))) )],[refute_0_290,refute_0_295]) ).
cnf(refute_0_297,plain,
join(complement(top),meet(X_52,complement(complement(X_52)))) = join(complement(top),meet(X_52,complement(complement(X_52)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_52,complement(complement(X_52)))))]]) ).
cnf(refute_0_298,plain,
( complement(top) != zero
| join(complement(top),meet(X_52,complement(complement(X_52)))) != join(complement(top),meet(X_52,complement(complement(X_52))))
| join(complement(top),meet(X_52,complement(complement(X_52)))) = join(zero,meet(X_52,complement(complement(X_52)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_52,complement(complement(X_52)))),join(complement(top),meet(X_52,complement(complement(X_52))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_299,plain,
( complement(top) != zero
| join(complement(top),meet(X_52,complement(complement(X_52)))) = join(zero,meet(X_52,complement(complement(X_52)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_52,complement(complement(X_52)))),join(complement(top),meet(X_52,complement(complement(X_52))))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
join(complement(top),meet(X_52,complement(complement(X_52)))) = join(zero,meet(X_52,complement(complement(X_52)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_299]) ).
cnf(refute_0_301,plain,
join(meet(X_52,complement(complement(X_52))),complement(top)) = join(complement(top),meet(X_52,complement(complement(X_52)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_52,complement(complement(X_52)))))]]) ).
cnf(refute_0_302,plain,
( join(complement(top),meet(X_52,complement(complement(X_52)))) != join(zero,meet(X_52,complement(complement(X_52))))
| join(meet(X_52,complement(complement(X_52))),complement(top)) != join(complement(top),meet(X_52,complement(complement(X_52))))
| join(meet(X_52,complement(complement(X_52))),complement(top)) = join(zero,meet(X_52,complement(complement(X_52)))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(X_52,complement(complement(X_52))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_52,complement(complement(X_52)))))),bind(Z,$fot(join(zero,meet(X_52,complement(complement(X_52))))))]]) ).
cnf(refute_0_303,plain,
( join(complement(top),meet(X_52,complement(complement(X_52)))) != join(zero,meet(X_52,complement(complement(X_52))))
| join(meet(X_52,complement(complement(X_52))),complement(top)) = join(zero,meet(X_52,complement(complement(X_52)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_52,complement(complement(X_52))),complement(top)),join(complement(top),meet(X_52,complement(complement(X_52))))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
join(meet(X_52,complement(complement(X_52))),complement(top)) = join(zero,meet(X_52,complement(complement(X_52)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_52,complement(complement(X_52)))),join(zero,meet(X_52,complement(complement(X_52))))) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
( X_52 != join(meet(X_52,complement(complement(X_52))),complement(top))
| join(meet(X_52,complement(complement(X_52))),complement(top)) != join(zero,meet(X_52,complement(complement(X_52))))
| X_52 = join(zero,meet(X_52,complement(complement(X_52)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,join(zero,meet(X_52,complement(complement(X_52))))) ),[0],$fot(join(meet(X_52,complement(complement(X_52))),complement(top)))]]) ).
cnf(refute_0_306,plain,
( X_52 != join(meet(X_52,complement(complement(X_52))),complement(top))
| X_52 = join(zero,meet(X_52,complement(complement(X_52)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_52,complement(complement(X_52))),complement(top)),join(zero,meet(X_52,complement(complement(X_52))))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
X_52 = join(zero,meet(X_52,complement(complement(X_52)))),
inference(resolve,[$cnf( $equal(X_52,join(meet(X_52,complement(complement(X_52))),complement(top))) )],[refute_0_296,refute_0_306]) ).
cnf(refute_0_308,plain,
meet(B,B) = complement(join(complement(B),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_309,plain,
join(complement(B),complement(B)) = complement(B),
inference(subst,[],[refute_0_261:[bind(X_40,$fot(B))]]) ).
cnf(refute_0_310,plain,
( join(complement(B),complement(B)) != complement(B)
| meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_311,plain,
( meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(join(complement(B),complement(B)),complement(B)) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
meet(B,B) = complement(complement(B)),
inference(resolve,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) )],[refute_0_308,refute_0_311]) ).
cnf(refute_0_313,plain,
X_52 = join(meet(X_52,complement(X_52)),complement(join(complement(X_52),complement(X_52)))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_52)),bind(B,$fot(complement(X_52)))]]) ).
cnf(refute_0_314,plain,
join(complement(X_52),complement(X_52)) = complement(X_52),
inference(subst,[],[refute_0_261:[bind(X_40,$fot(X_52))]]) ).
cnf(refute_0_315,plain,
( X_52 != join(meet(X_52,complement(X_52)),complement(join(complement(X_52),complement(X_52))))
| join(complement(X_52),complement(X_52)) != complement(X_52)
| X_52 = join(meet(X_52,complement(X_52)),complement(complement(X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(X_52,join(meet(X_52,complement(X_52)),complement(join(complement(X_52),complement(X_52))))) ),[1,1,0],$fot(complement(X_52))]]) ).
cnf(refute_0_316,plain,
( X_52 != join(meet(X_52,complement(X_52)),complement(join(complement(X_52),complement(X_52))))
| X_52 = join(meet(X_52,complement(X_52)),complement(complement(X_52))) ),
inference(resolve,[$cnf( $equal(join(complement(X_52),complement(X_52)),complement(X_52)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
X_52 = join(meet(X_52,complement(X_52)),complement(complement(X_52))),
inference(resolve,[$cnf( $equal(X_52,join(meet(X_52,complement(X_52)),complement(join(complement(X_52),complement(X_52))))) )],[refute_0_313,refute_0_316]) ).
cnf(refute_0_318,plain,
join(complement(complement(X_52)),zero) = join(zero,complement(complement(X_52))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_52))))]]) ).
cnf(refute_0_319,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_320,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_319]) ).
cnf(refute_0_321,plain,
meet(X_52,complement(X_52)) = zero,
inference(subst,[],[refute_0_320:[bind(A,$fot(X_52))]]) ).
cnf(refute_0_322,plain,
join(complement(complement(X_52)),meet(X_52,complement(X_52))) = join(complement(complement(X_52)),meet(X_52,complement(X_52))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_52)),meet(X_52,complement(X_52))))]]) ).
cnf(refute_0_323,plain,
( join(complement(complement(X_52)),meet(X_52,complement(X_52))) != join(complement(complement(X_52)),meet(X_52,complement(X_52)))
| meet(X_52,complement(X_52)) != zero
| join(complement(complement(X_52)),meet(X_52,complement(X_52))) = join(complement(complement(X_52)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_52)),meet(X_52,complement(X_52))),join(complement(complement(X_52)),meet(X_52,complement(X_52)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_324,plain,
( meet(X_52,complement(X_52)) != zero
| join(complement(complement(X_52)),meet(X_52,complement(X_52))) = join(complement(complement(X_52)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_52)),meet(X_52,complement(X_52))),join(complement(complement(X_52)),meet(X_52,complement(X_52)))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
join(complement(complement(X_52)),meet(X_52,complement(X_52))) = join(complement(complement(X_52)),zero),
inference(resolve,[$cnf( $equal(meet(X_52,complement(X_52)),zero) )],[refute_0_321,refute_0_324]) ).
cnf(refute_0_326,plain,
( join(complement(complement(X_52)),meet(X_52,complement(X_52))) != join(complement(complement(X_52)),zero)
| join(complement(complement(X_52)),zero) != join(zero,complement(complement(X_52)))
| join(complement(complement(X_52)),meet(X_52,complement(X_52))) = join(zero,complement(complement(X_52))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(complement(X_52)),meet(X_52,complement(X_52))))),bind(Y,$fot(join(complement(complement(X_52)),zero))),bind(Z,$fot(join(zero,complement(complement(X_52)))))]]) ).
cnf(refute_0_327,plain,
( join(complement(complement(X_52)),zero) != join(zero,complement(complement(X_52)))
| join(complement(complement(X_52)),meet(X_52,complement(X_52))) = join(zero,complement(complement(X_52))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_52)),meet(X_52,complement(X_52))),join(complement(complement(X_52)),zero)) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
join(complement(complement(X_52)),meet(X_52,complement(X_52))) = join(zero,complement(complement(X_52))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_52)),zero),join(zero,complement(complement(X_52)))) )],[refute_0_318,refute_0_327]) ).
cnf(refute_0_329,plain,
join(meet(X_52,complement(X_52)),complement(complement(X_52))) = join(complement(complement(X_52)),meet(X_52,complement(X_52))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(complement(X_52)))),bind(B,$fot(meet(X_52,complement(X_52))))]]) ).
cnf(refute_0_330,plain,
( join(complement(complement(X_52)),meet(X_52,complement(X_52))) != join(zero,complement(complement(X_52)))
| join(meet(X_52,complement(X_52)),complement(complement(X_52))) != join(complement(complement(X_52)),meet(X_52,complement(X_52)))
| join(meet(X_52,complement(X_52)),complement(complement(X_52))) = join(zero,complement(complement(X_52))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(X_52,complement(X_52)),complement(complement(X_52))))),bind(Y,$fot(join(complement(complement(X_52)),meet(X_52,complement(X_52))))),bind(Z,$fot(join(zero,complement(complement(X_52)))))]]) ).
cnf(refute_0_331,plain,
( join(complement(complement(X_52)),meet(X_52,complement(X_52))) != join(zero,complement(complement(X_52)))
| join(meet(X_52,complement(X_52)),complement(complement(X_52))) = join(zero,complement(complement(X_52))) ),
inference(resolve,[$cnf( $equal(join(meet(X_52,complement(X_52)),complement(complement(X_52))),join(complement(complement(X_52)),meet(X_52,complement(X_52)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
join(meet(X_52,complement(X_52)),complement(complement(X_52))) = join(zero,complement(complement(X_52))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_52)),meet(X_52,complement(X_52))),join(zero,complement(complement(X_52)))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( X_52 != join(meet(X_52,complement(X_52)),complement(complement(X_52)))
| join(meet(X_52,complement(X_52)),complement(complement(X_52))) != join(zero,complement(complement(X_52)))
| X_52 = join(zero,complement(complement(X_52))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,join(zero,complement(complement(X_52)))) ),[0],$fot(join(meet(X_52,complement(X_52)),complement(complement(X_52))))]]) ).
cnf(refute_0_334,plain,
( X_52 != join(meet(X_52,complement(X_52)),complement(complement(X_52)))
| X_52 = join(zero,complement(complement(X_52))) ),
inference(resolve,[$cnf( $equal(join(meet(X_52,complement(X_52)),complement(complement(X_52))),join(zero,complement(complement(X_52)))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
X_52 = join(zero,complement(complement(X_52))),
inference(resolve,[$cnf( $equal(X_52,join(meet(X_52,complement(X_52)),complement(complement(X_52)))) )],[refute_0_317,refute_0_334]) ).
cnf(refute_0_336,plain,
X_52 = join(meet(X_52,complement(B)),complement(join(complement(X_52),complement(B)))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_52)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_337,plain,
meet(X_52,B) = complement(join(complement(X_52),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_52))]]) ).
cnf(refute_0_338,plain,
( meet(X_52,B) != complement(join(complement(X_52),complement(B)))
| complement(join(complement(X_52),complement(B))) = meet(X_52,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_52,B))),bind(Y,$fot(complement(join(complement(X_52),complement(B)))))]]) ).
cnf(refute_0_339,plain,
complement(join(complement(X_52),complement(B))) = meet(X_52,B),
inference(resolve,[$cnf( $equal(meet(X_52,B),complement(join(complement(X_52),complement(B)))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
( X_52 != join(meet(X_52,complement(B)),complement(join(complement(X_52),complement(B))))
| complement(join(complement(X_52),complement(B))) != meet(X_52,B)
| X_52 = join(meet(X_52,complement(B)),meet(X_52,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_52,join(meet(X_52,complement(B)),complement(join(complement(X_52),complement(B))))) ),[1,1],$fot(meet(X_52,B))]]) ).
cnf(refute_0_341,plain,
( X_52 != join(meet(X_52,complement(B)),complement(join(complement(X_52),complement(B))))
| X_52 = join(meet(X_52,complement(B)),meet(X_52,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_52),complement(B))),meet(X_52,B)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
X_52 = join(meet(X_52,complement(B)),meet(X_52,B)),
inference(resolve,[$cnf( $equal(X_52,join(meet(X_52,complement(B)),complement(join(complement(X_52),complement(B))))) )],[refute_0_336,refute_0_341]) ).
cnf(refute_0_343,plain,
join(meet(X_52,complement(B)),meet(X_52,B)) = join(meet(X_52,B),meet(X_52,complement(B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(X_52,B))),bind(B,$fot(meet(X_52,complement(B))))]]) ).
cnf(refute_0_344,plain,
( X_52 != join(meet(X_52,complement(B)),meet(X_52,B))
| join(meet(X_52,complement(B)),meet(X_52,B)) != join(meet(X_52,B),meet(X_52,complement(B)))
| X_52 = join(meet(X_52,B),meet(X_52,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,join(meet(X_52,B),meet(X_52,complement(B)))) ),[0],$fot(join(meet(X_52,complement(B)),meet(X_52,B)))]]) ).
cnf(refute_0_345,plain,
( X_52 != join(meet(X_52,complement(B)),meet(X_52,B))
| X_52 = join(meet(X_52,B),meet(X_52,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_52,complement(B)),meet(X_52,B)),join(meet(X_52,B),meet(X_52,complement(B)))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
X_52 = join(meet(X_52,B),meet(X_52,complement(B))),
inference(resolve,[$cnf( $equal(X_52,join(meet(X_52,complement(B)),meet(X_52,B))) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
X_63 = join(meet(X_63,top),meet(X_63,complement(top))),
inference(subst,[],[refute_0_346:[bind(B,$fot(top)),bind(X_52,$fot(X_63))]]) ).
cnf(refute_0_348,plain,
( X_63 != join(meet(X_63,top),meet(X_63,complement(top)))
| complement(top) != zero
| X_63 = join(meet(X_63,top),meet(X_63,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(X_63,join(meet(X_63,top),meet(X_63,complement(top)))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_349,plain,
( X_63 != join(meet(X_63,top),meet(X_63,complement(top)))
| X_63 = join(meet(X_63,top),meet(X_63,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_348]) ).
cnf(refute_0_350,plain,
X_63 = join(meet(X_63,top),meet(X_63,zero)),
inference(resolve,[$cnf( $equal(X_63,join(meet(X_63,top),meet(X_63,complement(top)))) )],[refute_0_347,refute_0_349]) ).
cnf(refute_0_351,plain,
X_64 = join(meet(X_64,top),meet(X_64,zero)),
inference(subst,[],[refute_0_350:[bind(X_63,$fot(X_64))]]) ).
cnf(refute_0_352,plain,
meet(top,X_64) = meet(X_64,top),
inference(subst,[],[refute_0_35:[bind(X_6,$fot(top)),bind(X_7,$fot(X_64))]]) ).
cnf(refute_0_353,plain,
( meet(top,X_64) != meet(X_64,top)
| meet(X_64,top) = meet(top,X_64) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,X_64))),bind(Y,$fot(meet(X_64,top)))]]) ).
cnf(refute_0_354,plain,
meet(X_64,top) = meet(top,X_64),
inference(resolve,[$cnf( $equal(meet(top,X_64),meet(X_64,top)) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
( X_64 != join(meet(X_64,top),meet(X_64,zero))
| meet(X_64,top) != meet(top,X_64)
| X_64 = join(meet(top,X_64),meet(X_64,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(X_64,join(meet(X_64,top),meet(X_64,zero))) ),[1,0],$fot(meet(top,X_64))]]) ).
cnf(refute_0_356,plain,
( X_64 != join(meet(X_64,top),meet(X_64,zero))
| X_64 = join(meet(top,X_64),meet(X_64,zero)) ),
inference(resolve,[$cnf( $equal(meet(X_64,top),meet(top,X_64)) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
X_64 = join(meet(top,X_64),meet(X_64,zero)),
inference(resolve,[$cnf( $equal(X_64,join(meet(X_64,top),meet(X_64,zero))) )],[refute_0_351,refute_0_356]) ).
cnf(refute_0_358,plain,
complement(X_56) = join(meet(top,complement(X_56)),meet(complement(X_56),zero)),
inference(subst,[],[refute_0_357:[bind(X_64,$fot(complement(X_56)))]]) ).
cnf(refute_0_359,plain,
meet(top,complement(X_56)) = complement(join(zero,complement(complement(X_56)))),
inference(subst,[],[refute_0_92:[bind(B,$fot(complement(X_56)))]]) ).
cnf(refute_0_360,plain,
X_56 = join(zero,complement(complement(X_56))),
inference(subst,[],[refute_0_335:[bind(X_52,$fot(X_56))]]) ).
cnf(refute_0_361,plain,
( X_56 != join(zero,complement(complement(X_56)))
| join(zero,complement(complement(X_56))) = X_56 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_56)),bind(Y,$fot(join(zero,complement(complement(X_56)))))]]) ).
cnf(refute_0_362,plain,
join(zero,complement(complement(X_56))) = X_56,
inference(resolve,[$cnf( $equal(X_56,join(zero,complement(complement(X_56)))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
( join(zero,complement(complement(X_56))) != X_56
| meet(top,complement(X_56)) != complement(join(zero,complement(complement(X_56))))
| meet(top,complement(X_56)) = complement(X_56) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(X_56)),complement(join(zero,complement(complement(X_56))))) ),[1,0],$fot(X_56)]]) ).
cnf(refute_0_364,plain,
( meet(top,complement(X_56)) != complement(join(zero,complement(complement(X_56))))
| meet(top,complement(X_56)) = complement(X_56) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_56))),X_56) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
meet(top,complement(X_56)) = complement(X_56),
inference(resolve,[$cnf( $equal(meet(top,complement(X_56)),complement(join(zero,complement(complement(X_56))))) )],[refute_0_359,refute_0_364]) ).
cnf(refute_0_366,plain,
( complement(X_56) != join(meet(top,complement(X_56)),meet(complement(X_56),zero))
| meet(top,complement(X_56)) != complement(X_56)
| complement(X_56) = join(complement(X_56),meet(complement(X_56),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_56),join(meet(top,complement(X_56)),meet(complement(X_56),zero))) ),[1,0],$fot(complement(X_56))]]) ).
cnf(refute_0_367,plain,
( complement(X_56) != join(meet(top,complement(X_56)),meet(complement(X_56),zero))
| complement(X_56) = join(complement(X_56),meet(complement(X_56),zero)) ),
inference(resolve,[$cnf( $equal(meet(top,complement(X_56)),complement(X_56)) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
complement(X_56) = join(complement(X_56),meet(complement(X_56),zero)),
inference(resolve,[$cnf( $equal(complement(X_56),join(meet(top,complement(X_56)),meet(complement(X_56),zero))) )],[refute_0_358,refute_0_367]) ).
cnf(refute_0_369,plain,
( meet(X_6,X_7) != meet(X_7,X_6)
| meet(X_7,X_6) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(meet(X_7,X_6)))]]) ).
cnf(refute_0_370,plain,
meet(X_7,X_6) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),meet(X_7,X_6)) )],[refute_0_35,refute_0_369]) ).
cnf(refute_0_371,plain,
meet(complement(X_56),zero) = meet(zero,complement(X_56)),
inference(subst,[],[refute_0_370:[bind(X_6,$fot(zero)),bind(X_7,$fot(complement(X_56)))]]) ).
cnf(refute_0_372,plain,
join(complement(X_56),meet(complement(X_56),zero)) = join(complement(X_56),meet(complement(X_56),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_56),meet(complement(X_56),zero)))]]) ).
cnf(refute_0_373,plain,
( join(complement(X_56),meet(complement(X_56),zero)) != join(complement(X_56),meet(complement(X_56),zero))
| meet(complement(X_56),zero) != meet(zero,complement(X_56))
| join(complement(X_56),meet(complement(X_56),zero)) = join(complement(X_56),meet(zero,complement(X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_56),meet(complement(X_56),zero)),join(complement(X_56),meet(complement(X_56),zero))) ),[1,1],$fot(meet(zero,complement(X_56)))]]) ).
cnf(refute_0_374,plain,
( meet(complement(X_56),zero) != meet(zero,complement(X_56))
| join(complement(X_56),meet(complement(X_56),zero)) = join(complement(X_56),meet(zero,complement(X_56))) ),
inference(resolve,[$cnf( $equal(join(complement(X_56),meet(complement(X_56),zero)),join(complement(X_56),meet(complement(X_56),zero))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
join(complement(X_56),meet(complement(X_56),zero)) = join(complement(X_56),meet(zero,complement(X_56))),
inference(resolve,[$cnf( $equal(meet(complement(X_56),zero),meet(zero,complement(X_56))) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
( complement(X_56) != join(complement(X_56),meet(complement(X_56),zero))
| join(complement(X_56),meet(complement(X_56),zero)) != join(complement(X_56),meet(zero,complement(X_56)))
| complement(X_56) = join(complement(X_56),meet(zero,complement(X_56))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_56),join(complement(X_56),meet(zero,complement(X_56)))) ),[0],$fot(join(complement(X_56),meet(complement(X_56),zero)))]]) ).
cnf(refute_0_377,plain,
( complement(X_56) != join(complement(X_56),meet(complement(X_56),zero))
| complement(X_56) = join(complement(X_56),meet(zero,complement(X_56))) ),
inference(resolve,[$cnf( $equal(join(complement(X_56),meet(complement(X_56),zero)),join(complement(X_56),meet(zero,complement(X_56)))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
complement(X_56) = join(complement(X_56),meet(zero,complement(X_56))),
inference(resolve,[$cnf( $equal(complement(X_56),join(complement(X_56),meet(complement(X_56),zero))) )],[refute_0_368,refute_0_377]) ).
cnf(refute_0_379,plain,
join(complement(X_56),zero) = join(zero,complement(X_56)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(X_56)))]]) ).
cnf(refute_0_380,plain,
meet(zero,B) = complement(join(complement(zero),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(zero))]]) ).
cnf(refute_0_381,plain,
meet(zero,X_64) = meet(X_64,zero),
inference(subst,[],[refute_0_35:[bind(X_6,$fot(zero)),bind(X_7,$fot(X_64))]]) ).
cnf(refute_0_382,plain,
( meet(zero,X_64) != meet(X_64,zero)
| meet(X_64,zero) = meet(zero,X_64) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(zero,X_64))),bind(Y,$fot(meet(X_64,zero)))]]) ).
cnf(refute_0_383,plain,
meet(X_64,zero) = meet(zero,X_64),
inference(resolve,[$cnf( $equal(meet(zero,X_64),meet(X_64,zero)) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
( X_64 != join(meet(X_64,top),meet(X_64,zero))
| meet(X_64,zero) != meet(zero,X_64)
| X_64 = join(meet(X_64,top),meet(zero,X_64)) ),
introduced(tautology,[equality,[$cnf( $equal(X_64,join(meet(X_64,top),meet(X_64,zero))) ),[1,1],$fot(meet(zero,X_64))]]) ).
cnf(refute_0_385,plain,
( X_64 != join(meet(X_64,top),meet(X_64,zero))
| X_64 = join(meet(X_64,top),meet(zero,X_64)) ),
inference(resolve,[$cnf( $equal(meet(X_64,zero),meet(zero,X_64)) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
X_64 = join(meet(X_64,top),meet(zero,X_64)),
inference(resolve,[$cnf( $equal(X_64,join(meet(X_64,top),meet(X_64,zero))) )],[refute_0_351,refute_0_385]) ).
cnf(refute_0_387,plain,
complement(zero) = join(meet(complement(zero),top),meet(zero,complement(zero))),
inference(subst,[],[refute_0_386:[bind(X_64,$fot(complement(zero)))]]) ).
cnf(refute_0_388,plain,
zero = meet(zero,complement(zero)),
inference(subst,[],[def_zero_13:[bind(A,$fot(zero))]]) ).
cnf(refute_0_389,plain,
( zero != meet(zero,complement(zero))
| meet(zero,complement(zero)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(zero,complement(zero))))]]) ).
cnf(refute_0_390,plain,
meet(zero,complement(zero)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(zero,complement(zero))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
( complement(zero) != join(meet(complement(zero),top),meet(zero,complement(zero)))
| meet(zero,complement(zero)) != zero
| complement(zero) = join(meet(complement(zero),top),zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),meet(zero,complement(zero)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_392,plain,
( complement(zero) != join(meet(complement(zero),top),meet(zero,complement(zero)))
| complement(zero) = join(meet(complement(zero),top),zero) ),
inference(resolve,[$cnf( $equal(meet(zero,complement(zero)),zero) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
complement(zero) = join(meet(complement(zero),top),zero),
inference(resolve,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),meet(zero,complement(zero)))) )],[refute_0_387,refute_0_392]) ).
cnf(refute_0_394,plain,
join(zero,complement(zero)) = top,
inference(subst,[],[refute_0_71:[bind(A,$fot(zero))]]) ).
cnf(refute_0_395,plain,
meet(top,complement(zero)) = complement(zero),
inference(subst,[],[refute_0_365:[bind(X_56,$fot(zero))]]) ).
cnf(refute_0_396,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_397,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_398,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_397]) ).
cnf(refute_0_399,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_396,refute_0_398]) ).
cnf(refute_0_400,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_401,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_92,refute_0_400]) ).
cnf(refute_0_402,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_401:[bind(B,$fot(A))]]) ).
cnf(refute_0_403,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_404,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_405,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_406,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_409,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_402,refute_0_409]) ).
cnf(refute_0_411,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_412,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_399,refute_0_412]) ).
cnf(refute_0_414,plain,
meet(complement(zero),top) = meet(top,complement(zero)),
inference(subst,[],[refute_0_413:[bind(A,$fot(complement(zero)))]]) ).
cnf(refute_0_415,plain,
( meet(complement(zero),top) != meet(top,complement(zero))
| meet(top,complement(zero)) != complement(zero)
| meet(complement(zero),top) = complement(zero) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(complement(zero),top))),bind(Y,$fot(meet(top,complement(zero)))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_0_416,plain,
( meet(top,complement(zero)) != complement(zero)
| meet(complement(zero),top) = complement(zero) ),
inference(resolve,[$cnf( $equal(meet(complement(zero),top),meet(top,complement(zero))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
meet(complement(zero),top) = complement(zero),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),complement(zero)) )],[refute_0_395,refute_0_416]) ).
cnf(refute_0_418,plain,
join(zero,meet(complement(zero),top)) = join(zero,meet(complement(zero),top)),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(zero),top)))]]) ).
cnf(refute_0_419,plain,
( join(zero,meet(complement(zero),top)) != join(zero,meet(complement(zero),top))
| meet(complement(zero),top) != complement(zero)
| join(zero,meet(complement(zero),top)) = join(zero,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,meet(complement(zero),top))) ),[1,1],$fot(complement(zero))]]) ).
cnf(refute_0_420,plain,
( meet(complement(zero),top) != complement(zero)
| join(zero,meet(complement(zero),top)) = join(zero,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,meet(complement(zero),top))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
join(zero,meet(complement(zero),top)) = join(zero,complement(zero)),
inference(resolve,[$cnf( $equal(meet(complement(zero),top),complement(zero)) )],[refute_0_417,refute_0_420]) ).
cnf(refute_0_422,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(complement(zero),top)) != join(zero,complement(zero))
| join(zero,meet(complement(zero),top)) = top ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,meet(complement(zero),top)))),bind(Y,$fot(join(zero,complement(zero)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_423,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(complement(zero),top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,complement(zero))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
join(zero,meet(complement(zero),top)) = top,
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_394,refute_0_423]) ).
cnf(refute_0_425,plain,
join(meet(complement(zero),top),zero) = join(zero,meet(complement(zero),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(meet(complement(zero),top)))]]) ).
cnf(refute_0_426,plain,
( join(meet(complement(zero),top),zero) != join(zero,meet(complement(zero),top))
| join(zero,meet(complement(zero),top)) != top
| join(meet(complement(zero),top),zero) = top ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(complement(zero),top),zero))),bind(Y,$fot(join(zero,meet(complement(zero),top)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_427,plain,
( join(zero,meet(complement(zero),top)) != top
| join(meet(complement(zero),top),zero) = top ),
inference(resolve,[$cnf( $equal(join(meet(complement(zero),top),zero),join(zero,meet(complement(zero),top))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
join(meet(complement(zero),top),zero) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),top) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
( complement(zero) != join(meet(complement(zero),top),zero)
| join(meet(complement(zero),top),zero) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(meet(complement(zero),top),zero))]]) ).
cnf(refute_0_430,plain,
( complement(zero) != join(meet(complement(zero),top),zero)
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(meet(complement(zero),top),zero),top) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),zero)) )],[refute_0_393,refute_0_430]) ).
cnf(refute_0_432,plain,
( complement(zero) != top
| meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) ),[1,0,0],$fot(top)]]) ).
cnf(refute_0_433,plain,
( meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
meet(zero,B) = complement(join(top,complement(B))),
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) )],[refute_0_380,refute_0_433]) ).
cnf(refute_0_435,plain,
join(top,complement(B)) = top,
inference(subst,[],[refute_0_281:[bind(X_29,$fot(complement(B)))]]) ).
cnf(refute_0_436,plain,
complement(join(top,complement(B))) = complement(join(top,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(top,complement(B))))]]) ).
cnf(refute_0_437,plain,
( complement(join(top,complement(B))) != complement(join(top,complement(B)))
| join(top,complement(B)) != top
| complement(join(top,complement(B))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,complement(B))),complement(join(top,complement(B)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_438,plain,
( join(top,complement(B)) != top
| complement(join(top,complement(B))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),complement(join(top,complement(B)))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
complement(join(top,complement(B))) = complement(top),
inference(resolve,[$cnf( $equal(join(top,complement(B)),top) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
( complement(join(top,complement(B))) != complement(top)
| complement(top) != zero
| complement(join(top,complement(B))) = zero ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(top,complement(B))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_441,plain,
( complement(top) != zero
| complement(join(top,complement(B))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),complement(top)) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
complement(join(top,complement(B))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_441]) ).
cnf(refute_0_443,plain,
( complement(join(top,complement(B))) != zero
| meet(zero,B) != complement(join(top,complement(B)))
| meet(zero,B) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,B),complement(join(top,complement(B)))) ),[1],$fot(zero)]]) ).
cnf(refute_0_444,plain,
( meet(zero,B) != complement(join(top,complement(B)))
| meet(zero,B) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),zero) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
meet(zero,B) = zero,
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(top,complement(B)))) )],[refute_0_434,refute_0_444]) ).
cnf(refute_0_446,plain,
meet(zero,complement(X_56)) = zero,
inference(subst,[],[refute_0_445:[bind(B,$fot(complement(X_56)))]]) ).
cnf(refute_0_447,plain,
join(complement(X_56),meet(zero,complement(X_56))) = join(complement(X_56),meet(zero,complement(X_56))),
introduced(tautology,[refl,[$fot(join(complement(X_56),meet(zero,complement(X_56))))]]) ).
cnf(refute_0_448,plain,
( join(complement(X_56),meet(zero,complement(X_56))) != join(complement(X_56),meet(zero,complement(X_56)))
| meet(zero,complement(X_56)) != zero
| join(complement(X_56),meet(zero,complement(X_56))) = join(complement(X_56),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_56),meet(zero,complement(X_56))),join(complement(X_56),meet(zero,complement(X_56)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_449,plain,
( meet(zero,complement(X_56)) != zero
| join(complement(X_56),meet(zero,complement(X_56))) = join(complement(X_56),zero) ),
inference(resolve,[$cnf( $equal(join(complement(X_56),meet(zero,complement(X_56))),join(complement(X_56),meet(zero,complement(X_56)))) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
join(complement(X_56),meet(zero,complement(X_56))) = join(complement(X_56),zero),
inference(resolve,[$cnf( $equal(meet(zero,complement(X_56)),zero) )],[refute_0_446,refute_0_449]) ).
cnf(refute_0_451,plain,
( join(complement(X_56),meet(zero,complement(X_56))) != join(complement(X_56),zero)
| join(complement(X_56),zero) != join(zero,complement(X_56))
| join(complement(X_56),meet(zero,complement(X_56))) = join(zero,complement(X_56)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(X_56),meet(zero,complement(X_56))))),bind(Y,$fot(join(complement(X_56),zero))),bind(Z,$fot(join(zero,complement(X_56))))]]) ).
cnf(refute_0_452,plain,
( join(complement(X_56),zero) != join(zero,complement(X_56))
| join(complement(X_56),meet(zero,complement(X_56))) = join(zero,complement(X_56)) ),
inference(resolve,[$cnf( $equal(join(complement(X_56),meet(zero,complement(X_56))),join(complement(X_56),zero)) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
join(complement(X_56),meet(zero,complement(X_56))) = join(zero,complement(X_56)),
inference(resolve,[$cnf( $equal(join(complement(X_56),zero),join(zero,complement(X_56))) )],[refute_0_379,refute_0_452]) ).
cnf(refute_0_454,plain,
( complement(X_56) != join(complement(X_56),meet(zero,complement(X_56)))
| join(complement(X_56),meet(zero,complement(X_56))) != join(zero,complement(X_56))
| complement(X_56) = join(zero,complement(X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_56),join(zero,complement(X_56))) ),[0],$fot(join(complement(X_56),meet(zero,complement(X_56))))]]) ).
cnf(refute_0_455,plain,
( complement(X_56) != join(complement(X_56),meet(zero,complement(X_56)))
| complement(X_56) = join(zero,complement(X_56)) ),
inference(resolve,[$cnf( $equal(join(complement(X_56),meet(zero,complement(X_56))),join(zero,complement(X_56))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
complement(X_56) = join(zero,complement(X_56)),
inference(resolve,[$cnf( $equal(complement(X_56),join(complement(X_56),meet(zero,complement(X_56)))) )],[refute_0_378,refute_0_455]) ).
cnf(refute_0_457,plain,
( complement(X_56) != join(zero,complement(X_56))
| join(zero,complement(X_56)) = complement(X_56) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_56))),bind(Y,$fot(join(zero,complement(X_56))))]]) ).
cnf(refute_0_458,plain,
join(zero,complement(X_56)) = complement(X_56),
inference(resolve,[$cnf( $equal(complement(X_56),join(zero,complement(X_56))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
join(zero,complement(complement(X_52))) = complement(complement(X_52)),
inference(subst,[],[refute_0_458:[bind(X_56,$fot(complement(X_52)))]]) ).
cnf(refute_0_460,plain,
( X_52 != join(zero,complement(complement(X_52)))
| join(zero,complement(complement(X_52))) != complement(complement(X_52))
| X_52 = complement(complement(X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,complement(complement(X_52))) ),[0],$fot(join(zero,complement(complement(X_52))))]]) ).
cnf(refute_0_461,plain,
( X_52 != join(zero,complement(complement(X_52)))
| X_52 = complement(complement(X_52)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_52))),complement(complement(X_52))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
X_52 = complement(complement(X_52)),
inference(resolve,[$cnf( $equal(X_52,join(zero,complement(complement(X_52)))) )],[refute_0_335,refute_0_461]) ).
cnf(refute_0_463,plain,
( X_52 != complement(complement(X_52))
| complement(complement(X_52)) = X_52 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_52)),bind(Y,$fot(complement(complement(X_52))))]]) ).
cnf(refute_0_464,plain,
complement(complement(X_52)) = X_52,
inference(resolve,[$cnf( $equal(X_52,complement(complement(X_52))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
complement(complement(B)) = B,
inference(subst,[],[refute_0_464:[bind(X_52,$fot(B))]]) ).
cnf(refute_0_466,plain,
( complement(complement(B)) != B
| meet(B,B) != complement(complement(B))
| meet(B,B) = B ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(complement(B))) ),[1],$fot(B)]]) ).
cnf(refute_0_467,plain,
( meet(B,B) != complement(complement(B))
| meet(B,B) = B ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
meet(B,B) = B,
inference(resolve,[$cnf( $equal(meet(B,B),complement(complement(B))) )],[refute_0_312,refute_0_467]) ).
cnf(refute_0_469,plain,
meet(X_52,X_52) = X_52,
inference(subst,[],[refute_0_468:[bind(B,$fot(X_52))]]) ).
cnf(refute_0_470,plain,
meet(X_52,complement(complement(X_52))) = meet(X_52,complement(complement(X_52))),
introduced(tautology,[refl,[$fot(meet(X_52,complement(complement(X_52))))]]) ).
cnf(refute_0_471,plain,
( complement(complement(X_52)) != X_52
| meet(X_52,complement(complement(X_52))) != meet(X_52,complement(complement(X_52)))
| meet(X_52,complement(complement(X_52))) = meet(X_52,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_52,complement(complement(X_52))),meet(X_52,complement(complement(X_52)))) ),[1,1],$fot(X_52)]]) ).
cnf(refute_0_472,plain,
( complement(complement(X_52)) != X_52
| meet(X_52,complement(complement(X_52))) = meet(X_52,X_52) ),
inference(resolve,[$cnf( $equal(meet(X_52,complement(complement(X_52))),meet(X_52,complement(complement(X_52)))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
meet(X_52,complement(complement(X_52))) = meet(X_52,X_52),
inference(resolve,[$cnf( $equal(complement(complement(X_52)),X_52) )],[refute_0_464,refute_0_472]) ).
cnf(refute_0_474,plain,
( meet(X_52,X_52) != X_52
| meet(X_52,complement(complement(X_52))) != meet(X_52,X_52)
| meet(X_52,complement(complement(X_52))) = X_52 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(X_52,complement(complement(X_52))))),bind(Y,$fot(meet(X_52,X_52))),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_475,plain,
( meet(X_52,X_52) != X_52
| meet(X_52,complement(complement(X_52))) = X_52 ),
inference(resolve,[$cnf( $equal(meet(X_52,complement(complement(X_52))),meet(X_52,X_52)) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
meet(X_52,complement(complement(X_52))) = X_52,
inference(resolve,[$cnf( $equal(meet(X_52,X_52),X_52) )],[refute_0_469,refute_0_475]) ).
cnf(refute_0_477,plain,
join(zero,meet(X_52,complement(complement(X_52)))) = join(zero,meet(X_52,complement(complement(X_52)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_52,complement(complement(X_52)))))]]) ).
cnf(refute_0_478,plain,
( join(zero,meet(X_52,complement(complement(X_52)))) != join(zero,meet(X_52,complement(complement(X_52))))
| meet(X_52,complement(complement(X_52))) != X_52
| join(zero,meet(X_52,complement(complement(X_52)))) = join(zero,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_52,complement(complement(X_52)))),join(zero,meet(X_52,complement(complement(X_52))))) ),[1,1],$fot(X_52)]]) ).
cnf(refute_0_479,plain,
( meet(X_52,complement(complement(X_52))) != X_52
| join(zero,meet(X_52,complement(complement(X_52)))) = join(zero,X_52) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_52,complement(complement(X_52)))),join(zero,meet(X_52,complement(complement(X_52))))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
join(zero,meet(X_52,complement(complement(X_52)))) = join(zero,X_52),
inference(resolve,[$cnf( $equal(meet(X_52,complement(complement(X_52))),X_52) )],[refute_0_476,refute_0_479]) ).
cnf(refute_0_481,plain,
( X_52 != join(zero,meet(X_52,complement(complement(X_52))))
| join(zero,meet(X_52,complement(complement(X_52)))) != join(zero,X_52)
| X_52 = join(zero,X_52) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,join(zero,X_52)) ),[0],$fot(join(zero,meet(X_52,complement(complement(X_52)))))]]) ).
cnf(refute_0_482,plain,
( X_52 != join(zero,meet(X_52,complement(complement(X_52))))
| X_52 = join(zero,X_52) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_52,complement(complement(X_52)))),join(zero,X_52)) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
X_52 = join(zero,X_52),
inference(resolve,[$cnf( $equal(X_52,join(zero,meet(X_52,complement(complement(X_52))))) )],[refute_0_307,refute_0_482]) ).
cnf(refute_0_484,plain,
( X_52 != join(zero,X_52)
| join(zero,X_52) = X_52 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_52)),bind(Y,$fot(join(zero,X_52)))]]) ).
cnf(refute_0_485,plain,
join(zero,X_52) = X_52,
inference(resolve,[$cnf( $equal(X_52,join(zero,X_52)) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
join(zero,meet(X_52,join(X_52,X_83))) = meet(X_52,join(X_52,X_83)),
inference(subst,[],[refute_0_485:[bind(X_52,$fot(meet(X_52,join(X_52,X_83))))]]) ).
cnf(refute_0_487,plain,
join(complement(complement(X_52)),X_83) = join(complement(complement(X_52)),X_83),
introduced(tautology,[refl,[$fot(join(complement(complement(X_52)),X_83))]]) ).
cnf(refute_0_488,plain,
( complement(complement(X_52)) != X_52
| join(complement(complement(X_52)),X_83) != join(complement(complement(X_52)),X_83)
| join(complement(complement(X_52)),X_83) = join(X_52,X_83) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_52)),X_83),join(complement(complement(X_52)),X_83)) ),[1,0],$fot(X_52)]]) ).
cnf(refute_0_489,plain,
( complement(complement(X_52)) != X_52
| join(complement(complement(X_52)),X_83) = join(X_52,X_83) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_52)),X_83),join(complement(complement(X_52)),X_83)) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
join(complement(complement(X_52)),X_83) = join(X_52,X_83),
inference(resolve,[$cnf( $equal(complement(complement(X_52)),X_52) )],[refute_0_464,refute_0_489]) ).
cnf(refute_0_491,plain,
meet(X_52,join(complement(complement(X_52)),X_83)) = meet(X_52,join(complement(complement(X_52)),X_83)),
introduced(tautology,[refl,[$fot(meet(X_52,join(complement(complement(X_52)),X_83)))]]) ).
cnf(refute_0_492,plain,
( join(complement(complement(X_52)),X_83) != join(X_52,X_83)
| meet(X_52,join(complement(complement(X_52)),X_83)) != meet(X_52,join(complement(complement(X_52)),X_83))
| meet(X_52,join(complement(complement(X_52)),X_83)) = meet(X_52,join(X_52,X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_52,join(complement(complement(X_52)),X_83)),meet(X_52,join(complement(complement(X_52)),X_83))) ),[1,1],$fot(join(X_52,X_83))]]) ).
cnf(refute_0_493,plain,
( join(complement(complement(X_52)),X_83) != join(X_52,X_83)
| meet(X_52,join(complement(complement(X_52)),X_83)) = meet(X_52,join(X_52,X_83)) ),
inference(resolve,[$cnf( $equal(meet(X_52,join(complement(complement(X_52)),X_83)),meet(X_52,join(complement(complement(X_52)),X_83))) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
meet(X_52,join(complement(complement(X_52)),X_83)) = meet(X_52,join(X_52,X_83)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_52)),X_83),join(X_52,X_83)) )],[refute_0_490,refute_0_493]) ).
cnf(refute_0_495,plain,
meet(join(complement(complement(X_52)),X_83),X_52) = meet(X_52,join(complement(complement(X_52)),X_83)),
inference(subst,[],[refute_0_370:[bind(X_6,$fot(X_52)),bind(X_7,$fot(join(complement(complement(X_52)),X_83)))]]) ).
cnf(refute_0_496,plain,
( meet(X_52,join(complement(complement(X_52)),X_83)) != meet(X_52,join(X_52,X_83))
| meet(join(complement(complement(X_52)),X_83),X_52) != meet(X_52,join(complement(complement(X_52)),X_83))
| meet(join(complement(complement(X_52)),X_83),X_52) = meet(X_52,join(X_52,X_83)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(join(complement(complement(X_52)),X_83),X_52))),bind(Y,$fot(meet(X_52,join(complement(complement(X_52)),X_83)))),bind(Z,$fot(meet(X_52,join(X_52,X_83))))]]) ).
cnf(refute_0_497,plain,
( meet(X_52,join(complement(complement(X_52)),X_83)) != meet(X_52,join(X_52,X_83))
| meet(join(complement(complement(X_52)),X_83),X_52) = meet(X_52,join(X_52,X_83)) ),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_52)),X_83),X_52),meet(X_52,join(complement(complement(X_52)),X_83))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
meet(join(complement(complement(X_52)),X_83),X_52) = meet(X_52,join(X_52,X_83)),
inference(resolve,[$cnf( $equal(meet(X_52,join(complement(complement(X_52)),X_83)),meet(X_52,join(X_52,X_83))) )],[refute_0_494,refute_0_497]) ).
cnf(refute_0_499,plain,
join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(join(complement(complement(X_52)),X_83),X_52)),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(complement(X_52)),X_83),X_52)))]]) ).
cnf(refute_0_500,plain,
( join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) != join(zero,meet(join(complement(complement(X_52)),X_83),X_52))
| meet(join(complement(complement(X_52)),X_83),X_52) != meet(X_52,join(X_52,X_83))
| join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(X_52,join(X_52,X_83))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(complement(X_52)),X_83),X_52)),join(zero,meet(join(complement(complement(X_52)),X_83),X_52))) ),[1,1],$fot(meet(X_52,join(X_52,X_83)))]]) ).
cnf(refute_0_501,plain,
( meet(join(complement(complement(X_52)),X_83),X_52) != meet(X_52,join(X_52,X_83))
| join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(X_52,join(X_52,X_83))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_52)),X_83),X_52)),join(zero,meet(join(complement(complement(X_52)),X_83),X_52))) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(X_52,join(X_52,X_83))),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_52)),X_83),X_52),meet(X_52,join(X_52,X_83))) )],[refute_0_498,refute_0_501]) ).
cnf(refute_0_503,plain,
join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)))]]) ).
cnf(refute_0_504,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) != join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52))
| join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)),join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_505,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)),join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52))) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(join(complement(complement(X_52)),X_83),X_52)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_505]) ).
cnf(refute_0_507,plain,
( join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) != join(zero,meet(join(complement(complement(X_52)),X_83),X_52))
| join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) != join(zero,meet(X_52,join(X_52,X_83)))
| join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(X_52,join(X_52,X_83))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)))),bind(Y,$fot(join(zero,meet(join(complement(complement(X_52)),X_83),X_52)))),bind(Z,$fot(join(zero,meet(X_52,join(X_52,X_83)))))]]) ).
cnf(refute_0_508,plain,
( join(zero,meet(join(complement(complement(X_52)),X_83),X_52)) != join(zero,meet(X_52,join(X_52,X_83)))
| join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(X_52,join(X_52,X_83))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)),join(zero,meet(join(complement(complement(X_52)),X_83),X_52))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = join(zero,meet(X_52,join(X_52,X_83))),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_52)),X_83),X_52)),join(zero,meet(X_52,join(X_52,X_83)))) )],[refute_0_502,refute_0_508]) ).
cnf(refute_0_510,plain,
( join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) != join(zero,meet(X_52,join(X_52,X_83)))
| join(zero,meet(X_52,join(X_52,X_83))) != meet(X_52,join(X_52,X_83))
| join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = meet(X_52,join(X_52,X_83)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)))),bind(Y,$fot(join(zero,meet(X_52,join(X_52,X_83))))),bind(Z,$fot(meet(X_52,join(X_52,X_83))))]]) ).
cnf(refute_0_511,plain,
( join(zero,meet(X_52,join(X_52,X_83))) != meet(X_52,join(X_52,X_83))
| join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = meet(X_52,join(X_52,X_83)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)),join(zero,meet(X_52,join(X_52,X_83)))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) = meet(X_52,join(X_52,X_83)),
inference(resolve,[$cnf( $equal(join(zero,meet(X_52,join(X_52,X_83))),meet(X_52,join(X_52,X_83))) )],[refute_0_486,refute_0_511]) ).
cnf(refute_0_513,plain,
join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) = join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(join(complement(complement(X_52)),X_83),X_52)))]]) ).
cnf(refute_0_514,plain,
( join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) != meet(X_52,join(X_52,X_83))
| join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) != join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52))
| join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) = meet(X_52,join(X_52,X_83)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)))),bind(Y,$fot(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)))),bind(Z,$fot(meet(X_52,join(X_52,X_83))))]]) ).
cnf(refute_0_515,plain,
( join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)) != meet(X_52,join(X_52,X_83))
| join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) = meet(X_52,join(X_52,X_83)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)),join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) = meet(X_52,join(X_52,X_83)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_52)),X_83),X_52)),meet(X_52,join(X_52,X_83))) )],[refute_0_512,refute_0_515]) ).
cnf(refute_0_517,plain,
( X_52 != join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top))
| join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)) != meet(X_52,join(X_52,X_83))
| X_52 = meet(X_52,join(X_52,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,meet(X_52,join(X_52,X_83))) ),[0],$fot(join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)))]]) ).
cnf(refute_0_518,plain,
( X_52 != join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top))
| X_52 = meet(X_52,join(X_52,X_83)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top)),meet(X_52,join(X_52,X_83))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
X_52 = meet(X_52,join(X_52,X_83)),
inference(resolve,[$cnf( $equal(X_52,join(meet(join(complement(complement(X_52)),X_83),X_52),complement(top))) )],[refute_0_289,refute_0_518]) ).
cnf(refute_0_520,plain,
converse(A) = meet(converse(A),join(converse(A),converse(B))),
inference(subst,[],[refute_0_519:[bind(X_52,$fot(converse(A))),bind(X_83,$fot(converse(B)))]]) ).
cnf(refute_0_521,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_522,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_521]) ).
cnf(refute_0_523,plain,
( converse(A) != meet(converse(A),join(converse(A),converse(B)))
| join(converse(A),converse(B)) != converse(join(A,B))
| converse(A) = meet(converse(A),converse(join(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(A),meet(converse(A),join(converse(A),converse(B)))) ),[1,1],$fot(converse(join(A,B)))]]) ).
cnf(refute_0_524,plain,
( converse(A) != meet(converse(A),join(converse(A),converse(B)))
| converse(A) = meet(converse(A),converse(join(A,B))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),converse(join(A,B))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
converse(A) = meet(converse(A),converse(join(A,B))),
inference(resolve,[$cnf( $equal(converse(A),meet(converse(A),join(converse(A),converse(B)))) )],[refute_0_520,refute_0_524]) ).
cnf(refute_0_526,plain,
converse(complement(X_114)) = meet(converse(complement(X_114)),converse(join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))))),
inference(subst,[],[refute_0_525:[bind(A,$fot(complement(X_114))),bind(B,$fot(meet(X_114,converse(complement(converse(X_114))))))]]) ).
cnf(refute_0_527,plain,
X_63 = join(meet(X_63,X_62),meet(X_63,complement(X_62))),
inference(subst,[],[refute_0_346:[bind(B,$fot(X_62)),bind(X_52,$fot(X_63))]]) ).
cnf(refute_0_528,plain,
meet(complement(X_62),X_63) = meet(X_63,complement(X_62)),
inference(subst,[],[refute_0_35:[bind(X_6,$fot(complement(X_62))),bind(X_7,$fot(X_63))]]) ).
cnf(refute_0_529,plain,
( meet(complement(X_62),X_63) != meet(X_63,complement(X_62))
| meet(X_63,complement(X_62)) = meet(complement(X_62),X_63) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_62),X_63))),bind(Y,$fot(meet(X_63,complement(X_62))))]]) ).
cnf(refute_0_530,plain,
meet(X_63,complement(X_62)) = meet(complement(X_62),X_63),
inference(resolve,[$cnf( $equal(meet(complement(X_62),X_63),meet(X_63,complement(X_62))) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
( X_63 != join(meet(X_63,X_62),meet(X_63,complement(X_62)))
| meet(X_63,complement(X_62)) != meet(complement(X_62),X_63)
| X_63 = join(meet(X_63,X_62),meet(complement(X_62),X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(X_63,join(meet(X_63,X_62),meet(X_63,complement(X_62)))) ),[1,1],$fot(meet(complement(X_62),X_63))]]) ).
cnf(refute_0_532,plain,
( X_63 != join(meet(X_63,X_62),meet(X_63,complement(X_62)))
| X_63 = join(meet(X_63,X_62),meet(complement(X_62),X_63)) ),
inference(resolve,[$cnf( $equal(meet(X_63,complement(X_62)),meet(complement(X_62),X_63)) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
X_63 = join(meet(X_63,X_62),meet(complement(X_62),X_63)),
inference(resolve,[$cnf( $equal(X_63,join(meet(X_63,X_62),meet(X_63,complement(X_62)))) )],[refute_0_527,refute_0_532]) ).
cnf(refute_0_534,plain,
converse(complement(converse(complement(complement(X_114))))) = join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),meet(complement(X_114),converse(complement(converse(complement(complement(X_114))))))),
inference(subst,[],[refute_0_533:[bind(X_62,$fot(X_114)),bind(X_63,$fot(converse(complement(converse(complement(complement(X_114)))))))]]) ).
cnf(refute_0_535,plain,
A = join(meet(A,converse(complement(converse(complement(A))))),complement(join(complement(A),converse(complement(converse(complement(A))))))),
inference(subst,[],[refute_0_23:[bind(B,$fot(converse(complement(converse(complement(A))))))]]) ).
cnf(refute_0_536,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_537,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_538,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( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_537]) ).
cnf(refute_0_539,plain,
converse(join(converse(A),X_12)) = join(A,converse(X_12)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_12)),join(converse(converse(A)),converse(X_12))) )],[refute_0_536,refute_0_538]) ).
cnf(refute_0_540,plain,
converse(join(converse(X_15),complement(converse(X_15)))) = join(X_15,converse(complement(converse(X_15)))),
inference(subst,[],[refute_0_539:[bind(A,$fot(X_15)),bind(X_12,$fot(complement(converse(X_15))))]]) ).
cnf(refute_0_541,plain,
top = join(converse(X_15),complement(converse(X_15))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_15)))]]) ).
cnf(refute_0_542,plain,
( top != join(converse(X_15),complement(converse(X_15)))
| join(converse(X_15),complement(converse(X_15))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_15),complement(converse(X_15)))))]]) ).
cnf(refute_0_543,plain,
join(converse(X_15),complement(converse(X_15))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_15),complement(converse(X_15)))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
( converse(join(converse(X_15),complement(converse(X_15)))) != join(X_15,converse(complement(converse(X_15))))
| join(converse(X_15),complement(converse(X_15))) != top
| converse(top) = join(X_15,converse(complement(converse(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_15),complement(converse(X_15)))),join(X_15,converse(complement(converse(X_15))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_545,plain,
( converse(join(converse(X_15),complement(converse(X_15)))) != join(X_15,converse(complement(converse(X_15))))
| converse(top) = join(X_15,converse(complement(converse(X_15)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_15),complement(converse(X_15))),top) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
converse(top) = join(X_15,converse(complement(converse(X_15)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_15),complement(converse(X_15)))),join(X_15,converse(complement(converse(X_15))))) )],[refute_0_540,refute_0_545]) ).
cnf(refute_0_547,plain,
join(converse(X_12),converse(X_11)) = join(converse(X_11),converse(X_12)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(X_12))),bind(B,$fot(converse(X_11)))]]) ).
cnf(refute_0_548,plain,
converse(join(X_11,X_12)) = join(converse(X_11),converse(X_12)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_11)),bind(B,$fot(X_12))]]) ).
cnf(refute_0_549,plain,
( converse(join(X_11,X_12)) != join(converse(X_11),converse(X_12))
| join(converse(X_11),converse(X_12)) = converse(join(X_11,X_12)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_11,X_12)))),bind(Y,$fot(join(converse(X_11),converse(X_12))))]]) ).
cnf(refute_0_550,plain,
join(converse(X_11),converse(X_12)) = converse(join(X_11,X_12)),
inference(resolve,[$cnf( $equal(converse(join(X_11,X_12)),join(converse(X_11),converse(X_12))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
( join(converse(X_11),converse(X_12)) != converse(join(X_11,X_12))
| join(converse(X_12),converse(X_11)) != join(converse(X_11),converse(X_12))
| join(converse(X_12),converse(X_11)) = converse(join(X_11,X_12)) ),
introduced(tautology,[equality,[$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_552,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( $equal(join(converse(X_11),converse(X_12)),converse(join(X_11,X_12))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
join(converse(X_12),converse(X_11)) = converse(join(X_11,X_12)),
inference(resolve,[$cnf( $equal(join(converse(X_12),converse(X_11)),join(converse(X_11),converse(X_12))) )],[refute_0_547,refute_0_552]) ).
cnf(refute_0_554,plain,
join(converse(X_12),converse(X_11)) = converse(join(X_12,X_11)),
inference(subst,[],[refute_0_522:[bind(A,$fot(X_12)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_555,plain,
( join(converse(X_12),converse(X_11)) != converse(join(X_11,X_12))
| join(converse(X_12),converse(X_11)) != converse(join(X_12,X_11))
| converse(join(X_12,X_11)) = converse(join(X_11,X_12)) ),
introduced(tautology,[equality,[$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_556,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( $equal(join(converse(X_12),converse(X_11)),converse(join(X_12,X_11))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
converse(join(X_12,X_11)) = converse(join(X_11,X_12)),
inference(resolve,[$cnf( $equal(join(converse(X_12),converse(X_11)),converse(join(X_11,X_12))) )],[refute_0_553,refute_0_556]) ).
cnf(refute_0_558,plain,
converse(join(complement(converse(zero)),converse(top))) = converse(join(converse(top),complement(converse(zero)))),
inference(subst,[],[refute_0_557:[bind(X_11,$fot(converse(top))),bind(X_12,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_559,plain,
converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_557:[bind(X_11,$fot(top)),bind(X_12,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_560,plain,
join(top,join(zero,converse(complement(converse(zero))))) = join(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_167:[bind(X_31,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_561,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_546:[bind(X_15,$fot(zero))]]) ).
cnf(refute_0_562,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_563,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) != converse(top)
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_565,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_563,refute_0_564]) ).
cnf(refute_0_566,plain,
join(top,converse(top)) = join(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) )],[refute_0_560,refute_0_565]) ).
cnf(refute_0_567,plain,
( join(top,converse(top)) != join(top,converse(complement(converse(zero))))
| join(top,converse(complement(converse(zero)))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(top,converse(top)))),bind(Y,$fot(join(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_568,plain,
join(top,converse(complement(converse(zero)))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(zero))))) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(complement(converse(zero)))))
| join(top,converse(complement(converse(zero)))) != join(top,converse(top))
| converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(complement(converse(zero)))))) ),[1,0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_570,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(complement(converse(zero)))))
| converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(top))) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(zero)))),join(top,converse(top))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(top))),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(complement(converse(zero)))))) )],[refute_0_559,refute_0_570]) ).
cnf(refute_0_572,plain,
join(complement(converse(zero)),converse(top)) = join(converse(top),complement(converse(zero))),
inference(subst,[],[refute_0_4:[bind(A,$fot(converse(top))),bind(B,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_573,plain,
converse(join(converse(complement(converse(zero))),top)) = join(complement(converse(zero)),converse(top)),
inference(subst,[],[refute_0_539:[bind(A,$fot(complement(converse(zero)))),bind(X_12,$fot(top))]]) ).
cnf(refute_0_574,plain,
( converse(join(converse(complement(converse(zero))),top)) != join(complement(converse(zero)),converse(top))
| join(complement(converse(zero)),converse(top)) != join(converse(top),complement(converse(zero)))
| converse(join(converse(complement(converse(zero))),top)) = join(converse(top),complement(converse(zero))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(converse(join(converse(complement(converse(zero))),top)))),bind(Y,$fot(join(complement(converse(zero)),converse(top)))),bind(Z,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_575,plain,
( join(complement(converse(zero)),converse(top)) != join(converse(top),complement(converse(zero)))
| converse(join(converse(complement(converse(zero))),top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),join(complement(converse(zero)),converse(top))) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
converse(join(converse(complement(converse(zero))),top)) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(top)),join(converse(top),complement(converse(zero)))) )],[refute_0_572,refute_0_575]) ).
cnf(refute_0_577,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(top)))
| converse(join(converse(complement(converse(zero))),top)) != join(converse(top),complement(converse(zero)))
| join(converse(top),complement(converse(zero))) = converse(join(top,converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(top)))) ),[0],$fot(join(converse(top),complement(converse(zero))))]]) ).
cnf(refute_0_578,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = converse(join(top,converse(top))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),join(converse(top),complement(converse(zero)))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
join(converse(top),top) = join(top,converse(top)),
inference(subst,[],[refute_0_196:[bind(X_29,$fot(converse(top)))]]) ).
cnf(refute_0_580,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_581,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_582,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( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_581]) ).
cnf(refute_0_583,plain,
converse(join(X_11,converse(A))) = join(converse(X_11),A),
inference(resolve,[$cnf( $equal(converse(join(X_11,converse(A))),join(converse(X_11),converse(converse(A)))) )],[refute_0_580,refute_0_582]) ).
cnf(refute_0_584,plain,
converse(join(top,converse(top))) = join(converse(top),top),
inference(subst,[],[refute_0_583:[bind(A,$fot(top)),bind(X_11,$fot(top))]]) ).
cnf(refute_0_585,plain,
( converse(join(top,converse(top))) != join(converse(top),top)
| join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(converse(join(top,converse(top))))),bind(Y,$fot(join(converse(top),top))),bind(Z,$fot(join(top,converse(top))))]]) ).
cnf(refute_0_586,plain,
( join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),top)) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
converse(join(top,converse(top))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(converse(top),top),join(top,converse(top))) )],[refute_0_579,refute_0_586]) ).
cnf(refute_0_588,plain,
( converse(join(top,converse(top))) != join(top,converse(top))
| join(converse(top),complement(converse(zero))) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = join(top,converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(top),complement(converse(zero))),converse(join(top,converse(top)))) ),[1],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_589,plain,
( join(converse(top),complement(converse(zero))) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(top,converse(top))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),converse(join(top,converse(top)))) )],[refute_0_578,refute_0_589]) ).
cnf(refute_0_591,plain,
join(converse(top),complement(converse(zero))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(top)))) )],[refute_0_571,refute_0_590]) ).
cnf(refute_0_592,plain,
join(top,converse(top)) = top,
inference(subst,[],[refute_0_281:[bind(X_29,$fot(converse(top)))]]) ).
cnf(refute_0_593,plain,
( join(converse(top),complement(converse(zero))) != join(top,converse(top))
| join(top,converse(top)) != top
| join(converse(top),complement(converse(zero))) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(converse(top),complement(converse(zero))),top) ),[0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_594,plain,
( join(converse(top),complement(converse(zero))) != join(top,converse(top))
| join(converse(top),complement(converse(zero))) = top ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),top) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
join(converse(top),complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),join(top,converse(top))) )],[refute_0_591,refute_0_594]) ).
cnf(refute_0_596,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(join(converse(top),complement(converse(zero))))
| join(converse(top),complement(converse(zero))) != top
| converse(join(complement(converse(zero)),converse(top))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(join(converse(top),complement(converse(zero))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_597,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(join(converse(top),complement(converse(zero))))
| converse(join(complement(converse(zero)),converse(top))) = converse(top) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),top) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
converse(join(complement(converse(zero)),converse(top))) = converse(top),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(join(converse(top),complement(converse(zero))))) )],[refute_0_558,refute_0_597]) ).
cnf(refute_0_599,plain,
join(converse(complement(converse(zero))),top) = top,
inference(subst,[],[refute_0_275:[bind(X_46,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_600,plain,
converse(join(complement(converse(zero)),converse(top))) = join(converse(complement(converse(zero))),top),
inference(subst,[],[refute_0_583:[bind(A,$fot(top)),bind(X_11,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_601,plain,
( converse(join(complement(converse(zero)),converse(top))) != join(converse(complement(converse(zero))),top)
| join(converse(complement(converse(zero))),top) != top
| converse(join(complement(converse(zero)),converse(top))) = top ),
inference(subst,[],[refute_0_17:[bind(X,$fot(converse(join(complement(converse(zero)),converse(top))))),bind(Y,$fot(join(converse(complement(converse(zero))),top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_602,plain,
( join(converse(complement(converse(zero))),top) != top
| converse(join(complement(converse(zero)),converse(top))) = top ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),join(converse(complement(converse(zero))),top)) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
converse(join(complement(converse(zero)),converse(top))) = top,
inference(resolve,[$cnf( $equal(join(converse(complement(converse(zero))),top),top) )],[refute_0_599,refute_0_602]) ).
cnf(refute_0_604,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(top)
| converse(join(complement(converse(zero)),converse(top))) != top
| top = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(top)) ),[0],$fot(top)]]) ).
cnf(refute_0_605,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(top)
| top = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),top) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
top = converse(top),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(top)) )],[refute_0_598,refute_0_605]) ).
cnf(refute_0_607,plain,
( top != converse(top)
| converse(top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(top)))]]) ).
cnf(refute_0_608,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(top,converse(top)) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
( converse(top) != join(X_15,converse(complement(converse(X_15))))
| converse(top) != top
| top = join(X_15,converse(complement(converse(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_15,converse(complement(converse(X_15))))) ),[0],$fot(top)]]) ).
cnf(refute_0_610,plain,
( converse(top) != join(X_15,converse(complement(converse(X_15))))
| top = join(X_15,converse(complement(converse(X_15)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
top = join(X_15,converse(complement(converse(X_15)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_15,converse(complement(converse(X_15))))) )],[refute_0_546,refute_0_610]) ).
cnf(refute_0_612,plain,
top = join(complement(A),converse(complement(converse(complement(A))))),
inference(subst,[],[refute_0_611:[bind(X_15,$fot(complement(A)))]]) ).
cnf(refute_0_613,plain,
( top != join(complement(A),converse(complement(converse(complement(A)))))
| join(complement(A),converse(complement(converse(complement(A))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(A),converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_614,plain,
join(complement(A),converse(complement(converse(complement(A))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(A),converse(complement(converse(complement(A)))))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
( A != join(meet(A,converse(complement(converse(complement(A))))),complement(join(complement(A),converse(complement(converse(complement(A)))))))
| join(complement(A),converse(complement(converse(complement(A))))) != top
| A = join(meet(A,converse(complement(converse(complement(A))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(A,join(meet(A,converse(complement(converse(complement(A))))),complement(join(complement(A),converse(complement(converse(complement(A)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_616,plain,
( A != join(meet(A,converse(complement(converse(complement(A))))),complement(join(complement(A),converse(complement(converse(complement(A)))))))
| A = join(meet(A,converse(complement(converse(complement(A))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(A),converse(complement(converse(complement(A))))),top) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
A = join(meet(A,converse(complement(converse(complement(A))))),complement(top)),
inference(resolve,[$cnf( $equal(A,join(meet(A,converse(complement(converse(complement(A))))),complement(join(complement(A),converse(complement(converse(complement(A)))))))) )],[refute_0_535,refute_0_616]) ).
cnf(refute_0_618,plain,
join(zero,meet(A,converse(complement(converse(complement(A)))))) = meet(A,converse(complement(converse(complement(A))))),
inference(subst,[],[refute_0_485:[bind(X_52,$fot(meet(A,converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_619,plain,
join(complement(top),meet(A,converse(complement(converse(complement(A)))))) = join(complement(top),meet(A,converse(complement(converse(complement(A)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(A,converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_620,plain,
( complement(top) != zero
| join(complement(top),meet(A,converse(complement(converse(complement(A)))))) != join(complement(top),meet(A,converse(complement(converse(complement(A))))))
| join(complement(top),meet(A,converse(complement(converse(complement(A)))))) = join(zero,meet(A,converse(complement(converse(complement(A)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(A,converse(complement(converse(complement(A)))))),join(complement(top),meet(A,converse(complement(converse(complement(A))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_621,plain,
( complement(top) != zero
| join(complement(top),meet(A,converse(complement(converse(complement(A)))))) = join(zero,meet(A,converse(complement(converse(complement(A)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(A,converse(complement(converse(complement(A)))))),join(complement(top),meet(A,converse(complement(converse(complement(A))))))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
join(complement(top),meet(A,converse(complement(converse(complement(A)))))) = join(zero,meet(A,converse(complement(converse(complement(A)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_89,refute_0_621]) ).
cnf(refute_0_623,plain,
( join(complement(top),meet(A,converse(complement(converse(complement(A)))))) != join(zero,meet(A,converse(complement(converse(complement(A))))))
| join(zero,meet(A,converse(complement(converse(complement(A)))))) != meet(A,converse(complement(converse(complement(A)))))
| join(complement(top),meet(A,converse(complement(converse(complement(A)))))) = meet(A,converse(complement(converse(complement(A))))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(top),meet(A,converse(complement(converse(complement(A)))))))),bind(Y,$fot(join(zero,meet(A,converse(complement(converse(complement(A)))))))),bind(Z,$fot(meet(A,converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_624,plain,
( join(zero,meet(A,converse(complement(converse(complement(A)))))) != meet(A,converse(complement(converse(complement(A)))))
| join(complement(top),meet(A,converse(complement(converse(complement(A)))))) = meet(A,converse(complement(converse(complement(A))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(A,converse(complement(converse(complement(A)))))),join(zero,meet(A,converse(complement(converse(complement(A))))))) )],[refute_0_622,refute_0_623]) ).
cnf(refute_0_625,plain,
join(complement(top),meet(A,converse(complement(converse(complement(A)))))) = meet(A,converse(complement(converse(complement(A))))),
inference(resolve,[$cnf( $equal(join(zero,meet(A,converse(complement(converse(complement(A)))))),meet(A,converse(complement(converse(complement(A)))))) )],[refute_0_618,refute_0_624]) ).
cnf(refute_0_626,plain,
join(meet(A,converse(complement(converse(complement(A))))),complement(top)) = join(complement(top),meet(A,converse(complement(converse(complement(A)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(A,converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_627,plain,
( join(complement(top),meet(A,converse(complement(converse(complement(A)))))) != meet(A,converse(complement(converse(complement(A)))))
| join(meet(A,converse(complement(converse(complement(A))))),complement(top)) != join(complement(top),meet(A,converse(complement(converse(complement(A))))))
| join(meet(A,converse(complement(converse(complement(A))))),complement(top)) = meet(A,converse(complement(converse(complement(A))))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(A,converse(complement(converse(complement(A))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(A,converse(complement(converse(complement(A)))))))),bind(Z,$fot(meet(A,converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_628,plain,
( join(complement(top),meet(A,converse(complement(converse(complement(A)))))) != meet(A,converse(complement(converse(complement(A)))))
| join(meet(A,converse(complement(converse(complement(A))))),complement(top)) = meet(A,converse(complement(converse(complement(A))))) ),
inference(resolve,[$cnf( $equal(join(meet(A,converse(complement(converse(complement(A))))),complement(top)),join(complement(top),meet(A,converse(complement(converse(complement(A))))))) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
join(meet(A,converse(complement(converse(complement(A))))),complement(top)) = meet(A,converse(complement(converse(complement(A))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(A,converse(complement(converse(complement(A)))))),meet(A,converse(complement(converse(complement(A)))))) )],[refute_0_625,refute_0_628]) ).
cnf(refute_0_630,plain,
( A != join(meet(A,converse(complement(converse(complement(A))))),complement(top))
| join(meet(A,converse(complement(converse(complement(A))))),complement(top)) != meet(A,converse(complement(converse(complement(A)))))
| A = meet(A,converse(complement(converse(complement(A))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,meet(A,converse(complement(converse(complement(A)))))) ),[0],$fot(join(meet(A,converse(complement(converse(complement(A))))),complement(top)))]]) ).
cnf(refute_0_631,plain,
( A != join(meet(A,converse(complement(converse(complement(A))))),complement(top))
| A = meet(A,converse(complement(converse(complement(A))))) ),
inference(resolve,[$cnf( $equal(join(meet(A,converse(complement(converse(complement(A))))),complement(top)),meet(A,converse(complement(converse(complement(A)))))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
A = meet(A,converse(complement(converse(complement(A))))),
inference(resolve,[$cnf( $equal(A,join(meet(A,converse(complement(converse(complement(A))))),complement(top))) )],[refute_0_617,refute_0_631]) ).
cnf(refute_0_633,plain,
complement(X_114) = meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))),
inference(subst,[],[refute_0_632:[bind(A,$fot(complement(X_114)))]]) ).
cnf(refute_0_634,plain,
( complement(X_114) != meet(complement(X_114),converse(complement(converse(complement(complement(X_114))))))
| meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))) = complement(X_114) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_114))),bind(Y,$fot(meet(complement(X_114),converse(complement(converse(complement(complement(X_114))))))))]]) ).
cnf(refute_0_635,plain,
meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))) = complement(X_114),
inference(resolve,[$cnf( $equal(complement(X_114),meet(complement(X_114),converse(complement(converse(complement(complement(X_114))))))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
( converse(complement(converse(complement(complement(X_114))))) != join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))))
| meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))) != complement(X_114)
| converse(complement(converse(complement(complement(X_114))))) = join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))))) ),[1,1],$fot(complement(X_114))]]) ).
cnf(refute_0_637,plain,
( converse(complement(converse(complement(complement(X_114))))) != join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))))
| converse(complement(converse(complement(complement(X_114))))) = join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))),complement(X_114)) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
converse(complement(converse(complement(complement(X_114))))) = join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),meet(complement(X_114),converse(complement(converse(complement(complement(X_114)))))))) )],[refute_0_534,refute_0_637]) ).
cnf(refute_0_639,plain,
complement(complement(X_114)) = X_114,
inference(subst,[],[refute_0_464:[bind(X_52,$fot(X_114))]]) ).
cnf(refute_0_640,plain,
converse(complement(complement(X_114))) = converse(complement(complement(X_114))),
introduced(tautology,[refl,[$fot(converse(complement(complement(X_114))))]]) ).
cnf(refute_0_641,plain,
( complement(complement(X_114)) != X_114
| converse(complement(complement(X_114))) != converse(complement(complement(X_114)))
| converse(complement(complement(X_114))) = converse(X_114) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(complement(X_114))),converse(complement(complement(X_114)))) ),[1,0],$fot(X_114)]]) ).
cnf(refute_0_642,plain,
( complement(complement(X_114)) != X_114
| converse(complement(complement(X_114))) = converse(X_114) ),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_114))),converse(complement(complement(X_114)))) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
converse(complement(complement(X_114))) = converse(X_114),
inference(resolve,[$cnf( $equal(complement(complement(X_114)),X_114) )],[refute_0_639,refute_0_642]) ).
cnf(refute_0_644,plain,
complement(converse(complement(complement(X_114)))) = complement(converse(complement(complement(X_114)))),
introduced(tautology,[refl,[$fot(complement(converse(complement(complement(X_114)))))]]) ).
cnf(refute_0_645,plain,
( complement(converse(complement(complement(X_114)))) != complement(converse(complement(complement(X_114))))
| converse(complement(complement(X_114))) != converse(X_114)
| complement(converse(complement(complement(X_114)))) = complement(converse(X_114)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(complement(X_114)))),complement(converse(complement(complement(X_114))))) ),[1,0],$fot(converse(X_114))]]) ).
cnf(refute_0_646,plain,
( converse(complement(complement(X_114))) != converse(X_114)
| complement(converse(complement(complement(X_114)))) = complement(converse(X_114)) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_114)))),complement(converse(complement(complement(X_114))))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
complement(converse(complement(complement(X_114)))) = complement(converse(X_114)),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_114))),converse(X_114)) )],[refute_0_643,refute_0_646]) ).
cnf(refute_0_648,plain,
converse(complement(converse(complement(complement(X_114))))) = converse(complement(converse(complement(complement(X_114))))),
introduced(tautology,[refl,[$fot(converse(complement(converse(complement(complement(X_114))))))]]) ).
cnf(refute_0_649,plain,
( complement(converse(complement(complement(X_114)))) != complement(converse(X_114))
| converse(complement(converse(complement(complement(X_114))))) != converse(complement(converse(complement(complement(X_114)))))
| converse(complement(converse(complement(complement(X_114))))) = converse(complement(converse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),converse(complement(converse(complement(complement(X_114)))))) ),[1,0],$fot(complement(converse(X_114)))]]) ).
cnf(refute_0_650,plain,
( complement(converse(complement(complement(X_114)))) != complement(converse(X_114))
| converse(complement(converse(complement(complement(X_114))))) = converse(complement(converse(X_114))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),converse(complement(converse(complement(complement(X_114)))))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
converse(complement(converse(complement(complement(X_114))))) = converse(complement(converse(X_114))),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_114)))),complement(converse(X_114))) )],[refute_0_647,refute_0_650]) ).
cnf(refute_0_652,plain,
( converse(complement(converse(complement(complement(X_114))))) != converse(complement(converse(X_114)))
| converse(complement(converse(complement(complement(X_114))))) != join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))
| converse(complement(converse(X_114))) = join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))) ),[0],$fot(converse(complement(converse(X_114))))]]) ).
cnf(refute_0_653,plain,
( converse(complement(converse(complement(complement(X_114))))) != join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))
| converse(complement(converse(X_114))) = join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),converse(complement(converse(X_114)))) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
meet(X_114,converse(complement(converse(complement(complement(X_114)))))) = meet(X_114,converse(complement(converse(complement(complement(X_114)))))),
introduced(tautology,[refl,[$fot(meet(X_114,converse(complement(converse(complement(complement(X_114)))))))]]) ).
cnf(refute_0_655,plain,
( converse(complement(converse(complement(complement(X_114))))) != converse(complement(converse(X_114)))
| meet(X_114,converse(complement(converse(complement(complement(X_114)))))) != meet(X_114,converse(complement(converse(complement(complement(X_114))))))
| meet(X_114,converse(complement(converse(complement(complement(X_114)))))) = meet(X_114,converse(complement(converse(X_114)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_114,converse(complement(converse(complement(complement(X_114)))))),meet(X_114,converse(complement(converse(complement(complement(X_114))))))) ),[1,1],$fot(converse(complement(converse(X_114))))]]) ).
cnf(refute_0_656,plain,
( converse(complement(converse(complement(complement(X_114))))) != converse(complement(converse(X_114)))
| meet(X_114,converse(complement(converse(complement(complement(X_114)))))) = meet(X_114,converse(complement(converse(X_114)))) ),
inference(resolve,[$cnf( $equal(meet(X_114,converse(complement(converse(complement(complement(X_114)))))),meet(X_114,converse(complement(converse(complement(complement(X_114))))))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
meet(X_114,converse(complement(converse(complement(complement(X_114)))))) = meet(X_114,converse(complement(converse(X_114)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),converse(complement(converse(X_114)))) )],[refute_0_651,refute_0_656]) ).
cnf(refute_0_658,plain,
meet(converse(complement(converse(complement(complement(X_114))))),X_114) = meet(X_114,converse(complement(converse(complement(complement(X_114)))))),
inference(subst,[],[refute_0_370:[bind(X_6,$fot(X_114)),bind(X_7,$fot(converse(complement(converse(complement(complement(X_114)))))))]]) ).
cnf(refute_0_659,plain,
( meet(X_114,converse(complement(converse(complement(complement(X_114)))))) != meet(X_114,converse(complement(converse(X_114))))
| meet(converse(complement(converse(complement(complement(X_114))))),X_114) != meet(X_114,converse(complement(converse(complement(complement(X_114))))))
| meet(converse(complement(converse(complement(complement(X_114))))),X_114) = meet(X_114,converse(complement(converse(X_114)))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(converse(complement(converse(complement(complement(X_114))))),X_114))),bind(Y,$fot(meet(X_114,converse(complement(converse(complement(complement(X_114)))))))),bind(Z,$fot(meet(X_114,converse(complement(converse(X_114))))))]]) ).
cnf(refute_0_660,plain,
( meet(X_114,converse(complement(converse(complement(complement(X_114)))))) != meet(X_114,converse(complement(converse(X_114))))
| meet(converse(complement(converse(complement(complement(X_114))))),X_114) = meet(X_114,converse(complement(converse(X_114)))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(complement(X_114))))),X_114),meet(X_114,converse(complement(converse(complement(complement(X_114))))))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
meet(converse(complement(converse(complement(complement(X_114))))),X_114) = meet(X_114,converse(complement(converse(X_114)))),
inference(resolve,[$cnf( $equal(meet(X_114,converse(complement(converse(complement(complement(X_114)))))),meet(X_114,converse(complement(converse(X_114))))) )],[refute_0_657,refute_0_660]) ).
cnf(refute_0_662,plain,
join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)) = join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)),
introduced(tautology,[refl,[$fot(join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)))]]) ).
cnf(refute_0_663,plain,
( join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)) != join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114))
| meet(converse(complement(converse(complement(complement(X_114))))),X_114) != meet(X_114,converse(complement(converse(X_114))))
| join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)),join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114))) ),[1,1],$fot(meet(X_114,converse(complement(converse(X_114)))))]]) ).
cnf(refute_0_664,plain,
( meet(converse(complement(converse(complement(complement(X_114))))),X_114) != meet(X_114,converse(complement(converse(X_114))))
| join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)),join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(complement(X_114))))),X_114),meet(X_114,converse(complement(converse(X_114))))) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) = join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_114))),bind(B,$fot(meet(converse(complement(converse(complement(complement(X_114))))),X_114)))]]) ).
cnf(refute_0_667,plain,
( join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)) != join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))
| join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) != join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114))
| join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)))),bind(Y,$fot(join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)))),bind(Z,$fot(join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))))]]) ).
cnf(refute_0_668,plain,
( join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)) != join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))
| join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)),join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))),
inference(resolve,[$cnf( $equal(join(complement(X_114),meet(converse(complement(converse(complement(complement(X_114))))),X_114)),join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))) )],[refute_0_665,refute_0_668]) ).
cnf(refute_0_670,plain,
( converse(complement(converse(X_114))) != join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))
| join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)) != join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))
| converse(complement(converse(X_114))) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(X_114))),join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))) ),[0],$fot(join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)))]]) ).
cnf(refute_0_671,plain,
( converse(complement(converse(X_114))) != join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))
| converse(complement(converse(X_114))) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114)),join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
( converse(complement(converse(complement(complement(X_114))))) != join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))
| converse(complement(converse(X_114))) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_114))),join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))) )],[refute_0_653,refute_0_671]) ).
cnf(refute_0_673,plain,
converse(complement(converse(X_114))) = join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_114))))),join(meet(converse(complement(converse(complement(complement(X_114))))),X_114),complement(X_114))) )],[refute_0_638,refute_0_672]) ).
cnf(refute_0_674,plain,
( converse(complement(converse(X_114))) != join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))
| join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) = converse(complement(converse(X_114))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(complement(converse(X_114))))),bind(Y,$fot(join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))))]]) ).
cnf(refute_0_675,plain,
join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) = converse(complement(converse(X_114))),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_114))),join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
( converse(complement(X_114)) != meet(converse(complement(X_114)),converse(join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))))
| join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))) != converse(complement(converse(X_114)))
| converse(complement(X_114)) = meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(X_114)),meet(converse(complement(X_114)),converse(join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))))) ),[1,1,0],$fot(converse(complement(converse(X_114))))]]) ).
cnf(refute_0_677,plain,
( converse(complement(X_114)) != meet(converse(complement(X_114)),converse(join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))))
| converse(complement(X_114)) = meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_114),meet(X_114,converse(complement(converse(X_114))))),converse(complement(converse(X_114)))) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
converse(complement(X_114)) = meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))),
inference(resolve,[$cnf( $equal(converse(complement(X_114)),meet(converse(complement(X_114)),converse(join(complement(X_114),meet(X_114,converse(complement(converse(X_114)))))))) )],[refute_0_526,refute_0_677]) ).
cnf(refute_0_679,plain,
complement(X_148) = meet(complement(X_148),converse(complement(converse(complement(complement(X_148)))))),
inference(subst,[],[refute_0_632:[bind(A,$fot(complement(X_148)))]]) ).
cnf(refute_0_680,plain,
X_148 = complement(complement(X_148)),
inference(subst,[],[refute_0_462:[bind(X_52,$fot(X_148))]]) ).
cnf(refute_0_681,plain,
( X_148 != complement(complement(X_148))
| complement(complement(X_148)) = X_148 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_148)),bind(Y,$fot(complement(complement(X_148))))]]) ).
cnf(refute_0_682,plain,
complement(complement(X_148)) = X_148,
inference(resolve,[$cnf( $equal(X_148,complement(complement(X_148))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
( complement(X_148) != meet(complement(X_148),converse(complement(converse(complement(complement(X_148))))))
| complement(complement(X_148)) != X_148
| complement(X_148) = meet(complement(X_148),converse(complement(converse(X_148)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_148),meet(complement(X_148),converse(complement(converse(complement(complement(X_148))))))) ),[1,1,0,0,0],$fot(X_148)]]) ).
cnf(refute_0_684,plain,
( complement(X_148) != meet(complement(X_148),converse(complement(converse(complement(complement(X_148))))))
| complement(X_148) = meet(complement(X_148),converse(complement(converse(X_148)))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_148)),X_148) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
complement(X_148) = meet(complement(X_148),converse(complement(converse(X_148)))),
inference(resolve,[$cnf( $equal(complement(X_148),meet(complement(X_148),converse(complement(converse(complement(complement(X_148))))))) )],[refute_0_679,refute_0_684]) ).
cnf(refute_0_686,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(converse(converse(A))))),
inference(subst,[],[refute_0_685:[bind(X_148,$fot(converse(A)))]]) ).
cnf(refute_0_687,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(converse(converse(A)))))
| converse(converse(A)) != A
| complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(converse(converse(A)))))) ),[1,1,0,0],$fot(A)]]) ).
cnf(refute_0_688,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(converse(converse(A)))))
| complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_687]) ).
cnf(refute_0_689,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(converse(converse(A)))))) )],[refute_0_686,refute_0_688]) ).
cnf(refute_0_690,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(A)))
| meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(converse(A)))),bind(Y,$fot(meet(complement(converse(A)),converse(complement(A)))))]]) ).
cnf(refute_0_691,plain,
meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(A)))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
meet(complement(converse(X_114)),converse(complement(X_114))) = complement(converse(X_114)),
inference(subst,[],[refute_0_691:[bind(A,$fot(X_114))]]) ).
cnf(refute_0_693,plain,
meet(converse(complement(X_114)),complement(converse(X_114))) = meet(complement(converse(X_114)),converse(complement(X_114))),
inference(subst,[],[refute_0_370:[bind(X_6,$fot(complement(converse(X_114)))),bind(X_7,$fot(converse(complement(X_114))))]]) ).
cnf(refute_0_694,plain,
( meet(complement(converse(X_114)),converse(complement(X_114))) != complement(converse(X_114))
| meet(converse(complement(X_114)),complement(converse(X_114))) != meet(complement(converse(X_114)),converse(complement(X_114)))
| meet(converse(complement(X_114)),complement(converse(X_114))) = complement(converse(X_114)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(converse(complement(X_114)),complement(converse(X_114))))),bind(Y,$fot(meet(complement(converse(X_114)),converse(complement(X_114))))),bind(Z,$fot(complement(converse(X_114))))]]) ).
cnf(refute_0_695,plain,
( meet(complement(converse(X_114)),converse(complement(X_114))) != complement(converse(X_114))
| meet(converse(complement(X_114)),complement(converse(X_114))) = complement(converse(X_114)) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_114)),complement(converse(X_114))),meet(complement(converse(X_114)),converse(complement(X_114)))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
meet(converse(complement(X_114)),complement(converse(X_114))) = complement(converse(X_114)),
inference(resolve,[$cnf( $equal(meet(complement(converse(X_114)),converse(complement(X_114))),complement(converse(X_114))) )],[refute_0_692,refute_0_695]) ).
cnf(refute_0_697,plain,
converse(converse(complement(converse(X_114)))) = complement(converse(X_114)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(X_114))))]]) ).
cnf(refute_0_698,plain,
meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) = meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))),
introduced(tautology,[refl,[$fot(meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))))]]) ).
cnf(refute_0_699,plain,
( converse(converse(complement(converse(X_114)))) != complement(converse(X_114))
| meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) != meet(converse(complement(X_114)),converse(converse(complement(converse(X_114)))))
| meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) = meet(converse(complement(X_114)),complement(converse(X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))),meet(converse(complement(X_114)),converse(converse(complement(converse(X_114)))))) ),[1,1],$fot(complement(converse(X_114)))]]) ).
cnf(refute_0_700,plain,
( converse(converse(complement(converse(X_114)))) != complement(converse(X_114))
| meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) = meet(converse(complement(X_114)),complement(converse(X_114))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))),meet(converse(complement(X_114)),converse(converse(complement(converse(X_114)))))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) = meet(converse(complement(X_114)),complement(converse(X_114))),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(X_114)))),complement(converse(X_114))) )],[refute_0_697,refute_0_700]) ).
cnf(refute_0_702,plain,
( meet(converse(complement(X_114)),complement(converse(X_114))) != complement(converse(X_114))
| meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) != meet(converse(complement(X_114)),complement(converse(X_114)))
| meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) = complement(converse(X_114)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))))),bind(Y,$fot(meet(converse(complement(X_114)),complement(converse(X_114))))),bind(Z,$fot(complement(converse(X_114))))]]) ).
cnf(refute_0_703,plain,
( meet(converse(complement(X_114)),complement(converse(X_114))) != complement(converse(X_114))
| meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) = complement(converse(X_114)) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))),meet(converse(complement(X_114)),complement(converse(X_114)))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) = complement(converse(X_114)),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_114)),complement(converse(X_114))),complement(converse(X_114))) )],[refute_0_696,refute_0_703]) ).
cnf(refute_0_705,plain,
( converse(complement(X_114)) != meet(converse(complement(X_114)),converse(converse(complement(converse(X_114)))))
| meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))) != complement(converse(X_114))
| converse(complement(X_114)) = complement(converse(X_114)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(X_114)),complement(converse(X_114))) ),[0],$fot(meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))))]]) ).
cnf(refute_0_706,plain,
( converse(complement(X_114)) != meet(converse(complement(X_114)),converse(converse(complement(converse(X_114)))))
| converse(complement(X_114)) = complement(converse(X_114)) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_114)),converse(converse(complement(converse(X_114))))),complement(converse(X_114))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
converse(complement(X_114)) = complement(converse(X_114)),
inference(resolve,[$cnf( $equal(converse(complement(X_114)),meet(converse(complement(X_114)),converse(converse(complement(converse(X_114)))))) )],[refute_0_678,refute_0_706]) ).
cnf(refute_0_708,plain,
converse(complement(sk1)) = complement(converse(sk1)),
inference(subst,[],[refute_0_707:[bind(X_114,$fot(sk1))]]) ).
cnf(refute_0_709,plain,
( complement(converse(sk1)) != complement(converse(sk1))
| converse(complement(sk1)) != complement(converse(sk1))
| converse(complement(sk1)) = complement(converse(sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(sk1)),complement(converse(sk1))) ),[1],$fot(complement(converse(sk1)))]]) ).
cnf(refute_0_710,plain,
( complement(converse(sk1)) != complement(converse(sk1))
| converse(complement(sk1)) = complement(converse(sk1)) ),
inference(resolve,[$cnf( $equal(converse(complement(sk1)),complement(converse(sk1))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
complement(converse(sk1)) != complement(converse(sk1)),
inference(resolve,[$cnf( $equal(converse(complement(sk1)),complement(converse(sk1))) )],[refute_0_710,goals_14]) ).
cnf(refute_0_712,plain,
complement(converse(sk1)) = complement(converse(sk1)),
introduced(tautology,[refl,[$fot(complement(converse(sk1)))]]) ).
cnf(refute_0_713,plain,
$false,
inference(resolve,[$cnf( $equal(complement(converse(sk1)),complement(converse(sk1))) )],[refute_0_712,refute_0_711]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL004-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 11:47:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.54/1.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.54/1.71
% 1.54/1.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.66/1.83
%------------------------------------------------------------------------------