TSTP Solution File: REL012-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL012-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:43:17 EDT 2022
% Result : Unsatisfiable 123.13s 123.31s
% Output : CNFRefutation 123.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 240
% Syntax : Number of clauses : 1039 ( 525 unt; 0 nHn; 592 RR)
% Number of literals : 1778 (1777 equ; 742 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 1423 ( 32 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,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(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( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) = join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(sk1))),bind(B,$fot(composition(complement(composition(sk1,sk2)),converse(sk2))))]]) ).
cnf(refute_0_6,plain,
( join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) != complement(sk1)
| join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2)))
| join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)),join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2)))) ),[1],$fot(complement(sk1))]]) ).
cnf(refute_0_7,plain,
( join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) != complement(sk1)
| join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) = complement(sk1) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)),join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) != complement(sk1),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)),complement(sk1)) )],[refute_0_7,goals_14]) ).
cnf(refute_0_9,plain,
converse(join(converse(A),X_11)) = join(converse(converse(A)),converse(X_11)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_11))]]) ).
cnf(refute_0_10,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_11)) != join(converse(converse(A)),converse(X_11))
| converse(join(converse(A),X_11)) = join(A,converse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_11)),join(converse(converse(A)),converse(X_11))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_11,plain,
( converse(join(converse(A),X_11)) != join(converse(converse(A)),converse(X_11))
| converse(join(converse(A),X_11)) = join(A,converse(X_11)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_10]) ).
cnf(refute_0_12,plain,
converse(join(converse(A),X_11)) = join(A,converse(X_11)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_11)),join(converse(converse(A)),converse(X_11))) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
converse(join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),
inference(subst,[],[refute_0_12:[bind(X_11,$fot(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))]]) ).
cnf(refute_0_14,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_15,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_16,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_16]) ).
cnf(refute_0_18,plain,
join(complement(X_7),composition(converse(converse(A)),complement(composition(converse(A),X_7)))) = complement(X_7),
inference(subst,[],[refute_0_17:[bind(A,$fot(converse(A))),bind(B,$fot(X_7))]]) ).
cnf(refute_0_19,plain,
( converse(converse(A)) != A
| join(complement(X_7),composition(converse(converse(A)),complement(composition(converse(A),X_7)))) != complement(X_7)
| join(complement(X_7),composition(A,complement(composition(converse(A),X_7)))) = complement(X_7) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_7),composition(converse(converse(A)),complement(composition(converse(A),X_7)))),complement(X_7)) ),[0,1,0],$fot(A)]]) ).
cnf(refute_0_20,plain,
( join(complement(X_7),composition(converse(converse(A)),complement(composition(converse(A),X_7)))) != complement(X_7)
| join(complement(X_7),composition(A,complement(composition(converse(A),X_7)))) = complement(X_7) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_19]) ).
cnf(refute_0_21,plain,
join(complement(X_7),composition(A,complement(composition(converse(A),X_7)))) = complement(X_7),
inference(resolve,[$cnf( $equal(join(complement(X_7),composition(converse(converse(A)),complement(composition(converse(A),X_7)))),complement(X_7)) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
join(complement(complement(X_69)),composition(X_134,complement(composition(converse(X_134),complement(X_69))))) = complement(complement(X_69)),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_134)),bind(X_7,$fot(complement(X_69)))]]) ).
cnf(refute_0_23,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_24,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_25,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_25]) ).
cnf(refute_0_27,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_28,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_29,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_28]) ).
cnf(refute_0_30,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_31,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),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_32,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_34]) ).
cnf(refute_0_36,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_35:[bind(X,$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_37,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_27,refute_0_37]) ).
cnf(refute_0_39,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_40,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_26,refute_0_40]) ).
cnf(refute_0_42,plain,
X_34 = join(meet(X_34,complement(B)),complement(join(complement(X_34),complement(B)))),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_34)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_43,plain,
meet(X_34,B) = complement(join(complement(X_34),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_34))]]) ).
cnf(refute_0_44,plain,
( meet(X_34,B) != complement(join(complement(X_34),complement(B)))
| complement(join(complement(X_34),complement(B))) = meet(X_34,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_34,B))),bind(Y,$fot(complement(join(complement(X_34),complement(B)))))]]) ).
cnf(refute_0_45,plain,
complement(join(complement(X_34),complement(B))) = meet(X_34,B),
inference(resolve,[$cnf( $equal(meet(X_34,B),complement(join(complement(X_34),complement(B)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( X_34 != join(meet(X_34,complement(B)),complement(join(complement(X_34),complement(B))))
| complement(join(complement(X_34),complement(B))) != meet(X_34,B)
| X_34 = join(meet(X_34,complement(B)),meet(X_34,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_34,join(meet(X_34,complement(B)),complement(join(complement(X_34),complement(B))))) ),[1,1],$fot(meet(X_34,B))]]) ).
cnf(refute_0_47,plain,
( X_34 != join(meet(X_34,complement(B)),complement(join(complement(X_34),complement(B))))
| X_34 = join(meet(X_34,complement(B)),meet(X_34,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_34),complement(B))),meet(X_34,B)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
X_34 = join(meet(X_34,complement(B)),meet(X_34,B)),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,complement(B)),complement(join(complement(X_34),complement(B))))) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
join(meet(X_34,complement(B)),meet(X_34,B)) = join(meet(X_34,B),meet(X_34,complement(B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(X_34,B))),bind(B,$fot(meet(X_34,complement(B))))]]) ).
cnf(refute_0_50,plain,
( X_34 != join(meet(X_34,complement(B)),meet(X_34,B))
| join(meet(X_34,complement(B)),meet(X_34,B)) != join(meet(X_34,B),meet(X_34,complement(B)))
| X_34 = join(meet(X_34,B),meet(X_34,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,join(meet(X_34,B),meet(X_34,complement(B)))) ),[0],$fot(join(meet(X_34,complement(B)),meet(X_34,B)))]]) ).
cnf(refute_0_51,plain,
( X_34 != join(meet(X_34,complement(B)),meet(X_34,B))
| X_34 = join(meet(X_34,B),meet(X_34,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,complement(B)),meet(X_34,B)),join(meet(X_34,B),meet(X_34,complement(B)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
X_34 = join(meet(X_34,B),meet(X_34,complement(B))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,complement(B)),meet(X_34,B))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
meet(X_26,X_27) = complement(join(complement(X_26),complement(X_27))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_26)),bind(B,$fot(X_27))]]) ).
cnf(refute_0_54,plain,
join(complement(X_27),complement(X_26)) = join(complement(X_26),complement(X_27)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_27))),bind(B,$fot(complement(X_26)))]]) ).
cnf(refute_0_55,plain,
( join(complement(X_27),complement(X_26)) != join(complement(X_26),complement(X_27))
| join(complement(X_26),complement(X_27)) = join(complement(X_27),complement(X_26)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_27),complement(X_26)))),bind(Y,$fot(join(complement(X_26),complement(X_27))))]]) ).
cnf(refute_0_56,plain,
join(complement(X_26),complement(X_27)) = join(complement(X_27),complement(X_26)),
inference(resolve,[$cnf( $equal(join(complement(X_27),complement(X_26)),join(complement(X_26),complement(X_27))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( join(complement(X_26),complement(X_27)) != join(complement(X_27),complement(X_26))
| meet(X_26,X_27) != complement(join(complement(X_26),complement(X_27)))
| meet(X_26,X_27) = complement(join(complement(X_27),complement(X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_26,X_27),complement(join(complement(X_26),complement(X_27)))) ),[1,0],$fot(join(complement(X_27),complement(X_26)))]]) ).
cnf(refute_0_58,plain,
( meet(X_26,X_27) != complement(join(complement(X_26),complement(X_27)))
| meet(X_26,X_27) = complement(join(complement(X_27),complement(X_26))) ),
inference(resolve,[$cnf( $equal(join(complement(X_26),complement(X_27)),join(complement(X_27),complement(X_26))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
meet(X_26,X_27) = complement(join(complement(X_27),complement(X_26))),
inference(resolve,[$cnf( $equal(meet(X_26,X_27),complement(join(complement(X_26),complement(X_27)))) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
complement(join(complement(X_27),complement(X_26))) = meet(X_27,X_26),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_27)),bind(B,$fot(X_26))]]) ).
cnf(refute_0_61,plain,
( complement(join(complement(X_27),complement(X_26))) != meet(X_27,X_26)
| meet(X_26,X_27) != complement(join(complement(X_27),complement(X_26)))
| meet(X_26,X_27) = meet(X_27,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_26,X_27),complement(join(complement(X_27),complement(X_26)))) ),[1],$fot(meet(X_27,X_26))]]) ).
cnf(refute_0_62,plain,
( meet(X_26,X_27) != complement(join(complement(X_27),complement(X_26)))
| meet(X_26,X_27) = meet(X_27,X_26) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_27),complement(X_26))),meet(X_27,X_26)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
meet(X_26,X_27) = meet(X_27,X_26),
inference(resolve,[$cnf( $equal(meet(X_26,X_27),complement(join(complement(X_27),complement(X_26)))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
meet(X_34,B) = meet(B,X_34),
inference(subst,[],[refute_0_63:[bind(X_26,$fot(X_34)),bind(X_27,$fot(B))]]) ).
cnf(refute_0_65,plain,
( X_34 != join(meet(X_34,B),meet(X_34,complement(B)))
| meet(X_34,B) != meet(B,X_34)
| X_34 = join(meet(B,X_34),meet(X_34,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(X_34,join(meet(X_34,B),meet(X_34,complement(B)))) ),[1,0],$fot(meet(B,X_34))]]) ).
cnf(refute_0_66,plain,
( X_34 != join(meet(X_34,B),meet(X_34,complement(B)))
| X_34 = join(meet(B,X_34),meet(X_34,complement(B))) ),
inference(resolve,[$cnf( $equal(meet(X_34,B),meet(B,X_34)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
X_34 = join(meet(B,X_34),meet(X_34,complement(B))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,B),meet(X_34,complement(B)))) )],[refute_0_52,refute_0_66]) ).
cnf(refute_0_68,plain,
X_59 = join(meet(X_58,X_59),meet(X_59,complement(X_58))),
inference(subst,[],[refute_0_67:[bind(B,$fot(X_58)),bind(X_34,$fot(X_59))]]) ).
cnf(refute_0_69,plain,
meet(complement(X_58),X_59) = meet(X_59,complement(X_58)),
inference(subst,[],[refute_0_63:[bind(X_26,$fot(complement(X_58))),bind(X_27,$fot(X_59))]]) ).
cnf(refute_0_70,plain,
( meet(complement(X_58),X_59) != meet(X_59,complement(X_58))
| meet(X_59,complement(X_58)) = meet(complement(X_58),X_59) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_58),X_59))),bind(Y,$fot(meet(X_59,complement(X_58))))]]) ).
cnf(refute_0_71,plain,
meet(X_59,complement(X_58)) = meet(complement(X_58),X_59),
inference(resolve,[$cnf( $equal(meet(complement(X_58),X_59),meet(X_59,complement(X_58))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( X_59 != join(meet(X_58,X_59),meet(X_59,complement(X_58)))
| meet(X_59,complement(X_58)) != meet(complement(X_58),X_59)
| X_59 = join(meet(X_58,X_59),meet(complement(X_58),X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(X_59,join(meet(X_58,X_59),meet(X_59,complement(X_58)))) ),[1,1],$fot(meet(complement(X_58),X_59))]]) ).
cnf(refute_0_73,plain,
( X_59 != join(meet(X_58,X_59),meet(X_59,complement(X_58)))
| X_59 = join(meet(X_58,X_59),meet(complement(X_58),X_59)) ),
inference(resolve,[$cnf( $equal(meet(X_59,complement(X_58)),meet(complement(X_58),X_59)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
X_59 = join(meet(X_58,X_59),meet(complement(X_58),X_59)),
inference(resolve,[$cnf( $equal(X_59,join(meet(X_58,X_59),meet(X_59,complement(X_58)))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
complement(complement(X_69)) = join(meet(X_69,complement(complement(X_69))),meet(complement(X_69),complement(complement(X_69)))),
inference(subst,[],[refute_0_74:[bind(X_58,$fot(X_69)),bind(X_59,$fot(complement(complement(X_69))))]]) ).
cnf(refute_0_76,plain,
zero = meet(complement(X_69),complement(complement(X_69))),
inference(subst,[],[def_zero_13:[bind(A,$fot(complement(X_69)))]]) ).
cnf(refute_0_77,plain,
( zero != meet(complement(X_69),complement(complement(X_69)))
| meet(complement(X_69),complement(complement(X_69))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(complement(X_69),complement(complement(X_69)))))]]) ).
cnf(refute_0_78,plain,
meet(complement(X_69),complement(complement(X_69))) = zero,
inference(resolve,[$cnf( $equal(zero,meet(complement(X_69),complement(complement(X_69)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( complement(complement(X_69)) != join(meet(X_69,complement(complement(X_69))),meet(complement(X_69),complement(complement(X_69))))
| meet(complement(X_69),complement(complement(X_69))) != zero
| complement(complement(X_69)) = join(meet(X_69,complement(complement(X_69))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(X_69)),join(meet(X_69,complement(complement(X_69))),meet(complement(X_69),complement(complement(X_69))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_80,plain,
( complement(complement(X_69)) != join(meet(X_69,complement(complement(X_69))),meet(complement(X_69),complement(complement(X_69))))
| complement(complement(X_69)) = join(meet(X_69,complement(complement(X_69))),zero) ),
inference(resolve,[$cnf( $equal(meet(complement(X_69),complement(complement(X_69))),zero) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
complement(complement(X_69)) = join(meet(X_69,complement(complement(X_69))),zero),
inference(resolve,[$cnf( $equal(complement(complement(X_69)),join(meet(X_69,complement(complement(X_69))),meet(complement(X_69),complement(complement(X_69))))) )],[refute_0_75,refute_0_80]) ).
cnf(refute_0_82,plain,
X_34 = join(meet(X_34,complement(complement(X_34))),complement(join(complement(X_34),complement(complement(X_34))))),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_34)),bind(B,$fot(complement(complement(X_34))))]]) ).
cnf(refute_0_83,plain,
top = join(complement(X_34),complement(complement(X_34))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_34)))]]) ).
cnf(refute_0_84,plain,
( top != join(complement(X_34),complement(complement(X_34)))
| join(complement(X_34),complement(complement(X_34))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_34),complement(complement(X_34)))))]]) ).
cnf(refute_0_85,plain,
join(complement(X_34),complement(complement(X_34))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_34),complement(complement(X_34)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( X_34 != join(meet(X_34,complement(complement(X_34))),complement(join(complement(X_34),complement(complement(X_34)))))
| join(complement(X_34),complement(complement(X_34))) != top
| X_34 = join(meet(X_34,complement(complement(X_34))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_34,join(meet(X_34,complement(complement(X_34))),complement(join(complement(X_34),complement(complement(X_34)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_87,plain,
( X_34 != join(meet(X_34,complement(complement(X_34))),complement(join(complement(X_34),complement(complement(X_34)))))
| X_34 = join(meet(X_34,complement(complement(X_34))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_34),complement(complement(X_34))),top) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
X_34 = join(meet(X_34,complement(complement(X_34))),complement(top)),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,complement(complement(X_34))),complement(join(complement(X_34),complement(complement(X_34)))))) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
zero = meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_26),complement(X_27))))]]) ).
cnf(refute_0_90,plain,
( meet(X_26,X_27) != complement(join(complement(X_26),complement(X_27)))
| complement(join(complement(X_26),complement(X_27))) = meet(X_26,X_27) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_26,X_27))),bind(Y,$fot(complement(join(complement(X_26),complement(X_27)))))]]) ).
cnf(refute_0_91,plain,
complement(join(complement(X_26),complement(X_27))) = meet(X_26,X_27),
inference(resolve,[$cnf( $equal(meet(X_26,X_27),complement(join(complement(X_26),complement(X_27)))) )],[refute_0_53,refute_0_90]) ).
cnf(refute_0_92,plain,
( complement(join(complement(X_26),complement(X_27))) != meet(X_26,X_27)
| zero != meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| zero = meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) ),[1,1],$fot(meet(X_26,X_27))]]) ).
cnf(refute_0_93,plain,
( zero != meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| zero = meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_26),complement(X_27))),meet(X_26,X_27)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
zero = meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) )],[refute_0_89,refute_0_93]) ).
cnf(refute_0_95,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_96,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_95]) ).
cnf(refute_0_97,plain,
join(meet(X_26,X_27),complement(meet(X_26,X_27))) = top,
inference(subst,[],[refute_0_96:[bind(A,$fot(meet(X_26,X_27)))]]) ).
cnf(refute_0_98,plain,
complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))))]]) ).
cnf(refute_0_99,plain,
( complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) != complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))
| join(meet(X_26,X_27),complement(meet(X_26,X_27))) != top
| complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_100,plain,
( join(meet(X_26,X_27),complement(meet(X_26,X_27))) != top
| complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_26,X_27),complement(meet(X_26,X_27))),top) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
meet(join(complement(X_26),complement(X_27)),B) = complement(join(complement(join(complement(X_26),complement(X_27))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_26),complement(X_27))))]]) ).
cnf(refute_0_103,plain,
( complement(join(complement(X_26),complement(X_27))) != meet(X_26,X_27)
| meet(join(complement(X_26),complement(X_27)),B) != complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))
| meet(join(complement(X_26),complement(X_27)),B) = complement(join(meet(X_26,X_27),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),B),complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))) ),[1,0,0],$fot(meet(X_26,X_27))]]) ).
cnf(refute_0_104,plain,
( meet(join(complement(X_26),complement(X_27)),B) != complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))
| meet(join(complement(X_26),complement(X_27)),B) = complement(join(meet(X_26,X_27),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_26),complement(X_27))),meet(X_26,X_27)) )],[refute_0_91,refute_0_103]) ).
cnf(refute_0_105,plain,
meet(join(complement(X_26),complement(X_27)),B) = complement(join(meet(X_26,X_27),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),B),complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))) )],[refute_0_102,refute_0_104]) ).
cnf(refute_0_106,plain,
meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),
inference(subst,[],[refute_0_105:[bind(B,$fot(meet(X_26,X_27)))]]) ).
cnf(refute_0_107,plain,
( complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) != complement(top)
| meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) != complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))
| meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(top) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)))),bind(Y,$fot(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_108,plain,
( complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) != complement(top)
| meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),complement(top)) )],[refute_0_101,refute_0_108]) ).
cnf(refute_0_110,plain,
( meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) != complement(top)
| zero != meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_111,plain,
( zero != meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),complement(top)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) )],[refute_0_94,refute_0_111]) ).
cnf(refute_0_113,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_114,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
join(complement(top),meet(X_34,complement(complement(X_34)))) = join(complement(top),meet(X_34,complement(complement(X_34)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_34,complement(complement(X_34)))))]]) ).
cnf(refute_0_116,plain,
( complement(top) != zero
| join(complement(top),meet(X_34,complement(complement(X_34)))) != join(complement(top),meet(X_34,complement(complement(X_34))))
| join(complement(top),meet(X_34,complement(complement(X_34)))) = join(zero,meet(X_34,complement(complement(X_34)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_34,complement(complement(X_34)))),join(complement(top),meet(X_34,complement(complement(X_34))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_117,plain,
( complement(top) != zero
| join(complement(top),meet(X_34,complement(complement(X_34)))) = join(zero,meet(X_34,complement(complement(X_34)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_34,complement(complement(X_34)))),join(complement(top),meet(X_34,complement(complement(X_34))))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
join(complement(top),meet(X_34,complement(complement(X_34)))) = join(zero,meet(X_34,complement(complement(X_34)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
join(meet(X_34,complement(complement(X_34))),complement(top)) = join(complement(top),meet(X_34,complement(complement(X_34)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_34,complement(complement(X_34)))))]]) ).
cnf(refute_0_120,plain,
( join(complement(top),meet(X_34,complement(complement(X_34)))) != join(zero,meet(X_34,complement(complement(X_34))))
| join(meet(X_34,complement(complement(X_34))),complement(top)) != join(complement(top),meet(X_34,complement(complement(X_34))))
| join(meet(X_34,complement(complement(X_34))),complement(top)) = join(zero,meet(X_34,complement(complement(X_34)))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(X_34,complement(complement(X_34))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_34,complement(complement(X_34)))))),bind(Z,$fot(join(zero,meet(X_34,complement(complement(X_34))))))]]) ).
cnf(refute_0_121,plain,
( join(complement(top),meet(X_34,complement(complement(X_34)))) != join(zero,meet(X_34,complement(complement(X_34))))
| join(meet(X_34,complement(complement(X_34))),complement(top)) = join(zero,meet(X_34,complement(complement(X_34)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,complement(complement(X_34))),complement(top)),join(complement(top),meet(X_34,complement(complement(X_34))))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
join(meet(X_34,complement(complement(X_34))),complement(top)) = join(zero,meet(X_34,complement(complement(X_34)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_34,complement(complement(X_34)))),join(zero,meet(X_34,complement(complement(X_34))))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
( X_34 != join(meet(X_34,complement(complement(X_34))),complement(top))
| join(meet(X_34,complement(complement(X_34))),complement(top)) != join(zero,meet(X_34,complement(complement(X_34))))
| X_34 = join(zero,meet(X_34,complement(complement(X_34)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,join(zero,meet(X_34,complement(complement(X_34))))) ),[0],$fot(join(meet(X_34,complement(complement(X_34))),complement(top)))]]) ).
cnf(refute_0_124,plain,
( X_34 != join(meet(X_34,complement(complement(X_34))),complement(top))
| X_34 = join(zero,meet(X_34,complement(complement(X_34)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,complement(complement(X_34))),complement(top)),join(zero,meet(X_34,complement(complement(X_34))))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
X_34 = join(zero,meet(X_34,complement(complement(X_34)))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,complement(complement(X_34))),complement(top))) )],[refute_0_88,refute_0_124]) ).
cnf(refute_0_126,plain,
( X_34 != join(zero,meet(X_34,complement(complement(X_34))))
| join(zero,meet(X_34,complement(complement(X_34)))) = X_34 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_34)),bind(Y,$fot(join(zero,meet(X_34,complement(complement(X_34))))))]]) ).
cnf(refute_0_127,plain,
join(zero,meet(X_34,complement(complement(X_34)))) = X_34,
inference(resolve,[$cnf( $equal(X_34,join(zero,meet(X_34,complement(complement(X_34))))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
join(zero,meet(X_69,complement(complement(X_69)))) = X_69,
inference(subst,[],[refute_0_127:[bind(X_34,$fot(X_69))]]) ).
cnf(refute_0_129,plain,
join(meet(X_69,complement(complement(X_69))),zero) = join(zero,meet(X_69,complement(complement(X_69)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(meet(X_69,complement(complement(X_69)))))]]) ).
cnf(refute_0_130,plain,
( join(meet(X_69,complement(complement(X_69))),zero) != join(zero,meet(X_69,complement(complement(X_69))))
| join(zero,meet(X_69,complement(complement(X_69)))) != X_69
| join(meet(X_69,complement(complement(X_69))),zero) = X_69 ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(X_69,complement(complement(X_69))),zero))),bind(Y,$fot(join(zero,meet(X_69,complement(complement(X_69)))))),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_131,plain,
( join(zero,meet(X_69,complement(complement(X_69)))) != X_69
| join(meet(X_69,complement(complement(X_69))),zero) = X_69 ),
inference(resolve,[$cnf( $equal(join(meet(X_69,complement(complement(X_69))),zero),join(zero,meet(X_69,complement(complement(X_69))))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
join(meet(X_69,complement(complement(X_69))),zero) = X_69,
inference(resolve,[$cnf( $equal(join(zero,meet(X_69,complement(complement(X_69)))),X_69) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( complement(complement(X_69)) != join(meet(X_69,complement(complement(X_69))),zero)
| join(meet(X_69,complement(complement(X_69))),zero) != X_69
| complement(complement(X_69)) = X_69 ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(complement(X_69)),X_69) ),[0],$fot(join(meet(X_69,complement(complement(X_69))),zero))]]) ).
cnf(refute_0_134,plain,
( complement(complement(X_69)) != join(meet(X_69,complement(complement(X_69))),zero)
| complement(complement(X_69)) = X_69 ),
inference(resolve,[$cnf( $equal(join(meet(X_69,complement(complement(X_69))),zero),X_69) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
complement(complement(X_69)) = X_69,
inference(resolve,[$cnf( $equal(complement(complement(X_69)),join(meet(X_69,complement(complement(X_69))),zero)) )],[refute_0_81,refute_0_134]) ).
cnf(refute_0_136,plain,
( complement(complement(X_69)) != X_69
| join(complement(complement(X_69)),composition(X_134,complement(composition(converse(X_134),complement(X_69))))) != complement(complement(X_69))
| join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) = complement(complement(X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_69)),composition(X_134,complement(composition(converse(X_134),complement(X_69))))),complement(complement(X_69))) ),[0,0],$fot(X_69)]]) ).
cnf(refute_0_137,plain,
( join(complement(complement(X_69)),composition(X_134,complement(composition(converse(X_134),complement(X_69))))) != complement(complement(X_69))
| join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) = complement(complement(X_69)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_69)),X_69) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) = complement(complement(X_69)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_69)),composition(X_134,complement(composition(converse(X_134),complement(X_69))))),complement(complement(X_69))) )],[refute_0_22,refute_0_137]) ).
cnf(refute_0_139,plain,
( complement(complement(X_69)) != X_69
| join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) != complement(complement(X_69))
| join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) = X_69 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))),complement(complement(X_69))) ),[1],$fot(X_69)]]) ).
cnf(refute_0_140,plain,
( join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) != complement(complement(X_69))
| join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) = X_69 ),
inference(resolve,[$cnf( $equal(complement(complement(X_69)),X_69) )],[refute_0_135,refute_0_139]) ).
cnf(refute_0_141,plain,
join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))) = X_69,
inference(resolve,[$cnf( $equal(join(X_69,composition(X_134,complement(composition(converse(X_134),complement(X_69))))),complement(complement(X_69))) )],[refute_0_138,refute_0_140]) ).
cnf(refute_0_142,plain,
join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = converse(A),
inference(subst,[],[refute_0_141:[bind(X_134,$fot(X_136)),bind(X_69,$fot(converse(A)))]]) ).
cnf(refute_0_143,plain,
( converse(join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) != join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))
| join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) != converse(A)
| converse(converse(A)) = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))) ),[0,0],$fot(converse(A))]]) ).
cnf(refute_0_144,plain,
( converse(join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) != join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))
| converse(converse(A)) = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) ),
inference(resolve,[$cnf( $equal(join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))),converse(A)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
converse(converse(A)) = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),
inference(resolve,[$cnf( $equal(converse(join(converse(A),composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))) )],[refute_0_13,refute_0_144]) ).
cnf(refute_0_146,plain,
( converse(converse(A)) != A
| converse(converse(A)) != join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))
| A = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(A)),join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))) ),[0],$fot(A)]]) ).
cnf(refute_0_147,plain,
( converse(converse(A)) != join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))
| A = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_146]) ).
cnf(refute_0_148,plain,
A = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),
inference(resolve,[$cnf( $equal(converse(converse(A)),join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))) )],[refute_0_145,refute_0_147]) ).
cnf(refute_0_149,plain,
converse(composition(X_17,converse(A))) = composition(converse(converse(A)),converse(X_17)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_17)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_150,plain,
( converse(composition(X_17,converse(A))) != composition(converse(converse(A)),converse(X_17))
| converse(converse(A)) != A
| converse(composition(X_17,converse(A))) = composition(A,converse(X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_17,converse(A))),composition(converse(converse(A)),converse(X_17))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_151,plain,
( converse(composition(X_17,converse(A))) != composition(converse(converse(A)),converse(X_17))
| converse(composition(X_17,converse(A))) = composition(A,converse(X_17)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_150]) ).
cnf(refute_0_152,plain,
converse(composition(X_17,converse(A))) = composition(A,converse(X_17)),
inference(resolve,[$cnf( $equal(converse(composition(X_17,converse(A))),composition(converse(converse(A)),converse(X_17))) )],[refute_0_149,refute_0_151]) ).
cnf(refute_0_153,plain,
converse(composition(X_17,converse(complement(X_381)))) = composition(complement(X_381),converse(X_17)),
inference(subst,[],[refute_0_152:[bind(A,$fot(complement(X_381)))]]) ).
cnf(refute_0_154,plain,
join(B,join(B,C)) = join(join(B,B),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(B))]]) ).
cnf(refute_0_155,plain,
join(X_137,composition(one,complement(composition(converse(one),complement(X_137))))) = X_137,
inference(subst,[],[refute_0_141:[bind(X_134,$fot(one)),bind(X_69,$fot(X_137))]]) ).
cnf(refute_0_156,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_157,plain,
converse(composition(converse(A),X_18)) = composition(converse(X_18),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_18))]]) ).
cnf(refute_0_158,plain,
( converse(composition(converse(A),X_18)) != composition(converse(X_18),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_18)) = composition(converse(X_18),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_18)),composition(converse(X_18),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_159,plain,
( converse(composition(converse(A),X_18)) != composition(converse(X_18),converse(converse(A)))
| converse(composition(converse(A),X_18)) = composition(converse(X_18),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_158]) ).
cnf(refute_0_160,plain,
converse(composition(converse(A),X_18)) = composition(converse(X_18),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_18)),composition(converse(X_18),converse(converse(A)))) )],[refute_0_157,refute_0_159]) ).
cnf(refute_0_161,plain,
converse(composition(converse(X_22),one)) = composition(converse(one),X_22),
inference(subst,[],[refute_0_160:[bind(A,$fot(X_22)),bind(X_18,$fot(one))]]) ).
cnf(refute_0_162,plain,
composition(converse(X_22),one) = converse(X_22),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_22)))]]) ).
cnf(refute_0_163,plain,
( composition(converse(X_22),one) != converse(X_22)
| converse(composition(converse(X_22),one)) != composition(converse(one),X_22)
| converse(converse(X_22)) = composition(converse(one),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_22),one)),composition(converse(one),X_22)) ),[0,0],$fot(converse(X_22))]]) ).
cnf(refute_0_164,plain,
( converse(composition(converse(X_22),one)) != composition(converse(one),X_22)
| converse(converse(X_22)) = composition(converse(one),X_22) ),
inference(resolve,[$cnf( $equal(composition(converse(X_22),one),converse(X_22)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
converse(converse(X_22)) = composition(converse(one),X_22),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_22),one)),composition(converse(one),X_22)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
converse(converse(X_22)) = X_22,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_167,plain,
( converse(converse(X_22)) != X_22
| converse(converse(X_22)) != composition(converse(one),X_22)
| X_22 = composition(converse(one),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_22)),composition(converse(one),X_22)) ),[0],$fot(X_22)]]) ).
cnf(refute_0_168,plain,
( converse(converse(X_22)) != composition(converse(one),X_22)
| X_22 = composition(converse(one),X_22) ),
inference(resolve,[$cnf( $equal(converse(converse(X_22)),X_22) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
X_22 = composition(converse(one),X_22),
inference(resolve,[$cnf( $equal(converse(converse(X_22)),composition(converse(one),X_22)) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_169:[bind(X_22,$fot(one))]]) ).
cnf(refute_0_171,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_172,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_174,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_156,refute_0_174]) ).
cnf(refute_0_176,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_177,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( converse(one) != one
| join(X_137,composition(one,complement(composition(converse(one),complement(X_137))))) != X_137
| join(X_137,composition(one,complement(composition(one,complement(X_137))))) = X_137 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_137,composition(one,complement(composition(converse(one),complement(X_137))))),X_137) ),[0,1,1,0,0],$fot(one)]]) ).
cnf(refute_0_179,plain,
( join(X_137,composition(one,complement(composition(converse(one),complement(X_137))))) != X_137
| join(X_137,composition(one,complement(composition(one,complement(X_137))))) = X_137 ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
join(X_137,composition(one,complement(composition(one,complement(X_137))))) = X_137,
inference(resolve,[$cnf( $equal(join(X_137,composition(one,complement(composition(converse(one),complement(X_137))))),X_137) )],[refute_0_155,refute_0_179]) ).
cnf(refute_0_181,plain,
complement(complement(X_137)) = X_137,
inference(subst,[],[refute_0_135:[bind(X_69,$fot(X_137))]]) ).
cnf(refute_0_182,plain,
composition(converse(one),X_22) = composition(converse(one),X_22),
introduced(tautology,[refl,[$fot(composition(converse(one),X_22))]]) ).
cnf(refute_0_183,plain,
( composition(converse(one),X_22) != composition(converse(one),X_22)
| converse(one) != one
| composition(converse(one),X_22) = composition(one,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_22),composition(converse(one),X_22)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_184,plain,
( converse(one) != one
| composition(converse(one),X_22) = composition(one,X_22) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_22),composition(converse(one),X_22)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
composition(converse(one),X_22) = composition(one,X_22),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_177,refute_0_184]) ).
cnf(refute_0_186,plain,
( X_22 != composition(converse(one),X_22)
| composition(converse(one),X_22) != composition(one,X_22)
| X_22 = composition(one,X_22) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_22,composition(one,X_22)) ),[0],$fot(composition(converse(one),X_22))]]) ).
cnf(refute_0_187,plain,
( X_22 != composition(converse(one),X_22)
| X_22 = composition(one,X_22) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_22),composition(one,X_22)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
X_22 = composition(one,X_22),
inference(resolve,[$cnf( $equal(X_22,composition(converse(one),X_22)) )],[refute_0_169,refute_0_187]) ).
cnf(refute_0_189,plain,
( X_22 != composition(one,X_22)
| composition(one,X_22) = X_22 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_22)),bind(Y,$fot(composition(one,X_22)))]]) ).
cnf(refute_0_190,plain,
composition(one,X_22) = X_22,
inference(resolve,[$cnf( $equal(X_22,composition(one,X_22)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
composition(one,complement(X_137)) = complement(X_137),
inference(subst,[],[refute_0_190:[bind(X_22,$fot(complement(X_137)))]]) ).
cnf(refute_0_192,plain,
complement(composition(one,complement(X_137))) = complement(composition(one,complement(X_137))),
introduced(tautology,[refl,[$fot(complement(composition(one,complement(X_137))))]]) ).
cnf(refute_0_193,plain,
( complement(composition(one,complement(X_137))) != complement(composition(one,complement(X_137)))
| composition(one,complement(X_137)) != complement(X_137)
| complement(composition(one,complement(X_137))) = complement(complement(X_137)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(one,complement(X_137))),complement(composition(one,complement(X_137)))) ),[1,0],$fot(complement(X_137))]]) ).
cnf(refute_0_194,plain,
( composition(one,complement(X_137)) != complement(X_137)
| complement(composition(one,complement(X_137))) = complement(complement(X_137)) ),
inference(resolve,[$cnf( $equal(complement(composition(one,complement(X_137))),complement(composition(one,complement(X_137)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
complement(composition(one,complement(X_137))) = complement(complement(X_137)),
inference(resolve,[$cnf( $equal(composition(one,complement(X_137)),complement(X_137)) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
( complement(complement(X_137)) != X_137
| complement(composition(one,complement(X_137))) != complement(complement(X_137))
| complement(composition(one,complement(X_137))) = X_137 ),
inference(subst,[],[refute_0_35:[bind(X,$fot(complement(composition(one,complement(X_137))))),bind(Y,$fot(complement(complement(X_137)))),bind(Z,$fot(X_137))]]) ).
cnf(refute_0_197,plain,
( complement(complement(X_137)) != X_137
| complement(composition(one,complement(X_137))) = X_137 ),
inference(resolve,[$cnf( $equal(complement(composition(one,complement(X_137))),complement(complement(X_137))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
complement(composition(one,complement(X_137))) = X_137,
inference(resolve,[$cnf( $equal(complement(complement(X_137)),X_137) )],[refute_0_181,refute_0_197]) ).
cnf(refute_0_199,plain,
composition(one,complement(composition(one,complement(X_137)))) = complement(composition(one,complement(X_137))),
inference(subst,[],[refute_0_190:[bind(X_22,$fot(complement(composition(one,complement(X_137)))))]]) ).
cnf(refute_0_200,plain,
( complement(composition(one,complement(X_137))) != X_137
| composition(one,complement(composition(one,complement(X_137)))) != complement(composition(one,complement(X_137)))
| composition(one,complement(composition(one,complement(X_137)))) = X_137 ),
inference(subst,[],[refute_0_35:[bind(X,$fot(composition(one,complement(composition(one,complement(X_137)))))),bind(Y,$fot(complement(composition(one,complement(X_137))))),bind(Z,$fot(X_137))]]) ).
cnf(refute_0_201,plain,
( complement(composition(one,complement(X_137))) != X_137
| composition(one,complement(composition(one,complement(X_137)))) = X_137 ),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,complement(X_137)))),complement(composition(one,complement(X_137)))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
composition(one,complement(composition(one,complement(X_137)))) = X_137,
inference(resolve,[$cnf( $equal(complement(composition(one,complement(X_137))),X_137) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
join(X_137,composition(one,complement(composition(one,complement(X_137))))) = join(X_137,composition(one,complement(composition(one,complement(X_137))))),
introduced(tautology,[refl,[$fot(join(X_137,composition(one,complement(composition(one,complement(X_137))))))]]) ).
cnf(refute_0_204,plain,
( composition(one,complement(composition(one,complement(X_137)))) != X_137
| join(X_137,composition(one,complement(composition(one,complement(X_137))))) != join(X_137,composition(one,complement(composition(one,complement(X_137)))))
| join(X_137,composition(one,complement(composition(one,complement(X_137))))) = join(X_137,X_137) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_137,composition(one,complement(composition(one,complement(X_137))))),join(X_137,composition(one,complement(composition(one,complement(X_137)))))) ),[1,1],$fot(X_137)]]) ).
cnf(refute_0_205,plain,
( composition(one,complement(composition(one,complement(X_137)))) != X_137
| join(X_137,composition(one,complement(composition(one,complement(X_137))))) = join(X_137,X_137) ),
inference(resolve,[$cnf( $equal(join(X_137,composition(one,complement(composition(one,complement(X_137))))),join(X_137,composition(one,complement(composition(one,complement(X_137)))))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
join(X_137,composition(one,complement(composition(one,complement(X_137))))) = join(X_137,X_137),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,complement(X_137)))),X_137) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
( join(X_137,composition(one,complement(composition(one,complement(X_137))))) != X_137
| join(X_137,composition(one,complement(composition(one,complement(X_137))))) != join(X_137,X_137)
| join(X_137,X_137) = X_137 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_137,composition(one,complement(composition(one,complement(X_137))))),X_137) ),[0],$fot(join(X_137,X_137))]]) ).
cnf(refute_0_208,plain,
( join(X_137,composition(one,complement(composition(one,complement(X_137))))) != X_137
| join(X_137,X_137) = X_137 ),
inference(resolve,[$cnf( $equal(join(X_137,composition(one,complement(composition(one,complement(X_137))))),join(X_137,X_137)) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
join(X_137,X_137) = X_137,
inference(resolve,[$cnf( $equal(join(X_137,composition(one,complement(composition(one,complement(X_137))))),X_137) )],[refute_0_180,refute_0_208]) ).
cnf(refute_0_210,plain,
join(B,B) = B,
inference(subst,[],[refute_0_209:[bind(X_137,$fot(B))]]) ).
cnf(refute_0_211,plain,
( join(B,B) != B
| join(B,join(B,C)) != join(join(B,B),C)
| join(B,join(B,C)) = join(B,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(B,C)),join(join(B,B),C)) ),[1,0],$fot(B)]]) ).
cnf(refute_0_212,plain,
( join(B,join(B,C)) != join(join(B,B),C)
| join(B,join(B,C)) = join(B,C) ),
inference(resolve,[$cnf( $equal(join(B,B),B) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
join(B,join(B,C)) = join(B,C),
inference(resolve,[$cnf( $equal(join(B,join(B,C)),join(join(B,B),C)) )],[refute_0_154,refute_0_212]) ).
cnf(refute_0_214,plain,
join(meet(X_58,X_59),join(meet(X_58,X_59),meet(complement(X_58),X_59))) = join(meet(X_58,X_59),meet(complement(X_58),X_59)),
inference(subst,[],[refute_0_213:[bind(B,$fot(meet(X_58,X_59))),bind(C,$fot(meet(complement(X_58),X_59)))]]) ).
cnf(refute_0_215,plain,
( X_59 != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(meet(X_58,X_59),meet(complement(X_58),X_59)) = X_59 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_59)),bind(Y,$fot(join(meet(X_58,X_59),meet(complement(X_58),X_59))))]]) ).
cnf(refute_0_216,plain,
join(meet(X_58,X_59),meet(complement(X_58),X_59)) = X_59,
inference(resolve,[$cnf( $equal(X_59,join(meet(X_58,X_59),meet(complement(X_58),X_59))) )],[refute_0_74,refute_0_215]) ).
cnf(refute_0_217,plain,
( join(meet(X_58,X_59),join(meet(X_58,X_59),meet(complement(X_58),X_59))) != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(meet(X_58,X_59),meet(complement(X_58),X_59)) != X_59
| join(meet(X_58,X_59),X_59) = join(meet(X_58,X_59),meet(complement(X_58),X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_58,X_59),join(meet(X_58,X_59),meet(complement(X_58),X_59))),join(meet(X_58,X_59),meet(complement(X_58),X_59))) ),[0,1],$fot(X_59)]]) ).
cnf(refute_0_218,plain,
( join(meet(X_58,X_59),join(meet(X_58,X_59),meet(complement(X_58),X_59))) != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(meet(X_58,X_59),X_59) = join(meet(X_58,X_59),meet(complement(X_58),X_59)) ),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_59) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
join(meet(X_58,X_59),X_59) = join(meet(X_58,X_59),meet(complement(X_58),X_59)),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_59),join(meet(X_58,X_59),meet(complement(X_58),X_59))),join(meet(X_58,X_59),meet(complement(X_58),X_59))) )],[refute_0_214,refute_0_218]) ).
cnf(refute_0_220,plain,
join(meet(X_58,X_59),X_59) = join(X_59,meet(X_58,X_59)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_59)),bind(B,$fot(meet(X_58,X_59)))]]) ).
cnf(refute_0_221,plain,
( join(meet(X_58,X_59),X_59) != join(X_59,meet(X_58,X_59))
| join(meet(X_58,X_59),X_59) != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(X_59,meet(X_58,X_59)) = join(meet(X_58,X_59),meet(complement(X_58),X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_58,X_59),X_59),join(meet(X_58,X_59),meet(complement(X_58),X_59))) ),[0],$fot(join(X_59,meet(X_58,X_59)))]]) ).
cnf(refute_0_222,plain,
( join(meet(X_58,X_59),X_59) != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(X_59,meet(X_58,X_59)) = join(meet(X_58,X_59),meet(complement(X_58),X_59)) ),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_59),X_59),join(X_59,meet(X_58,X_59))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
( join(X_59,meet(X_58,X_59)) != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(meet(X_58,X_59),meet(complement(X_58),X_59)) != X_59
| join(X_59,meet(X_58,X_59)) = X_59 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_59,meet(X_58,X_59)),X_59) ),[0],$fot(join(meet(X_58,X_59),meet(complement(X_58),X_59)))]]) ).
cnf(refute_0_224,plain,
( join(X_59,meet(X_58,X_59)) != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(X_59,meet(X_58,X_59)) = X_59 ),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_59) )],[refute_0_216,refute_0_223]) ).
cnf(refute_0_225,plain,
( join(meet(X_58,X_59),X_59) != join(meet(X_58,X_59),meet(complement(X_58),X_59))
| join(X_59,meet(X_58,X_59)) = X_59 ),
inference(resolve,[$cnf( $equal(join(X_59,meet(X_58,X_59)),join(meet(X_58,X_59),meet(complement(X_58),X_59))) )],[refute_0_222,refute_0_224]) ).
cnf(refute_0_226,plain,
join(X_59,meet(X_58,X_59)) = X_59,
inference(resolve,[$cnf( $equal(join(meet(X_58,X_59),X_59),join(meet(X_58,X_59),meet(complement(X_58),X_59))) )],[refute_0_219,refute_0_225]) ).
cnf(refute_0_227,plain,
join(converse(complement(X_380)),meet(converse(X_380),converse(complement(X_380)))) = converse(complement(X_380)),
inference(subst,[],[refute_0_226:[bind(X_58,$fot(converse(X_380))),bind(X_59,$fot(converse(complement(X_380))))]]) ).
cnf(refute_0_228,plain,
X_34 = join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(join(complement(X_34),converse(complement(converse(complement(X_34))))))),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_34)),bind(B,$fot(converse(complement(converse(complement(X_34))))))]]) ).
cnf(refute_0_229,plain,
converse(join(converse(X_14),complement(converse(X_14)))) = join(X_14,converse(complement(converse(X_14)))),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_14)),bind(X_11,$fot(complement(converse(X_14))))]]) ).
cnf(refute_0_230,plain,
top = join(converse(X_14),complement(converse(X_14))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_14)))]]) ).
cnf(refute_0_231,plain,
( top != join(converse(X_14),complement(converse(X_14)))
| join(converse(X_14),complement(converse(X_14))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_14),complement(converse(X_14)))))]]) ).
cnf(refute_0_232,plain,
join(converse(X_14),complement(converse(X_14))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_14),complement(converse(X_14)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( converse(join(converse(X_14),complement(converse(X_14)))) != join(X_14,converse(complement(converse(X_14))))
| join(converse(X_14),complement(converse(X_14))) != top
| converse(top) = join(X_14,converse(complement(converse(X_14)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_14),complement(converse(X_14)))),join(X_14,converse(complement(converse(X_14))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_234,plain,
( converse(join(converse(X_14),complement(converse(X_14)))) != join(X_14,converse(complement(converse(X_14))))
| converse(top) = join(X_14,converse(complement(converse(X_14)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_14),complement(converse(X_14))),top) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
converse(top) = join(X_14,converse(complement(converse(X_14)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_14),complement(converse(X_14)))),join(X_14,converse(complement(converse(X_14))))) )],[refute_0_229,refute_0_234]) ).
cnf(refute_0_236,plain,
converse(top) = join(complement(X_34),converse(complement(converse(complement(X_34))))),
inference(subst,[],[refute_0_235:[bind(X_14,$fot(complement(X_34)))]]) ).
cnf(refute_0_237,plain,
( converse(top) != join(complement(X_34),converse(complement(converse(complement(X_34)))))
| join(complement(X_34),converse(complement(converse(complement(X_34))))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_34),converse(complement(converse(complement(X_34)))))))]]) ).
cnf(refute_0_238,plain,
join(complement(X_34),converse(complement(converse(complement(X_34))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_34),converse(complement(converse(complement(X_34)))))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
( X_34 != join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(join(complement(X_34),converse(complement(converse(complement(X_34)))))))
| join(complement(X_34),converse(complement(converse(complement(X_34))))) != converse(top)
| X_34 = join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_34,join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(join(complement(X_34),converse(complement(converse(complement(X_34)))))))) ),[1,1,0],$fot(converse(top))]]) ).
cnf(refute_0_240,plain,
( X_34 != join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(join(complement(X_34),converse(complement(converse(complement(X_34)))))))
| X_34 = join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(complement(X_34),converse(complement(converse(complement(X_34))))),converse(top)) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
X_34 = join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(join(complement(X_34),converse(complement(converse(complement(X_34)))))))) )],[refute_0_228,refute_0_240]) ).
cnf(refute_0_242,plain,
join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top))) = join(complement(converse(top)),meet(X_34,converse(complement(converse(complement(X_34)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(converse(top)))),bind(B,$fot(meet(X_34,converse(complement(converse(complement(X_34)))))))]]) ).
cnf(refute_0_243,plain,
( X_34 != join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top)))
| join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top))) != join(complement(converse(top)),meet(X_34,converse(complement(converse(complement(X_34))))))
| X_34 = join(complement(converse(top)),meet(X_34,converse(complement(converse(complement(X_34)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,join(complement(converse(top)),meet(X_34,converse(complement(converse(complement(X_34))))))) ),[0],$fot(join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top))))]]) ).
cnf(refute_0_244,plain,
( X_34 != join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top)))
| X_34 = join(complement(converse(top)),meet(X_34,converse(complement(converse(complement(X_34)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top))),join(complement(converse(top)),meet(X_34,converse(complement(converse(complement(X_34))))))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
X_34 = join(complement(converse(top)),meet(X_34,converse(complement(converse(complement(X_34)))))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,converse(complement(converse(complement(X_34))))),complement(converse(top)))) )],[refute_0_241,refute_0_244]) ).
cnf(refute_0_246,plain,
complement(X_72) = join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(complement(complement(X_72))))))),
inference(subst,[],[refute_0_245:[bind(X_34,$fot(complement(X_72)))]]) ).
cnf(refute_0_247,plain,
complement(complement(X_72)) = X_72,
inference(subst,[],[refute_0_135:[bind(X_69,$fot(X_72))]]) ).
cnf(refute_0_248,plain,
( complement(X_72) != join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(complement(complement(X_72)))))))
| complement(complement(X_72)) != X_72
| complement(X_72) = join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_72),join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(complement(complement(X_72)))))))) ),[1,1,1,0,0,0],$fot(X_72)]]) ).
cnf(refute_0_249,plain,
( complement(X_72) != join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(complement(complement(X_72)))))))
| complement(X_72) = join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_72)),X_72) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
complement(X_72) = join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))),
inference(resolve,[$cnf( $equal(complement(X_72),join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(complement(complement(X_72)))))))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
join(zero,join(zero,X_82)) = join(join(zero,zero),X_82),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(zero)),bind(C,$fot(X_82))]]) ).
cnf(refute_0_252,plain,
join(complement(top),composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(subst,[],[refute_0_17:[bind(B,$fot(top))]]) ).
cnf(refute_0_253,plain,
( complement(top) != zero
| join(complement(top),composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(A),complement(composition(A,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_254,plain,
( join(complement(top),composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_253]) ).
cnf(refute_0_255,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(A),complement(composition(A,top)))),complement(top)) )],[refute_0_252,refute_0_254]) ).
cnf(refute_0_256,plain,
( complement(top) != zero
| join(zero,composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_257,plain,
( join(zero,composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_256]) ).
cnf(refute_0_258,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),complement(top)) )],[refute_0_255,refute_0_257]) ).
cnf(refute_0_259,plain,
join(zero,composition(converse(one),complement(composition(one,top)))) = zero,
inference(subst,[],[refute_0_258:[bind(A,$fot(one))]]) ).
cnf(refute_0_260,plain,
top = composition(one,top),
inference(subst,[],[refute_0_188:[bind(X_22,$fot(top))]]) ).
cnf(refute_0_261,plain,
( top != composition(one,top)
| composition(one,top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(composition(one,top)))]]) ).
cnf(refute_0_262,plain,
composition(one,top) = top,
inference(resolve,[$cnf( $equal(top,composition(one,top)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( composition(one,top) != top
| join(zero,composition(converse(one),complement(composition(one,top)))) != zero
| join(zero,composition(converse(one),complement(top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(one),complement(composition(one,top)))),zero) ),[0,1,1,0],$fot(top)]]) ).
cnf(refute_0_264,plain,
( join(zero,composition(converse(one),complement(composition(one,top)))) != zero
| join(zero,composition(converse(one),complement(top))) = zero ),
inference(resolve,[$cnf( $equal(composition(one,top),top) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
join(zero,composition(converse(one),complement(top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(one),complement(composition(one,top)))),zero) )],[refute_0_259,refute_0_264]) ).
cnf(refute_0_266,plain,
composition(one,zero) = zero,
inference(subst,[],[refute_0_190:[bind(X_22,$fot(zero))]]) ).
cnf(refute_0_267,plain,
composition(one,complement(top)) = composition(one,complement(top)),
introduced(tautology,[refl,[$fot(composition(one,complement(top)))]]) ).
cnf(refute_0_268,plain,
( complement(top) != zero
| composition(one,complement(top)) != composition(one,complement(top))
| composition(one,complement(top)) = composition(one,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(one,complement(top)),composition(one,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_269,plain,
( complement(top) != zero
| composition(one,complement(top)) = composition(one,zero) ),
inference(resolve,[$cnf( $equal(composition(one,complement(top)),composition(one,complement(top))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
composition(one,complement(top)) = composition(one,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_269]) ).
cnf(refute_0_271,plain,
composition(converse(one),complement(top)) = composition(converse(one),complement(top)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(top)))]]) ).
cnf(refute_0_272,plain,
( composition(converse(one),complement(top)) != composition(converse(one),complement(top))
| converse(one) != one
| composition(converse(one),complement(top)) = composition(one,complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(top)),composition(converse(one),complement(top))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_273,plain,
( converse(one) != one
| composition(converse(one),complement(top)) = composition(one,complement(top)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(top)),composition(converse(one),complement(top))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
composition(converse(one),complement(top)) = composition(one,complement(top)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_177,refute_0_273]) ).
cnf(refute_0_275,plain,
( composition(converse(one),complement(top)) != composition(one,complement(top))
| composition(one,complement(top)) != composition(one,zero)
| composition(converse(one),complement(top)) = composition(one,zero) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(composition(converse(one),complement(top)))),bind(Y,$fot(composition(one,complement(top)))),bind(Z,$fot(composition(one,zero)))]]) ).
cnf(refute_0_276,plain,
( composition(one,complement(top)) != composition(one,zero)
| composition(converse(one),complement(top)) = composition(one,zero) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(top)),composition(one,complement(top))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
composition(converse(one),complement(top)) = composition(one,zero),
inference(resolve,[$cnf( $equal(composition(one,complement(top)),composition(one,zero)) )],[refute_0_270,refute_0_276]) ).
cnf(refute_0_278,plain,
( composition(converse(one),complement(top)) != composition(one,zero)
| composition(one,zero) != zero
| composition(converse(one),complement(top)) = zero ),
inference(subst,[],[refute_0_35:[bind(X,$fot(composition(converse(one),complement(top)))),bind(Y,$fot(composition(one,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_279,plain,
( composition(one,zero) != zero
| composition(converse(one),complement(top)) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(top)),composition(one,zero)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
composition(converse(one),complement(top)) = zero,
inference(resolve,[$cnf( $equal(composition(one,zero),zero) )],[refute_0_266,refute_0_279]) ).
cnf(refute_0_281,plain,
join(zero,composition(converse(one),complement(top))) = join(zero,composition(converse(one),complement(top))),
introduced(tautology,[refl,[$fot(join(zero,composition(converse(one),complement(top))))]]) ).
cnf(refute_0_282,plain,
( composition(converse(one),complement(top)) != zero
| join(zero,composition(converse(one),complement(top))) != join(zero,composition(converse(one),complement(top)))
| join(zero,composition(converse(one),complement(top))) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(one),complement(top))),join(zero,composition(converse(one),complement(top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_283,plain,
( composition(converse(one),complement(top)) != zero
| join(zero,composition(converse(one),complement(top))) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(one),complement(top))),join(zero,composition(converse(one),complement(top)))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
join(zero,composition(converse(one),complement(top))) = join(zero,zero),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(top)),zero) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
( join(zero,composition(converse(one),complement(top))) != join(zero,zero)
| join(zero,composition(converse(one),complement(top))) != zero
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(one),complement(top))),zero) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_286,plain,
( join(zero,composition(converse(one),complement(top))) != zero
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(one),complement(top))),join(zero,zero)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(one),complement(top))),zero) )],[refute_0_265,refute_0_286]) ).
cnf(refute_0_288,plain,
( join(zero,join(zero,X_82)) != join(join(zero,zero),X_82)
| join(zero,zero) != zero
| join(zero,join(zero,X_82)) = join(zero,X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_82)),join(join(zero,zero),X_82)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_289,plain,
( join(zero,join(zero,X_82)) != join(join(zero,zero),X_82)
| join(zero,join(zero,X_82)) = join(zero,X_82) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
join(zero,join(zero,X_82)) = join(zero,X_82),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_82)),join(join(zero,zero),X_82)) )],[refute_0_251,refute_0_289]) ).
cnf(refute_0_291,plain,
join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),
inference(subst,[],[refute_0_290:[bind(X_82,$fot(meet(X_34,join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_292,plain,
X_34 = join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(join(complement(X_34),join(complement(X_27),meet(X_34,X_27))))),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_34)),bind(B,$fot(join(complement(X_27),meet(X_34,X_27))))]]) ).
cnf(refute_0_293,plain,
top = join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_26),complement(X_27))))]]) ).
cnf(refute_0_294,plain,
( complement(join(complement(X_26),complement(X_27))) != meet(X_26,X_27)
| top != join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| top = join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) ),[1,1],$fot(meet(X_26,X_27))]]) ).
cnf(refute_0_295,plain,
( top != join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| top = join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_26),complement(X_27))),meet(X_26,X_27)) )],[refute_0_91,refute_0_294]) ).
cnf(refute_0_296,plain,
top = join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) )],[refute_0_293,refute_0_295]) ).
cnf(refute_0_297,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_298,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_297]) ).
cnf(refute_0_299,plain,
join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))),
inference(subst,[],[refute_0_298:[bind(A,$fot(complement(X_26))),bind(B,$fot(complement(X_27))),bind(C,$fot(meet(X_26,X_27)))]]) ).
cnf(refute_0_300,plain,
( join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) != join(complement(X_26),join(complement(X_27),meet(X_26,X_27)))
| top != join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| top = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) ),[1],$fot(join(complement(X_26),join(complement(X_27),meet(X_26,X_27))))]]) ).
cnf(refute_0_301,plain,
( top != join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| top = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),join(complement(X_26),join(complement(X_27),meet(X_26,X_27)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
top = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) )],[refute_0_296,refute_0_301]) ).
cnf(refute_0_303,plain,
top = join(complement(X_34),join(complement(X_27),meet(X_34,X_27))),
inference(subst,[],[refute_0_302:[bind(X_26,$fot(X_34))]]) ).
cnf(refute_0_304,plain,
( top != join(complement(X_34),join(complement(X_27),meet(X_34,X_27)))
| join(complement(X_34),join(complement(X_27),meet(X_34,X_27))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_34),join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_305,plain,
join(complement(X_34),join(complement(X_27),meet(X_34,X_27))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_34),join(complement(X_27),meet(X_34,X_27)))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
( X_34 != join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(join(complement(X_34),join(complement(X_27),meet(X_34,X_27)))))
| join(complement(X_34),join(complement(X_27),meet(X_34,X_27))) != top
| X_34 = join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_34,join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(join(complement(X_34),join(complement(X_27),meet(X_34,X_27)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_307,plain,
( X_34 != join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(join(complement(X_34),join(complement(X_27),meet(X_34,X_27)))))
| X_34 = join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_34),join(complement(X_27),meet(X_34,X_27))),top) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
X_34 = join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(join(complement(X_34),join(complement(X_27),meet(X_34,X_27)))))) )],[refute_0_292,refute_0_307]) ).
cnf(refute_0_309,plain,
join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) = join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_310,plain,
( complement(top) != zero
| join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))),join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_311,plain,
( complement(top) != zero
| join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))),join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_311]) ).
cnf(refute_0_313,plain,
join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) = join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_34,join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_314,plain,
( join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) != join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))))),bind(Z,$fot(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))))]]) ).
cnf(refute_0_315,plain,
( join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)),join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_34,join(complement(X_27),meet(X_34,X_27)))),join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_312,refute_0_315]) ).
cnf(refute_0_317,plain,
( X_34 != join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top))
| join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| X_34 = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) ),[0],$fot(join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)))]]) ).
cnf(refute_0_318,plain,
( X_34 != join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top))
| X_34 = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top)),join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
X_34 = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,join(complement(X_27),meet(X_34,X_27))),complement(top))) )],[refute_0_308,refute_0_318]) ).
cnf(refute_0_320,plain,
( X_34 != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) = X_34 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_34)),bind(Y,$fot(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))))]]) ).
cnf(refute_0_321,plain,
join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) = X_34,
inference(resolve,[$cnf( $equal(X_34,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
( join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != X_34
| join(zero,X_34) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) ),[0,1],$fot(X_34)]]) ).
cnf(refute_0_323,plain,
( join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,X_34) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),X_34) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
join(zero,X_34) = join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_291,refute_0_323]) ).
cnf(refute_0_325,plain,
( join(zero,X_34) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != X_34
| join(zero,X_34) = X_34 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_34),X_34) ),[0],$fot(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_326,plain,
( join(zero,X_34) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,X_34) = X_34 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),X_34) )],[refute_0_321,refute_0_325]) ).
cnf(refute_0_327,plain,
join(zero,X_34) = X_34,
inference(resolve,[$cnf( $equal(join(zero,X_34),join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_324,refute_0_326]) ).
cnf(refute_0_328,plain,
join(zero,meet(complement(X_72),converse(complement(converse(X_72))))) = meet(complement(X_72),converse(complement(converse(X_72)))),
inference(subst,[],[refute_0_327:[bind(X_34,$fot(meet(complement(X_72),converse(complement(converse(X_72))))))]]) ).
cnf(refute_0_329,plain,
converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))))),
inference(subst,[],[refute_0_41:[bind(A,$fot(converse(top))),bind(B,$fot(meet(zero,converse(complement(converse(top))))))]]) ).
cnf(refute_0_330,plain,
zero = join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero)))))),
inference(subst,[],[refute_0_245:[bind(X_34,$fot(zero))]]) ).
cnf(refute_0_331,plain,
X_34 = join(meet(X_34,top),complement(join(complement(X_34),top))),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_34)),bind(B,$fot(top))]]) ).
cnf(refute_0_332,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_333,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_334,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_333]) ).
cnf(refute_0_335,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_332,refute_0_334]) ).
cnf(refute_0_336,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_337,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_338,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_337]) ).
cnf(refute_0_339,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_336,refute_0_338]) ).
cnf(refute_0_340,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_341,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_341:[bind(B,$fot(A))]]) ).
cnf(refute_0_343,plain,
join(complement(A),zero) = join(zero,complement(A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(A)))]]) ).
cnf(refute_0_344,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_345,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_346,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_343,refute_0_346]) ).
cnf(refute_0_348,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_349,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_342,refute_0_349]) ).
cnf(refute_0_351,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_352,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_335,refute_0_352]) ).
cnf(refute_0_354,plain,
meet(X_34,top) = meet(top,X_34),
inference(subst,[],[refute_0_353:[bind(A,$fot(X_34))]]) ).
cnf(refute_0_355,plain,
( X_34 != join(meet(X_34,top),complement(join(complement(X_34),top)))
| meet(X_34,top) != meet(top,X_34)
| X_34 = join(meet(top,X_34),complement(join(complement(X_34),top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_34,join(meet(X_34,top),complement(join(complement(X_34),top)))) ),[1,0],$fot(meet(top,X_34))]]) ).
cnf(refute_0_356,plain,
( X_34 != join(meet(X_34,top),complement(join(complement(X_34),top)))
| X_34 = join(meet(top,X_34),complement(join(complement(X_34),top))) ),
inference(resolve,[$cnf( $equal(meet(X_34,top),meet(top,X_34)) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
X_34 = join(meet(top,X_34),complement(join(complement(X_34),top))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,top),complement(join(complement(X_34),top)))) )],[refute_0_331,refute_0_356]) ).
cnf(refute_0_358,plain,
join(complement(X_34),top) = join(top,complement(X_34)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(X_34)))]]) ).
cnf(refute_0_359,plain,
complement(join(complement(X_34),top)) = complement(join(complement(X_34),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(X_34),top)))]]) ).
cnf(refute_0_360,plain,
( complement(join(complement(X_34),top)) != complement(join(complement(X_34),top))
| join(complement(X_34),top) != join(top,complement(X_34))
| complement(join(complement(X_34),top)) = complement(join(top,complement(X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X_34),top)),complement(join(complement(X_34),top))) ),[1,0],$fot(join(top,complement(X_34)))]]) ).
cnf(refute_0_361,plain,
( join(complement(X_34),top) != join(top,complement(X_34))
| complement(join(complement(X_34),top)) = complement(join(top,complement(X_34))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_34),top)),complement(join(complement(X_34),top))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
complement(join(complement(X_34),top)) = complement(join(top,complement(X_34))),
inference(resolve,[$cnf( $equal(join(complement(X_34),top),join(top,complement(X_34))) )],[refute_0_358,refute_0_361]) ).
cnf(refute_0_363,plain,
join(meet(top,X_34),complement(join(complement(X_34),top))) = join(meet(top,X_34),complement(join(complement(X_34),top))),
introduced(tautology,[refl,[$fot(join(meet(top,X_34),complement(join(complement(X_34),top))))]]) ).
cnf(refute_0_364,plain,
( complement(join(complement(X_34),top)) != complement(join(top,complement(X_34)))
| join(meet(top,X_34),complement(join(complement(X_34),top))) != join(meet(top,X_34),complement(join(complement(X_34),top)))
| join(meet(top,X_34),complement(join(complement(X_34),top))) = join(meet(top,X_34),complement(join(top,complement(X_34)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_34),complement(join(complement(X_34),top))),join(meet(top,X_34),complement(join(complement(X_34),top)))) ),[1,1],$fot(complement(join(top,complement(X_34))))]]) ).
cnf(refute_0_365,plain,
( complement(join(complement(X_34),top)) != complement(join(top,complement(X_34)))
| join(meet(top,X_34),complement(join(complement(X_34),top))) = join(meet(top,X_34),complement(join(top,complement(X_34)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_34),complement(join(complement(X_34),top))),join(meet(top,X_34),complement(join(complement(X_34),top)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
join(meet(top,X_34),complement(join(complement(X_34),top))) = join(meet(top,X_34),complement(join(top,complement(X_34)))),
inference(resolve,[$cnf( $equal(complement(join(complement(X_34),top)),complement(join(top,complement(X_34)))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
( X_34 != join(meet(top,X_34),complement(join(complement(X_34),top)))
| join(meet(top,X_34),complement(join(complement(X_34),top))) != join(meet(top,X_34),complement(join(top,complement(X_34))))
| X_34 = join(meet(top,X_34),complement(join(top,complement(X_34)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,join(meet(top,X_34),complement(join(top,complement(X_34))))) ),[0],$fot(join(meet(top,X_34),complement(join(complement(X_34),top))))]]) ).
cnf(refute_0_368,plain,
( X_34 != join(meet(top,X_34),complement(join(complement(X_34),top)))
| X_34 = join(meet(top,X_34),complement(join(top,complement(X_34)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_34),complement(join(complement(X_34),top))),join(meet(top,X_34),complement(join(top,complement(X_34))))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
X_34 = join(meet(top,X_34),complement(join(top,complement(X_34)))),
inference(resolve,[$cnf( $equal(X_34,join(meet(top,X_34),complement(join(complement(X_34),top)))) )],[refute_0_357,refute_0_368]) ).
cnf(refute_0_370,plain,
complement(zero) = join(meet(top,complement(zero)),complement(join(top,complement(complement(zero))))),
inference(subst,[],[refute_0_369:[bind(X_34,$fot(complement(zero)))]]) ).
cnf(refute_0_371,plain,
top = join(complement(X_30),join(complement(top),meet(X_30,top))),
inference(subst,[],[refute_0_302:[bind(X_26,$fot(X_30)),bind(X_27,$fot(top))]]) ).
cnf(refute_0_372,plain,
( complement(top) != zero
| top != join(complement(X_30),join(complement(top),meet(X_30,top)))
| top = join(complement(X_30),join(zero,meet(X_30,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_30),join(complement(top),meet(X_30,top)))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_373,plain,
( top != join(complement(X_30),join(complement(top),meet(X_30,top)))
| top = join(complement(X_30),join(zero,meet(X_30,top))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_372]) ).
cnf(refute_0_374,plain,
top = join(complement(X_30),join(zero,meet(X_30,top))),
inference(resolve,[$cnf( $equal(top,join(complement(X_30),join(complement(top),meet(X_30,top)))) )],[refute_0_371,refute_0_373]) ).
cnf(refute_0_375,plain,
top = join(complement(X_51),join(zero,meet(X_51,top))),
inference(subst,[],[refute_0_374:[bind(X_30,$fot(X_51))]]) ).
cnf(refute_0_376,plain,
meet(X_51,top) = meet(top,X_51),
inference(subst,[],[refute_0_353:[bind(A,$fot(X_51))]]) ).
cnf(refute_0_377,plain,
( meet(X_51,top) != meet(top,X_51)
| top != join(complement(X_51),join(zero,meet(X_51,top)))
| top = join(complement(X_51),join(zero,meet(top,X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_51),join(zero,meet(X_51,top)))) ),[1,1,1],$fot(meet(top,X_51))]]) ).
cnf(refute_0_378,plain,
( top != join(complement(X_51),join(zero,meet(X_51,top)))
| top = join(complement(X_51),join(zero,meet(top,X_51))) ),
inference(resolve,[$cnf( $equal(meet(X_51,top),meet(top,X_51)) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
top = join(complement(X_51),join(zero,meet(top,X_51))),
inference(resolve,[$cnf( $equal(top,join(complement(X_51),join(zero,meet(X_51,top)))) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
top = join(complement(complement(complement(top))),join(zero,meet(top,complement(complement(top))))),
inference(subst,[],[refute_0_379:[bind(X_51,$fot(complement(complement(top))))]]) ).
cnf(refute_0_381,plain,
top = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_125:[bind(X_34,$fot(top))]]) ).
cnf(refute_0_382,plain,
( top != join(zero,meet(top,complement(complement(top))))
| join(zero,meet(top,complement(complement(top)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(complement(top))))))]]) ).
cnf(refute_0_383,plain,
join(zero,meet(top,complement(complement(top)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
( join(zero,meet(top,complement(complement(top)))) != top
| top != join(complement(complement(complement(top))),join(zero,meet(top,complement(complement(top)))))
| top = join(complement(complement(complement(top))),top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(complement(complement(top))),join(zero,meet(top,complement(complement(top)))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_385,plain,
( top != join(complement(complement(complement(top))),join(zero,meet(top,complement(complement(top)))))
| top = join(complement(complement(complement(top))),top) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(complement(top)))),top) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
top = join(complement(complement(complement(top))),top),
inference(resolve,[$cnf( $equal(top,join(complement(complement(complement(top))),join(zero,meet(top,complement(complement(top)))))) )],[refute_0_380,refute_0_385]) ).
cnf(refute_0_387,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_388,plain,
( complement(complement(top)) != complement(complement(top))
| complement(top) != zero
| complement(complement(top)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),complement(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_389,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_389]) ).
cnf(refute_0_391,plain,
complement(complement(complement(top))) = complement(complement(complement(top))),
introduced(tautology,[refl,[$fot(complement(complement(complement(top))))]]) ).
cnf(refute_0_392,plain,
( complement(complement(complement(top))) != complement(complement(complement(top)))
| complement(complement(top)) != complement(zero)
| complement(complement(complement(top))) = complement(complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(complement(top))),complement(complement(complement(top)))) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_393,plain,
( complement(complement(top)) != complement(zero)
| complement(complement(complement(top))) = complement(complement(zero)) ),
inference(resolve,[$cnf( $equal(complement(complement(complement(top))),complement(complement(complement(top)))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
complement(complement(complement(top))) = complement(complement(zero)),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_390,refute_0_393]) ).
cnf(refute_0_395,plain,
join(top,complement(complement(complement(top)))) = join(top,complement(complement(complement(top)))),
introduced(tautology,[refl,[$fot(join(top,complement(complement(complement(top)))))]]) ).
cnf(refute_0_396,plain,
( complement(complement(complement(top))) != complement(complement(zero))
| join(top,complement(complement(complement(top)))) != join(top,complement(complement(complement(top))))
| join(top,complement(complement(complement(top)))) = join(top,complement(complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(complement(complement(top)))),join(top,complement(complement(complement(top))))) ),[1,1],$fot(complement(complement(zero)))]]) ).
cnf(refute_0_397,plain,
( complement(complement(complement(top))) != complement(complement(zero))
| join(top,complement(complement(complement(top)))) = join(top,complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(complement(top)))),join(top,complement(complement(complement(top))))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
join(top,complement(complement(complement(top)))) = join(top,complement(complement(zero))),
inference(resolve,[$cnf( $equal(complement(complement(complement(top))),complement(complement(zero))) )],[refute_0_394,refute_0_397]) ).
cnf(refute_0_399,plain,
join(complement(complement(complement(top))),top) = join(top,complement(complement(complement(top)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(complement(complement(top)))))]]) ).
cnf(refute_0_400,plain,
( join(complement(complement(complement(top))),top) != join(top,complement(complement(complement(top))))
| join(top,complement(complement(complement(top)))) != join(top,complement(complement(zero)))
| join(complement(complement(complement(top))),top) = join(top,complement(complement(zero))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(complement(complement(top))),top))),bind(Y,$fot(join(top,complement(complement(complement(top)))))),bind(Z,$fot(join(top,complement(complement(zero)))))]]) ).
cnf(refute_0_401,plain,
( join(top,complement(complement(complement(top)))) != join(top,complement(complement(zero)))
| join(complement(complement(complement(top))),top) = join(top,complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(complement(top))),top),join(top,complement(complement(complement(top))))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
join(complement(complement(complement(top))),top) = join(top,complement(complement(zero))),
inference(resolve,[$cnf( $equal(join(top,complement(complement(complement(top)))),join(top,complement(complement(zero)))) )],[refute_0_398,refute_0_401]) ).
cnf(refute_0_403,plain,
( join(complement(complement(complement(top))),top) != join(top,complement(complement(zero)))
| top != join(complement(complement(complement(top))),top)
| top = join(top,complement(complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(complement(complement(top))),top)) ),[1],$fot(join(top,complement(complement(zero))))]]) ).
cnf(refute_0_404,plain,
( top != join(complement(complement(complement(top))),top)
| top = join(top,complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(complement(top))),top),join(top,complement(complement(zero)))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
top = join(top,complement(complement(zero))),
inference(resolve,[$cnf( $equal(top,join(complement(complement(complement(top))),top)) )],[refute_0_386,refute_0_404]) ).
cnf(refute_0_406,plain,
( top != join(top,complement(complement(zero)))
| join(top,complement(complement(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(complement(zero)))))]]) ).
cnf(refute_0_407,plain,
join(top,complement(complement(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(complement(zero)))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
( complement(zero) != join(meet(top,complement(zero)),complement(join(top,complement(complement(zero)))))
| join(top,complement(complement(zero))) != top
| complement(zero) = join(meet(top,complement(zero)),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(zero),join(meet(top,complement(zero)),complement(join(top,complement(complement(zero)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_409,plain,
( complement(zero) != join(meet(top,complement(zero)),complement(join(top,complement(complement(zero)))))
| complement(zero) = join(meet(top,complement(zero)),complement(top)) ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(zero))),top) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
complement(zero) = join(meet(top,complement(zero)),complement(top)),
inference(resolve,[$cnf( $equal(complement(zero),join(meet(top,complement(zero)),complement(join(top,complement(complement(zero)))))) )],[refute_0_370,refute_0_409]) ).
cnf(refute_0_411,plain,
( complement(top) != zero
| top != join(zero,meet(top,complement(complement(top))))
| top = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) ),[1,1,1,0],$fot(zero)]]) ).
cnf(refute_0_412,plain,
( top != join(zero,meet(top,complement(complement(top))))
| top = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_411]) ).
cnf(refute_0_413,plain,
top = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_381,refute_0_412]) ).
cnf(refute_0_414,plain,
( top != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(zero)))))]]) ).
cnf(refute_0_415,plain,
join(zero,meet(top,complement(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(zero)))) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
join(complement(top),meet(top,complement(zero))) = join(complement(top),meet(top,complement(zero))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(top,complement(zero))))]]) ).
cnf(refute_0_417,plain,
( complement(top) != zero
| join(complement(top),meet(top,complement(zero))) != join(complement(top),meet(top,complement(zero)))
| join(complement(top),meet(top,complement(zero))) = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(top,complement(zero))),join(complement(top),meet(top,complement(zero)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_418,plain,
( complement(top) != zero
| join(complement(top),meet(top,complement(zero))) = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(zero))),join(complement(top),meet(top,complement(zero)))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
join(complement(top),meet(top,complement(zero))) = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_418]) ).
cnf(refute_0_420,plain,
( join(complement(top),meet(top,complement(zero))) != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) != top
| join(complement(top),meet(top,complement(zero))) = top ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(top),meet(top,complement(zero))))),bind(Y,$fot(join(zero,meet(top,complement(zero))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_421,plain,
( join(zero,meet(top,complement(zero))) != top
| join(complement(top),meet(top,complement(zero))) = top ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(zero))),join(zero,meet(top,complement(zero)))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
join(complement(top),meet(top,complement(zero))) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(zero))),top) )],[refute_0_415,refute_0_421]) ).
cnf(refute_0_423,plain,
join(meet(top,complement(zero)),complement(top)) = join(complement(top),meet(top,complement(zero))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_424,plain,
( join(complement(top),meet(top,complement(zero))) != top
| join(meet(top,complement(zero)),complement(top)) != join(complement(top),meet(top,complement(zero)))
| join(meet(top,complement(zero)),complement(top)) = top ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(top,complement(zero)),complement(top)))),bind(Y,$fot(join(complement(top),meet(top,complement(zero))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_425,plain,
( join(complement(top),meet(top,complement(zero))) != top
| join(meet(top,complement(zero)),complement(top)) = top ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(zero)),complement(top)),join(complement(top),meet(top,complement(zero)))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
join(meet(top,complement(zero)),complement(top)) = top,
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(zero))),top) )],[refute_0_422,refute_0_425]) ).
cnf(refute_0_427,plain,
( complement(zero) != join(meet(top,complement(zero)),complement(top))
| join(meet(top,complement(zero)),complement(top)) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(meet(top,complement(zero)),complement(top)))]]) ).
cnf(refute_0_428,plain,
( complement(zero) != join(meet(top,complement(zero)),complement(top))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(zero)),complement(top)),top) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(zero),join(meet(top,complement(zero)),complement(top))) )],[refute_0_410,refute_0_428]) ).
cnf(refute_0_430,plain,
( complement(zero) != top
| zero != join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))
| zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))) ),[1,1,1,0,0,0],$fot(top)]]) ).
cnf(refute_0_431,plain,
( zero != join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))
| zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),
inference(resolve,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))) )],[refute_0_330,refute_0_431]) ).
cnf(refute_0_433,plain,
( zero != join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_434,plain,
join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = zero,
inference(resolve,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) != zero
| converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_436,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))
| converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),zero) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
converse(top) = join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))))) )],[refute_0_329,refute_0_436]) ).
cnf(refute_0_438,plain,
join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_439,plain,
( complement(zero) != top
| join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) != join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_440,plain,
( complement(zero) != top
| join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_429,refute_0_440]) ).
cnf(refute_0_442,plain,
join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(zero))),bind(B,$fot(meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_443,plain,
( join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) != join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)))),bind(Y,$fot(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))))),bind(Z,$fot(join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))))]]) ).
cnf(refute_0_444,plain,
( join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)),join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),meet(zero,converse(complement(converse(top)))))),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_441,refute_0_444]) ).
cnf(refute_0_446,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero))
| join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| converse(top) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) ),[0],$fot(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)))]]) ).
cnf(refute_0_447,plain,
( converse(top) != join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero))
| converse(top) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero)),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
converse(top) = join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(zero,converse(complement(converse(top))))),complement(zero))) )],[refute_0_437,refute_0_447]) ).
cnf(refute_0_449,plain,
top = join(complement(X_27),join(complement(X_27),meet(X_27,X_27))),
inference(subst,[],[refute_0_302:[bind(X_26,$fot(X_27))]]) ).
cnf(refute_0_450,plain,
join(zero,join(zero,meet(X_34,join(zero,X_34)))) = join(zero,meet(X_34,join(zero,X_34))),
inference(subst,[],[refute_0_290:[bind(X_82,$fot(meet(X_34,join(zero,X_34))))]]) ).
cnf(refute_0_451,plain,
X_34 = join(meet(X_34,join(zero,complement(complement(X_34)))),complement(join(complement(X_34),join(zero,complement(complement(X_34)))))),
inference(subst,[],[refute_0_41:[bind(A,$fot(X_34)),bind(B,$fot(join(zero,complement(complement(X_34)))))]]) ).
cnf(refute_0_452,plain,
top = join(complement(X_30),join(complement(complement(X_30)),meet(X_30,complement(X_30)))),
inference(subst,[],[refute_0_302:[bind(X_26,$fot(X_30)),bind(X_27,$fot(complement(X_30)))]]) ).
cnf(refute_0_453,plain,
zero = meet(X_30,complement(X_30)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_30))]]) ).
cnf(refute_0_454,plain,
( zero != meet(X_30,complement(X_30))
| meet(X_30,complement(X_30)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_30,complement(X_30))))]]) ).
cnf(refute_0_455,plain,
meet(X_30,complement(X_30)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_30,complement(X_30))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
( meet(X_30,complement(X_30)) != zero
| top != join(complement(X_30),join(complement(complement(X_30)),meet(X_30,complement(X_30))))
| top = join(complement(X_30),join(complement(complement(X_30)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_30),join(complement(complement(X_30)),meet(X_30,complement(X_30))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_457,plain,
( top != join(complement(X_30),join(complement(complement(X_30)),meet(X_30,complement(X_30))))
| top = join(complement(X_30),join(complement(complement(X_30)),zero)) ),
inference(resolve,[$cnf( $equal(meet(X_30,complement(X_30)),zero) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
top = join(complement(X_30),join(complement(complement(X_30)),zero)),
inference(resolve,[$cnf( $equal(top,join(complement(X_30),join(complement(complement(X_30)),meet(X_30,complement(X_30))))) )],[refute_0_452,refute_0_457]) ).
cnf(refute_0_459,plain,
join(complement(complement(X_30)),zero) = join(zero,complement(complement(X_30))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_30))))]]) ).
cnf(refute_0_460,plain,
join(complement(X_30),join(complement(complement(X_30)),zero)) = join(complement(X_30),join(complement(complement(X_30)),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_30),join(complement(complement(X_30)),zero)))]]) ).
cnf(refute_0_461,plain,
( join(complement(X_30),join(complement(complement(X_30)),zero)) != join(complement(X_30),join(complement(complement(X_30)),zero))
| join(complement(complement(X_30)),zero) != join(zero,complement(complement(X_30)))
| join(complement(X_30),join(complement(complement(X_30)),zero)) = join(complement(X_30),join(zero,complement(complement(X_30)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_30),join(complement(complement(X_30)),zero)),join(complement(X_30),join(complement(complement(X_30)),zero))) ),[1,1],$fot(join(zero,complement(complement(X_30))))]]) ).
cnf(refute_0_462,plain,
( join(complement(complement(X_30)),zero) != join(zero,complement(complement(X_30)))
| join(complement(X_30),join(complement(complement(X_30)),zero)) = join(complement(X_30),join(zero,complement(complement(X_30)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_30),join(complement(complement(X_30)),zero)),join(complement(X_30),join(complement(complement(X_30)),zero))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
join(complement(X_30),join(complement(complement(X_30)),zero)) = join(complement(X_30),join(zero,complement(complement(X_30)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_30)),zero),join(zero,complement(complement(X_30)))) )],[refute_0_459,refute_0_462]) ).
cnf(refute_0_464,plain,
( join(complement(X_30),join(complement(complement(X_30)),zero)) != join(complement(X_30),join(zero,complement(complement(X_30))))
| top != join(complement(X_30),join(complement(complement(X_30)),zero))
| top = join(complement(X_30),join(zero,complement(complement(X_30)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_30),join(complement(complement(X_30)),zero))) ),[1],$fot(join(complement(X_30),join(zero,complement(complement(X_30)))))]]) ).
cnf(refute_0_465,plain,
( top != join(complement(X_30),join(complement(complement(X_30)),zero))
| top = join(complement(X_30),join(zero,complement(complement(X_30)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_30),join(complement(complement(X_30)),zero)),join(complement(X_30),join(zero,complement(complement(X_30))))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
top = join(complement(X_30),join(zero,complement(complement(X_30)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_30),join(complement(complement(X_30)),zero))) )],[refute_0_458,refute_0_465]) ).
cnf(refute_0_467,plain,
top = join(complement(X_34),join(zero,complement(complement(X_34)))),
inference(subst,[],[refute_0_466:[bind(X_30,$fot(X_34))]]) ).
cnf(refute_0_468,plain,
( top != join(complement(X_34),join(zero,complement(complement(X_34))))
| join(complement(X_34),join(zero,complement(complement(X_34)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_34),join(zero,complement(complement(X_34))))))]]) ).
cnf(refute_0_469,plain,
join(complement(X_34),join(zero,complement(complement(X_34)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_34),join(zero,complement(complement(X_34))))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
( X_34 != join(meet(X_34,join(zero,complement(complement(X_34)))),complement(join(complement(X_34),join(zero,complement(complement(X_34))))))
| join(complement(X_34),join(zero,complement(complement(X_34)))) != top
| X_34 = join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_34,join(meet(X_34,join(zero,complement(complement(X_34)))),complement(join(complement(X_34),join(zero,complement(complement(X_34))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_471,plain,
( X_34 != join(meet(X_34,join(zero,complement(complement(X_34)))),complement(join(complement(X_34),join(zero,complement(complement(X_34))))))
| X_34 = join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_34),join(zero,complement(complement(X_34)))),top) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
X_34 = join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,join(zero,complement(complement(X_34)))),complement(join(complement(X_34),join(zero,complement(complement(X_34))))))) )],[refute_0_451,refute_0_471]) ).
cnf(refute_0_473,plain,
join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))) = join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))))]]) ).
cnf(refute_0_474,plain,
( complement(top) != zero
| join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))) != join(complement(top),meet(X_34,join(zero,complement(complement(X_34)))))
| join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))) = join(zero,meet(X_34,join(zero,complement(complement(X_34))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))),join(complement(top),meet(X_34,join(zero,complement(complement(X_34)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_475,plain,
( complement(top) != zero
| join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))) = join(zero,meet(X_34,join(zero,complement(complement(X_34))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))),join(complement(top),meet(X_34,join(zero,complement(complement(X_34)))))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))) = join(zero,meet(X_34,join(zero,complement(complement(X_34))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_475]) ).
cnf(refute_0_477,plain,
join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) = join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_34,join(zero,complement(complement(X_34))))))]]) ).
cnf(refute_0_478,plain,
( join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))) != join(zero,meet(X_34,join(zero,complement(complement(X_34)))))
| join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) != join(complement(top),meet(X_34,join(zero,complement(complement(X_34)))))
| join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) = join(zero,meet(X_34,join(zero,complement(complement(X_34))))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))))),bind(Z,$fot(join(zero,meet(X_34,join(zero,complement(complement(X_34)))))))]]) ).
cnf(refute_0_479,plain,
( join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))) != join(zero,meet(X_34,join(zero,complement(complement(X_34)))))
| join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) = join(zero,meet(X_34,join(zero,complement(complement(X_34))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)),join(complement(top),meet(X_34,join(zero,complement(complement(X_34)))))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) = join(zero,meet(X_34,join(zero,complement(complement(X_34))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_34,join(zero,complement(complement(X_34))))),join(zero,meet(X_34,join(zero,complement(complement(X_34)))))) )],[refute_0_476,refute_0_479]) ).
cnf(refute_0_481,plain,
( X_34 != join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top))
| join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)) != join(zero,meet(X_34,join(zero,complement(complement(X_34)))))
| X_34 = join(zero,meet(X_34,join(zero,complement(complement(X_34))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,join(zero,meet(X_34,join(zero,complement(complement(X_34)))))) ),[0],$fot(join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)))]]) ).
cnf(refute_0_482,plain,
( X_34 != join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top))
| X_34 = join(zero,meet(X_34,join(zero,complement(complement(X_34))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top)),join(zero,meet(X_34,join(zero,complement(complement(X_34)))))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
X_34 = join(zero,meet(X_34,join(zero,complement(complement(X_34))))),
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,join(zero,complement(complement(X_34)))),complement(top))) )],[refute_0_472,refute_0_482]) ).
cnf(refute_0_484,plain,
complement(complement(X_34)) = X_34,
inference(subst,[],[refute_0_135:[bind(X_69,$fot(X_34))]]) ).
cnf(refute_0_485,plain,
join(zero,complement(complement(X_34))) = join(zero,complement(complement(X_34))),
introduced(tautology,[refl,[$fot(join(zero,complement(complement(X_34))))]]) ).
cnf(refute_0_486,plain,
( complement(complement(X_34)) != X_34
| join(zero,complement(complement(X_34))) != join(zero,complement(complement(X_34)))
| join(zero,complement(complement(X_34))) = join(zero,X_34) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(complement(X_34))),join(zero,complement(complement(X_34)))) ),[1,1],$fot(X_34)]]) ).
cnf(refute_0_487,plain,
( complement(complement(X_34)) != X_34
| join(zero,complement(complement(X_34))) = join(zero,X_34) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_34))),join(zero,complement(complement(X_34)))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
join(zero,complement(complement(X_34))) = join(zero,X_34),
inference(resolve,[$cnf( $equal(complement(complement(X_34)),X_34) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
meet(X_34,join(zero,complement(complement(X_34)))) = meet(X_34,join(zero,complement(complement(X_34)))),
introduced(tautology,[refl,[$fot(meet(X_34,join(zero,complement(complement(X_34)))))]]) ).
cnf(refute_0_490,plain,
( join(zero,complement(complement(X_34))) != join(zero,X_34)
| meet(X_34,join(zero,complement(complement(X_34)))) != meet(X_34,join(zero,complement(complement(X_34))))
| meet(X_34,join(zero,complement(complement(X_34)))) = meet(X_34,join(zero,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_34,join(zero,complement(complement(X_34)))),meet(X_34,join(zero,complement(complement(X_34))))) ),[1,1],$fot(join(zero,X_34))]]) ).
cnf(refute_0_491,plain,
( join(zero,complement(complement(X_34))) != join(zero,X_34)
| meet(X_34,join(zero,complement(complement(X_34)))) = meet(X_34,join(zero,X_34)) ),
inference(resolve,[$cnf( $equal(meet(X_34,join(zero,complement(complement(X_34)))),meet(X_34,join(zero,complement(complement(X_34))))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
meet(X_34,join(zero,complement(complement(X_34)))) = meet(X_34,join(zero,X_34)),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_34))),join(zero,X_34)) )],[refute_0_488,refute_0_491]) ).
cnf(refute_0_493,plain,
join(zero,meet(X_34,join(zero,complement(complement(X_34))))) = join(zero,meet(X_34,join(zero,complement(complement(X_34))))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_34,join(zero,complement(complement(X_34))))))]]) ).
cnf(refute_0_494,plain,
( join(zero,meet(X_34,join(zero,complement(complement(X_34))))) != join(zero,meet(X_34,join(zero,complement(complement(X_34)))))
| meet(X_34,join(zero,complement(complement(X_34)))) != meet(X_34,join(zero,X_34))
| join(zero,meet(X_34,join(zero,complement(complement(X_34))))) = join(zero,meet(X_34,join(zero,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_34,join(zero,complement(complement(X_34))))),join(zero,meet(X_34,join(zero,complement(complement(X_34)))))) ),[1,1],$fot(meet(X_34,join(zero,X_34)))]]) ).
cnf(refute_0_495,plain,
( meet(X_34,join(zero,complement(complement(X_34)))) != meet(X_34,join(zero,X_34))
| join(zero,meet(X_34,join(zero,complement(complement(X_34))))) = join(zero,meet(X_34,join(zero,X_34))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(zero,complement(complement(X_34))))),join(zero,meet(X_34,join(zero,complement(complement(X_34)))))) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
join(zero,meet(X_34,join(zero,complement(complement(X_34))))) = join(zero,meet(X_34,join(zero,X_34))),
inference(resolve,[$cnf( $equal(meet(X_34,join(zero,complement(complement(X_34)))),meet(X_34,join(zero,X_34))) )],[refute_0_492,refute_0_495]) ).
cnf(refute_0_497,plain,
( X_34 != join(zero,meet(X_34,join(zero,complement(complement(X_34)))))
| join(zero,meet(X_34,join(zero,complement(complement(X_34))))) != join(zero,meet(X_34,join(zero,X_34)))
| X_34 = join(zero,meet(X_34,join(zero,X_34))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,join(zero,meet(X_34,join(zero,X_34)))) ),[0],$fot(join(zero,meet(X_34,join(zero,complement(complement(X_34))))))]]) ).
cnf(refute_0_498,plain,
( X_34 != join(zero,meet(X_34,join(zero,complement(complement(X_34)))))
| X_34 = join(zero,meet(X_34,join(zero,X_34))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(zero,complement(complement(X_34))))),join(zero,meet(X_34,join(zero,X_34)))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
X_34 = join(zero,meet(X_34,join(zero,X_34))),
inference(resolve,[$cnf( $equal(X_34,join(zero,meet(X_34,join(zero,complement(complement(X_34)))))) )],[refute_0_483,refute_0_498]) ).
cnf(refute_0_500,plain,
( X_34 != join(zero,meet(X_34,join(zero,X_34)))
| join(zero,meet(X_34,join(zero,X_34))) = X_34 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_34)),bind(Y,$fot(join(zero,meet(X_34,join(zero,X_34)))))]]) ).
cnf(refute_0_501,plain,
join(zero,meet(X_34,join(zero,X_34))) = X_34,
inference(resolve,[$cnf( $equal(X_34,join(zero,meet(X_34,join(zero,X_34)))) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
( join(zero,join(zero,meet(X_34,join(zero,X_34)))) != join(zero,meet(X_34,join(zero,X_34)))
| join(zero,meet(X_34,join(zero,X_34))) != X_34
| join(zero,X_34) = join(zero,meet(X_34,join(zero,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(zero,X_34)))),join(zero,meet(X_34,join(zero,X_34)))) ),[0,1],$fot(X_34)]]) ).
cnf(refute_0_503,plain,
( join(zero,join(zero,meet(X_34,join(zero,X_34)))) != join(zero,meet(X_34,join(zero,X_34)))
| join(zero,X_34) = join(zero,meet(X_34,join(zero,X_34))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(zero,X_34))),X_34) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
join(zero,X_34) = join(zero,meet(X_34,join(zero,X_34))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(zero,X_34)))),join(zero,meet(X_34,join(zero,X_34)))) )],[refute_0_450,refute_0_503]) ).
cnf(refute_0_505,plain,
( join(zero,X_34) != X_34
| join(zero,X_34) != join(zero,meet(X_34,join(zero,X_34)))
| X_34 = join(zero,meet(X_34,join(zero,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,X_34),join(zero,meet(X_34,join(zero,X_34)))) ),[0],$fot(X_34)]]) ).
cnf(refute_0_506,plain,
( join(zero,X_34) != join(zero,meet(X_34,join(zero,X_34)))
| X_34 = join(zero,meet(X_34,join(zero,X_34))) ),
inference(resolve,[$cnf( $equal(join(zero,X_34),X_34) )],[refute_0_327,refute_0_505]) ).
cnf(refute_0_507,plain,
meet(X_34,join(zero,X_34)) = meet(X_34,join(zero,X_34)),
introduced(tautology,[refl,[$fot(meet(X_34,join(zero,X_34)))]]) ).
cnf(refute_0_508,plain,
( join(zero,X_34) != X_34
| meet(X_34,join(zero,X_34)) != meet(X_34,join(zero,X_34))
| meet(X_34,join(zero,X_34)) = meet(X_34,X_34) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_34,join(zero,X_34)),meet(X_34,join(zero,X_34))) ),[1,1],$fot(X_34)]]) ).
cnf(refute_0_509,plain,
( join(zero,X_34) != X_34
| meet(X_34,join(zero,X_34)) = meet(X_34,X_34) ),
inference(resolve,[$cnf( $equal(meet(X_34,join(zero,X_34)),meet(X_34,join(zero,X_34))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
meet(X_34,join(zero,X_34)) = meet(X_34,X_34),
inference(resolve,[$cnf( $equal(join(zero,X_34),X_34) )],[refute_0_327,refute_0_509]) ).
cnf(refute_0_511,plain,
join(zero,meet(X_34,join(zero,X_34))) = meet(X_34,join(zero,X_34)),
inference(subst,[],[refute_0_327:[bind(X_34,$fot(meet(X_34,join(zero,X_34))))]]) ).
cnf(refute_0_512,plain,
( join(zero,meet(X_34,join(zero,X_34))) != meet(X_34,join(zero,X_34))
| meet(X_34,join(zero,X_34)) != meet(X_34,X_34)
| join(zero,meet(X_34,join(zero,X_34))) = meet(X_34,X_34) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(zero,meet(X_34,join(zero,X_34))))),bind(Y,$fot(meet(X_34,join(zero,X_34)))),bind(Z,$fot(meet(X_34,X_34)))]]) ).
cnf(refute_0_513,plain,
( meet(X_34,join(zero,X_34)) != meet(X_34,X_34)
| join(zero,meet(X_34,join(zero,X_34))) = meet(X_34,X_34) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(zero,X_34))),meet(X_34,join(zero,X_34))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
join(zero,meet(X_34,join(zero,X_34))) = meet(X_34,X_34),
inference(resolve,[$cnf( $equal(meet(X_34,join(zero,X_34)),meet(X_34,X_34)) )],[refute_0_510,refute_0_513]) ).
cnf(refute_0_515,plain,
( X_34 != join(zero,meet(X_34,join(zero,X_34)))
| join(zero,meet(X_34,join(zero,X_34))) != meet(X_34,X_34)
| X_34 = meet(X_34,X_34) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_34,meet(X_34,X_34)) ),[0],$fot(join(zero,meet(X_34,join(zero,X_34))))]]) ).
cnf(refute_0_516,plain,
( X_34 != join(zero,meet(X_34,join(zero,X_34)))
| X_34 = meet(X_34,X_34) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(zero,X_34))),meet(X_34,X_34)) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
( join(zero,X_34) != join(zero,meet(X_34,join(zero,X_34)))
| X_34 = meet(X_34,X_34) ),
inference(resolve,[$cnf( $equal(X_34,join(zero,meet(X_34,join(zero,X_34)))) )],[refute_0_506,refute_0_516]) ).
cnf(refute_0_518,plain,
X_34 = meet(X_34,X_34),
inference(resolve,[$cnf( $equal(join(zero,X_34),join(zero,meet(X_34,join(zero,X_34)))) )],[refute_0_504,refute_0_517]) ).
cnf(refute_0_519,plain,
X_27 = meet(X_27,X_27),
inference(subst,[],[refute_0_518:[bind(X_34,$fot(X_27))]]) ).
cnf(refute_0_520,plain,
( X_27 != meet(X_27,X_27)
| meet(X_27,X_27) = X_27 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_27)),bind(Y,$fot(meet(X_27,X_27)))]]) ).
cnf(refute_0_521,plain,
meet(X_27,X_27) = X_27,
inference(resolve,[$cnf( $equal(X_27,meet(X_27,X_27)) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
( meet(X_27,X_27) != X_27
| top != join(complement(X_27),join(complement(X_27),meet(X_27,X_27)))
| top = join(complement(X_27),join(complement(X_27),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_27),join(complement(X_27),meet(X_27,X_27)))) ),[1,1,1],$fot(X_27)]]) ).
cnf(refute_0_523,plain,
( top != join(complement(X_27),join(complement(X_27),meet(X_27,X_27)))
| top = join(complement(X_27),join(complement(X_27),X_27)) ),
inference(resolve,[$cnf( $equal(meet(X_27,X_27),X_27) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
top = join(complement(X_27),join(complement(X_27),X_27)),
inference(resolve,[$cnf( $equal(top,join(complement(X_27),join(complement(X_27),meet(X_27,X_27)))) )],[refute_0_449,refute_0_523]) ).
cnf(refute_0_525,plain,
join(X_80,join(complement(X_80),X_82)) = join(join(X_80,complement(X_80)),X_82),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_80)),bind(B,$fot(complement(X_80))),bind(C,$fot(X_82))]]) ).
cnf(refute_0_526,plain,
top = join(X_80,complement(X_80)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_80))]]) ).
cnf(refute_0_527,plain,
( top != join(X_80,complement(X_80))
| join(X_80,complement(X_80)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_80,complement(X_80))))]]) ).
cnf(refute_0_528,plain,
join(X_80,complement(X_80)) = top,
inference(resolve,[$cnf( $equal(top,join(X_80,complement(X_80))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
( join(X_80,complement(X_80)) != top
| join(X_80,join(complement(X_80),X_82)) != join(join(X_80,complement(X_80)),X_82)
| join(X_80,join(complement(X_80),X_82)) = join(top,X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_80,join(complement(X_80),X_82)),join(join(X_80,complement(X_80)),X_82)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_530,plain,
( join(X_80,join(complement(X_80),X_82)) != join(join(X_80,complement(X_80)),X_82)
| join(X_80,join(complement(X_80),X_82)) = join(top,X_82) ),
inference(resolve,[$cnf( $equal(join(X_80,complement(X_80)),top) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
join(X_80,join(complement(X_80),X_82)) = join(top,X_82),
inference(resolve,[$cnf( $equal(join(X_80,join(complement(X_80),X_82)),join(join(X_80,complement(X_80)),X_82)) )],[refute_0_525,refute_0_530]) ).
cnf(refute_0_532,plain,
join(X_27,join(complement(X_27),complement(X_27))) = join(top,complement(X_27)),
inference(subst,[],[refute_0_531:[bind(X_80,$fot(X_27)),bind(X_82,$fot(complement(X_27)))]]) ).
cnf(refute_0_533,plain,
join(X_80,join(X_81,X_82)) = join(join(X_80,X_81),X_82),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_80)),bind(B,$fot(X_81)),bind(C,$fot(X_82))]]) ).
cnf(refute_0_534,plain,
join(X_81,X_80) = join(X_80,X_81),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_81)),bind(B,$fot(X_80))]]) ).
cnf(refute_0_535,plain,
( join(X_81,X_80) != join(X_80,X_81)
| join(X_80,X_81) = join(X_81,X_80) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_81,X_80))),bind(Y,$fot(join(X_80,X_81)))]]) ).
cnf(refute_0_536,plain,
join(X_80,X_81) = join(X_81,X_80),
inference(resolve,[$cnf( $equal(join(X_81,X_80),join(X_80,X_81)) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
( join(X_80,X_81) != join(X_81,X_80)
| join(X_80,join(X_81,X_82)) != join(join(X_80,X_81),X_82)
| join(X_80,join(X_81,X_82)) = join(join(X_81,X_80),X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_80,join(X_81,X_82)),join(join(X_80,X_81),X_82)) ),[1,0],$fot(join(X_81,X_80))]]) ).
cnf(refute_0_538,plain,
( join(X_80,join(X_81,X_82)) != join(join(X_80,X_81),X_82)
| join(X_80,join(X_81,X_82)) = join(join(X_81,X_80),X_82) ),
inference(resolve,[$cnf( $equal(join(X_80,X_81),join(X_81,X_80)) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
join(X_80,join(X_81,X_82)) = join(join(X_81,X_80),X_82),
inference(resolve,[$cnf( $equal(join(X_80,join(X_81,X_82)),join(join(X_80,X_81),X_82)) )],[refute_0_533,refute_0_538]) ).
cnf(refute_0_540,plain,
join(join(X_81,X_80),X_82) = join(X_81,join(X_80,X_82)),
inference(subst,[],[refute_0_298:[bind(A,$fot(X_81)),bind(B,$fot(X_80)),bind(C,$fot(X_82))]]) ).
cnf(refute_0_541,plain,
( join(X_80,join(X_81,X_82)) != join(join(X_81,X_80),X_82)
| join(join(X_81,X_80),X_82) != join(X_81,join(X_80,X_82))
| join(X_80,join(X_81,X_82)) = join(X_81,join(X_80,X_82)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_80,join(X_81,X_82)),join(X_81,join(X_80,X_82))) ),[0],$fot(join(join(X_81,X_80),X_82))]]) ).
cnf(refute_0_542,plain,
( join(X_80,join(X_81,X_82)) != join(join(X_81,X_80),X_82)
| join(X_80,join(X_81,X_82)) = join(X_81,join(X_80,X_82)) ),
inference(resolve,[$cnf( $equal(join(join(X_81,X_80),X_82),join(X_81,join(X_80,X_82))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
join(X_80,join(X_81,X_82)) = join(X_81,join(X_80,X_82)),
inference(resolve,[$cnf( $equal(join(X_80,join(X_81,X_82)),join(join(X_81,X_80),X_82)) )],[refute_0_539,refute_0_542]) ).
cnf(refute_0_544,plain,
( join(X_80,join(X_81,X_82)) != join(X_81,join(X_80,X_82))
| join(X_81,join(X_80,X_82)) = join(X_80,join(X_81,X_82)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_80,join(X_81,X_82)))),bind(Y,$fot(join(X_81,join(X_80,X_82))))]]) ).
cnf(refute_0_545,plain,
join(X_81,join(X_80,X_82)) = join(X_80,join(X_81,X_82)),
inference(resolve,[$cnf( $equal(join(X_80,join(X_81,X_82)),join(X_81,join(X_80,X_82))) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
join(complement(X_27),join(X_27,complement(X_27))) = join(X_27,join(complement(X_27),complement(X_27))),
inference(subst,[],[refute_0_545:[bind(X_80,$fot(X_27)),bind(X_81,$fot(complement(X_27))),bind(X_82,$fot(complement(X_27)))]]) ).
cnf(refute_0_547,plain,
( join(X_27,join(complement(X_27),complement(X_27))) != join(top,complement(X_27))
| join(complement(X_27),join(X_27,complement(X_27))) != join(X_27,join(complement(X_27),complement(X_27)))
| join(complement(X_27),join(X_27,complement(X_27))) = join(top,complement(X_27)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(X_27),join(X_27,complement(X_27))))),bind(Y,$fot(join(X_27,join(complement(X_27),complement(X_27))))),bind(Z,$fot(join(top,complement(X_27))))]]) ).
cnf(refute_0_548,plain,
( join(X_27,join(complement(X_27),complement(X_27))) != join(top,complement(X_27))
| join(complement(X_27),join(X_27,complement(X_27))) = join(top,complement(X_27)) ),
inference(resolve,[$cnf( $equal(join(complement(X_27),join(X_27,complement(X_27))),join(X_27,join(complement(X_27),complement(X_27)))) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
join(complement(X_27),join(X_27,complement(X_27))) = join(top,complement(X_27)),
inference(resolve,[$cnf( $equal(join(X_27,join(complement(X_27),complement(X_27))),join(top,complement(X_27))) )],[refute_0_532,refute_0_548]) ).
cnf(refute_0_550,plain,
join(X_82,X_81) = join(X_81,X_82),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_82)),bind(B,$fot(X_81))]]) ).
cnf(refute_0_551,plain,
( join(X_82,X_81) != join(X_81,X_82)
| join(X_81,X_82) = join(X_82,X_81) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_82,X_81))),bind(Y,$fot(join(X_81,X_82)))]]) ).
cnf(refute_0_552,plain,
join(X_81,X_82) = join(X_82,X_81),
inference(resolve,[$cnf( $equal(join(X_82,X_81),join(X_81,X_82)) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
( join(X_80,join(X_81,X_82)) != join(join(X_80,X_81),X_82)
| join(X_81,X_82) != join(X_82,X_81)
| join(X_80,join(X_82,X_81)) = join(join(X_80,X_81),X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_80,join(X_81,X_82)),join(join(X_80,X_81),X_82)) ),[0,1],$fot(join(X_82,X_81))]]) ).
cnf(refute_0_554,plain,
( join(X_80,join(X_81,X_82)) != join(join(X_80,X_81),X_82)
| join(X_80,join(X_82,X_81)) = join(join(X_80,X_81),X_82) ),
inference(resolve,[$cnf( $equal(join(X_81,X_82),join(X_82,X_81)) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
join(X_80,join(X_82,X_81)) = join(join(X_80,X_81),X_82),
inference(resolve,[$cnf( $equal(join(X_80,join(X_81,X_82)),join(join(X_80,X_81),X_82)) )],[refute_0_533,refute_0_554]) ).
cnf(refute_0_556,plain,
join(join(X_80,X_81),X_82) = join(X_80,join(X_81,X_82)),
inference(subst,[],[refute_0_298:[bind(A,$fot(X_80)),bind(B,$fot(X_81)),bind(C,$fot(X_82))]]) ).
cnf(refute_0_557,plain,
( join(X_80,join(X_82,X_81)) != join(join(X_80,X_81),X_82)
| join(join(X_80,X_81),X_82) != join(X_80,join(X_81,X_82))
| join(X_80,join(X_82,X_81)) = join(X_80,join(X_81,X_82)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_80,join(X_82,X_81)),join(X_80,join(X_81,X_82))) ),[0],$fot(join(join(X_80,X_81),X_82))]]) ).
cnf(refute_0_558,plain,
( join(X_80,join(X_82,X_81)) != join(join(X_80,X_81),X_82)
| join(X_80,join(X_82,X_81)) = join(X_80,join(X_81,X_82)) ),
inference(resolve,[$cnf( $equal(join(join(X_80,X_81),X_82),join(X_80,join(X_81,X_82))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
join(X_80,join(X_82,X_81)) = join(X_80,join(X_81,X_82)),
inference(resolve,[$cnf( $equal(join(X_80,join(X_82,X_81)),join(join(X_80,X_81),X_82)) )],[refute_0_555,refute_0_558]) ).
cnf(refute_0_560,plain,
( join(X_80,join(X_82,X_81)) != join(X_80,join(X_81,X_82))
| join(X_80,join(X_81,X_82)) = join(X_80,join(X_82,X_81)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_80,join(X_82,X_81)))),bind(Y,$fot(join(X_80,join(X_81,X_82))))]]) ).
cnf(refute_0_561,plain,
join(X_80,join(X_81,X_82)) = join(X_80,join(X_82,X_81)),
inference(resolve,[$cnf( $equal(join(X_80,join(X_82,X_81)),join(X_80,join(X_81,X_82))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
join(complement(X_27),join(complement(X_27),X_27)) = join(complement(X_27),join(X_27,complement(X_27))),
inference(subst,[],[refute_0_561:[bind(X_80,$fot(complement(X_27))),bind(X_81,$fot(complement(X_27))),bind(X_82,$fot(X_27))]]) ).
cnf(refute_0_563,plain,
( join(complement(X_27),join(X_27,complement(X_27))) != join(top,complement(X_27))
| join(complement(X_27),join(complement(X_27),X_27)) != join(complement(X_27),join(X_27,complement(X_27)))
| join(complement(X_27),join(complement(X_27),X_27)) = join(top,complement(X_27)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(X_27),join(complement(X_27),X_27)))),bind(Y,$fot(join(complement(X_27),join(X_27,complement(X_27))))),bind(Z,$fot(join(top,complement(X_27))))]]) ).
cnf(refute_0_564,plain,
( join(complement(X_27),join(X_27,complement(X_27))) != join(top,complement(X_27))
| join(complement(X_27),join(complement(X_27),X_27)) = join(top,complement(X_27)) ),
inference(resolve,[$cnf( $equal(join(complement(X_27),join(complement(X_27),X_27)),join(complement(X_27),join(X_27,complement(X_27)))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
join(complement(X_27),join(complement(X_27),X_27)) = join(top,complement(X_27)),
inference(resolve,[$cnf( $equal(join(complement(X_27),join(X_27,complement(X_27))),join(top,complement(X_27))) )],[refute_0_549,refute_0_564]) ).
cnf(refute_0_566,plain,
( join(complement(X_27),join(complement(X_27),X_27)) != join(top,complement(X_27))
| top != join(complement(X_27),join(complement(X_27),X_27))
| top = join(top,complement(X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_27),join(complement(X_27),X_27))) ),[1],$fot(join(top,complement(X_27)))]]) ).
cnf(refute_0_567,plain,
( top != join(complement(X_27),join(complement(X_27),X_27))
| top = join(top,complement(X_27)) ),
inference(resolve,[$cnf( $equal(join(complement(X_27),join(complement(X_27),X_27)),join(top,complement(X_27))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
top = join(top,complement(X_27)),
inference(resolve,[$cnf( $equal(top,join(complement(X_27),join(complement(X_27),X_27))) )],[refute_0_524,refute_0_567]) ).
cnf(refute_0_569,plain,
top = join(top,complement(complement(X_69))),
inference(subst,[],[refute_0_568:[bind(X_27,$fot(complement(X_69)))]]) ).
cnf(refute_0_570,plain,
( complement(complement(X_69)) != X_69
| top != join(top,complement(complement(X_69)))
| top = join(top,X_69) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(complement(X_69)))) ),[1,1],$fot(X_69)]]) ).
cnf(refute_0_571,plain,
( top != join(top,complement(complement(X_69)))
| top = join(top,X_69) ),
inference(resolve,[$cnf( $equal(complement(complement(X_69)),X_69) )],[refute_0_135,refute_0_570]) ).
cnf(refute_0_572,plain,
top = join(top,X_69),
inference(resolve,[$cnf( $equal(top,join(top,complement(complement(X_69)))) )],[refute_0_569,refute_0_571]) ).
cnf(refute_0_573,plain,
( top != join(top,X_69)
| join(top,X_69) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_69)))]]) ).
cnf(refute_0_574,plain,
join(top,X_69) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_69)) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) = top,
inference(subst,[],[refute_0_574:[bind(X_69,$fot(meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_576,plain,
( converse(top) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))) != top
| converse(top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),top) ),[0],$fot(join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))))]]) ).
cnf(refute_0_577,plain,
( converse(top) != join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(converse(top),meet(zero,converse(complement(converse(top)))))),top) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(top),join(top,meet(converse(top),meet(zero,converse(complement(converse(top))))))) )],[refute_0_448,refute_0_577]) ).
cnf(refute_0_579,plain,
complement(converse(top)) = complement(converse(top)),
introduced(tautology,[refl,[$fot(complement(converse(top)))]]) ).
cnf(refute_0_580,plain,
( complement(converse(top)) != complement(converse(top))
| converse(top) != top
| complement(converse(top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(top)),complement(converse(top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_581,plain,
( converse(top) != top
| complement(converse(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(converse(top))) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
complement(converse(top)) = complement(top),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_578,refute_0_581]) ).
cnf(refute_0_583,plain,
( complement(converse(top)) != complement(top)
| complement(top) != zero
| complement(converse(top)) = zero ),
inference(subst,[],[refute_0_35:[bind(X,$fot(complement(converse(top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_584,plain,
( complement(top) != zero
| complement(converse(top)) = zero ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(top)) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
complement(converse(top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_584]) ).
cnf(refute_0_586,plain,
join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) = join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))))]]) ).
cnf(refute_0_587,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) != join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72)))))
| join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) = join(zero,meet(complement(X_72),converse(complement(converse(X_72))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))),join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_588,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) = join(zero,meet(complement(X_72),converse(complement(converse(X_72))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))),join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72)))))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) = join(zero,meet(complement(X_72),converse(complement(converse(X_72))))),
inference(resolve,[$cnf( $equal(complement(converse(top)),zero) )],[refute_0_585,refute_0_588]) ).
cnf(refute_0_590,plain,
( join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) != join(zero,meet(complement(X_72),converse(complement(converse(X_72)))))
| join(zero,meet(complement(X_72),converse(complement(converse(X_72))))) != meet(complement(X_72),converse(complement(converse(X_72))))
| join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) = meet(complement(X_72),converse(complement(converse(X_72)))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))))),bind(Y,$fot(join(zero,meet(complement(X_72),converse(complement(converse(X_72))))))),bind(Z,$fot(meet(complement(X_72),converse(complement(converse(X_72))))))]]) ).
cnf(refute_0_591,plain,
( join(zero,meet(complement(X_72),converse(complement(converse(X_72))))) != meet(complement(X_72),converse(complement(converse(X_72))))
| join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) = meet(complement(X_72),converse(complement(converse(X_72)))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))),join(zero,meet(complement(X_72),converse(complement(converse(X_72)))))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) = meet(complement(X_72),converse(complement(converse(X_72)))),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(X_72),converse(complement(converse(X_72))))),meet(complement(X_72),converse(complement(converse(X_72))))) )],[refute_0_328,refute_0_591]) ).
cnf(refute_0_593,plain,
( complement(X_72) != join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72)))))
| join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))) != meet(complement(X_72),converse(complement(converse(X_72))))
| complement(X_72) = meet(complement(X_72),converse(complement(converse(X_72)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_72),meet(complement(X_72),converse(complement(converse(X_72))))) ),[0],$fot(join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))))]]) ).
cnf(refute_0_594,plain,
( complement(X_72) != join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72)))))
| complement(X_72) = meet(complement(X_72),converse(complement(converse(X_72)))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72))))),meet(complement(X_72),converse(complement(converse(X_72))))) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
complement(X_72) = meet(complement(X_72),converse(complement(converse(X_72)))),
inference(resolve,[$cnf( $equal(complement(X_72),join(complement(converse(top)),meet(complement(X_72),converse(complement(converse(X_72)))))) )],[refute_0_250,refute_0_594]) ).
cnf(refute_0_596,plain,
complement(complement(meet(converse(X_374),converse(complement(X_374))))) = meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(converse(complement(meet(converse(X_374),converse(complement(X_374)))))))),
inference(subst,[],[refute_0_595:[bind(X_72,$fot(complement(meet(converse(X_374),converse(complement(X_374))))))]]) ).
cnf(refute_0_597,plain,
converse(join(converse(A),join(complement(converse(A)),X_97))) = join(A,converse(join(complement(converse(A)),X_97))),
inference(subst,[],[refute_0_12:[bind(X_11,$fot(join(complement(converse(A)),X_97)))]]) ).
cnf(refute_0_598,plain,
join(top,X_82) = top,
inference(subst,[],[refute_0_574:[bind(X_69,$fot(X_82))]]) ).
cnf(refute_0_599,plain,
( join(X_80,join(complement(X_80),X_82)) != join(top,X_82)
| join(top,X_82) != top
| join(X_80,join(complement(X_80),X_82)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_80,join(complement(X_80),X_82)),top) ),[0],$fot(join(top,X_82))]]) ).
cnf(refute_0_600,plain,
( join(X_80,join(complement(X_80),X_82)) != join(top,X_82)
| join(X_80,join(complement(X_80),X_82)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_82),top) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
join(X_80,join(complement(X_80),X_82)) = top,
inference(resolve,[$cnf( $equal(join(X_80,join(complement(X_80),X_82)),join(top,X_82)) )],[refute_0_531,refute_0_600]) ).
cnf(refute_0_602,plain,
join(converse(A),join(complement(converse(A)),X_97)) = top,
inference(subst,[],[refute_0_601:[bind(X_80,$fot(converse(A))),bind(X_82,$fot(X_97))]]) ).
cnf(refute_0_603,plain,
( converse(join(converse(A),join(complement(converse(A)),X_97))) != join(A,converse(join(complement(converse(A)),X_97)))
| join(converse(A),join(complement(converse(A)),X_97)) != top
| converse(top) = join(A,converse(join(complement(converse(A)),X_97))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),join(complement(converse(A)),X_97))),join(A,converse(join(complement(converse(A)),X_97)))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_604,plain,
( converse(join(converse(A),join(complement(converse(A)),X_97))) != join(A,converse(join(complement(converse(A)),X_97)))
| converse(top) = join(A,converse(join(complement(converse(A)),X_97))) ),
inference(resolve,[$cnf( $equal(join(converse(A),join(complement(converse(A)),X_97)),top) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
converse(top) = join(A,converse(join(complement(converse(A)),X_97))),
inference(resolve,[$cnf( $equal(converse(join(converse(A),join(complement(converse(A)),X_97))),join(A,converse(join(complement(converse(A)),X_97)))) )],[refute_0_597,refute_0_604]) ).
cnf(refute_0_606,plain,
( converse(top) != join(A,converse(join(complement(converse(A)),X_97)))
| converse(top) != top
| top = join(A,converse(join(complement(converse(A)),X_97))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(A,converse(join(complement(converse(A)),X_97)))) ),[0],$fot(top)]]) ).
cnf(refute_0_607,plain,
( converse(top) != join(A,converse(join(complement(converse(A)),X_97)))
| top = join(A,converse(join(complement(converse(A)),X_97))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_578,refute_0_606]) ).
cnf(refute_0_608,plain,
top = join(A,converse(join(complement(converse(A)),X_97))),
inference(resolve,[$cnf( $equal(converse(top),join(A,converse(join(complement(converse(A)),X_97)))) )],[refute_0_605,refute_0_607]) ).
cnf(refute_0_609,plain,
top = join(X_114,converse(join(complement(converse(X_114)),X_115))),
inference(subst,[],[refute_0_608:[bind(A,$fot(X_114)),bind(X_97,$fot(X_115))]]) ).
cnf(refute_0_610,plain,
join(X_115,complement(converse(X_114))) = join(complement(converse(X_114)),X_115),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_115)),bind(B,$fot(complement(converse(X_114))))]]) ).
cnf(refute_0_611,plain,
( join(X_115,complement(converse(X_114))) != join(complement(converse(X_114)),X_115)
| join(complement(converse(X_114)),X_115) = join(X_115,complement(converse(X_114))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_115,complement(converse(X_114))))),bind(Y,$fot(join(complement(converse(X_114)),X_115)))]]) ).
cnf(refute_0_612,plain,
join(complement(converse(X_114)),X_115) = join(X_115,complement(converse(X_114))),
inference(resolve,[$cnf( $equal(join(X_115,complement(converse(X_114))),join(complement(converse(X_114)),X_115)) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
( join(complement(converse(X_114)),X_115) != join(X_115,complement(converse(X_114)))
| top != join(X_114,converse(join(complement(converse(X_114)),X_115)))
| top = join(X_114,converse(join(X_115,complement(converse(X_114))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(X_114,converse(join(complement(converse(X_114)),X_115)))) ),[1,1,0],$fot(join(X_115,complement(converse(X_114))))]]) ).
cnf(refute_0_614,plain,
( top != join(X_114,converse(join(complement(converse(X_114)),X_115)))
| top = join(X_114,converse(join(X_115,complement(converse(X_114))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X_114)),X_115),join(X_115,complement(converse(X_114)))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
top = join(X_114,converse(join(X_115,complement(converse(X_114))))),
inference(resolve,[$cnf( $equal(top,join(X_114,converse(join(complement(converse(X_114)),X_115)))) )],[refute_0_609,refute_0_614]) ).
cnf(refute_0_616,plain,
top = join(X_180,converse(join(converse(A),complement(converse(X_180))))),
inference(subst,[],[refute_0_615:[bind(X_114,$fot(X_180)),bind(X_115,$fot(converse(A)))]]) ).
cnf(refute_0_617,plain,
converse(join(converse(A),complement(converse(X_180)))) = join(A,converse(complement(converse(X_180)))),
inference(subst,[],[refute_0_12:[bind(X_11,$fot(complement(converse(X_180))))]]) ).
cnf(refute_0_618,plain,
( converse(join(converse(A),complement(converse(X_180)))) != join(A,converse(complement(converse(X_180))))
| top != join(X_180,converse(join(converse(A),complement(converse(X_180)))))
| top = join(X_180,join(A,converse(complement(converse(X_180))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(X_180,converse(join(converse(A),complement(converse(X_180)))))) ),[1,1],$fot(join(A,converse(complement(converse(X_180)))))]]) ).
cnf(refute_0_619,plain,
( top != join(X_180,converse(join(converse(A),complement(converse(X_180)))))
| top = join(X_180,join(A,converse(complement(converse(X_180))))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),complement(converse(X_180)))),join(A,converse(complement(converse(X_180))))) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
top = join(X_180,join(A,converse(complement(converse(X_180))))),
inference(resolve,[$cnf( $equal(top,join(X_180,converse(join(converse(A),complement(converse(X_180)))))) )],[refute_0_616,refute_0_619]) ).
cnf(refute_0_621,plain,
top = join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362)))))),
inference(subst,[],[refute_0_620:[bind(A,$fot(meet(complement(X_361),X_362))),bind(X_180,$fot(meet(X_361,X_362)))]]) ).
cnf(refute_0_622,plain,
join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)) = join(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_82),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(meet(X_58,X_59))),bind(B,$fot(meet(complement(X_58),X_59))),bind(C,$fot(X_82))]]) ).
cnf(refute_0_623,plain,
( join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)) != join(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_82)
| join(meet(X_58,X_59),meet(complement(X_58),X_59)) != X_59
| join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)) = join(X_59,X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)),join(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_82)) ),[1,0],$fot(X_59)]]) ).
cnf(refute_0_624,plain,
( join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)) != join(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_82)
| join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)) = join(X_59,X_82) ),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_59) )],[refute_0_216,refute_0_623]) ).
cnf(refute_0_625,plain,
join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)) = join(X_59,X_82),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_59),join(meet(complement(X_58),X_59),X_82)),join(join(meet(X_58,X_59),meet(complement(X_58),X_59)),X_82)) )],[refute_0_622,refute_0_624]) ).
cnf(refute_0_626,plain,
join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362)))))) = join(X_362,converse(complement(converse(meet(X_361,X_362))))),
inference(subst,[],[refute_0_625:[bind(X_58,$fot(X_361)),bind(X_59,$fot(X_362)),bind(X_82,$fot(converse(complement(converse(meet(X_361,X_362))))))]]) ).
cnf(refute_0_627,plain,
( join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362)))))) != join(X_362,converse(complement(converse(meet(X_361,X_362)))))
| top != join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362))))))
| top = join(X_362,converse(complement(converse(meet(X_361,X_362))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362))))))) ),[1],$fot(join(X_362,converse(complement(converse(meet(X_361,X_362))))))]]) ).
cnf(refute_0_628,plain,
( top != join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362))))))
| top = join(X_362,converse(complement(converse(meet(X_361,X_362))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362)))))),join(X_362,converse(complement(converse(meet(X_361,X_362)))))) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
top = join(X_362,converse(complement(converse(meet(X_361,X_362))))),
inference(resolve,[$cnf( $equal(top,join(meet(X_361,X_362),join(meet(complement(X_361),X_362),converse(complement(converse(meet(X_361,X_362))))))) )],[refute_0_621,refute_0_628]) ).
cnf(refute_0_630,plain,
top = join(converse(complement(converse(X_72))),converse(complement(converse(meet(complement(X_72),converse(complement(converse(X_72)))))))),
inference(subst,[],[refute_0_629:[bind(X_361,$fot(complement(X_72))),bind(X_362,$fot(converse(complement(converse(X_72)))))]]) ).
cnf(refute_0_631,plain,
( complement(X_72) != meet(complement(X_72),converse(complement(converse(X_72))))
| meet(complement(X_72),converse(complement(converse(X_72)))) = complement(X_72) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_72))),bind(Y,$fot(meet(complement(X_72),converse(complement(converse(X_72))))))]]) ).
cnf(refute_0_632,plain,
meet(complement(X_72),converse(complement(converse(X_72)))) = complement(X_72),
inference(resolve,[$cnf( $equal(complement(X_72),meet(complement(X_72),converse(complement(converse(X_72))))) )],[refute_0_595,refute_0_631]) ).
cnf(refute_0_633,plain,
( meet(complement(X_72),converse(complement(converse(X_72)))) != complement(X_72)
| top != join(converse(complement(converse(X_72))),converse(complement(converse(meet(complement(X_72),converse(complement(converse(X_72))))))))
| top = join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(converse(complement(converse(X_72))),converse(complement(converse(meet(complement(X_72),converse(complement(converse(X_72))))))))) ),[1,1,0,0,0],$fot(complement(X_72))]]) ).
cnf(refute_0_634,plain,
( top != join(converse(complement(converse(X_72))),converse(complement(converse(meet(complement(X_72),converse(complement(converse(X_72))))))))
| top = join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_72),converse(complement(converse(X_72)))),complement(X_72)) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
top = join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))),
inference(resolve,[$cnf( $equal(top,join(converse(complement(converse(X_72))),converse(complement(converse(meet(complement(X_72),converse(complement(converse(X_72))))))))) )],[refute_0_630,refute_0_634]) ).
cnf(refute_0_636,plain,
complement(complement(join(complement(A),complement(B)))) = join(complement(A),complement(B)),
inference(subst,[],[refute_0_135:[bind(X_69,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_637,plain,
( complement(complement(join(complement(A),complement(B)))) != join(complement(A),complement(B))
| complement(join(complement(A),complement(B))) != meet(A,B)
| complement(meet(A,B)) = join(complement(A),complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(join(complement(A),complement(B)))),join(complement(A),complement(B))) ),[0,0],$fot(meet(A,B))]]) ).
cnf(refute_0_638,plain,
( complement(complement(join(complement(A),complement(B)))) != join(complement(A),complement(B))
| complement(meet(A,B)) = join(complement(A),complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_29,refute_0_637]) ).
cnf(refute_0_639,plain,
complement(meet(A,B)) = join(complement(A),complement(B)),
inference(resolve,[$cnf( $equal(complement(complement(join(complement(A),complement(B)))),join(complement(A),complement(B))) )],[refute_0_636,refute_0_638]) ).
cnf(refute_0_640,plain,
( complement(meet(A,B)) != join(complement(A),complement(B))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(meet(A,B)))),bind(Y,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_641,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(complement(meet(A,B)),join(complement(A),complement(B))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
join(complement(converse(X_72)),complement(converse(complement(X_72)))) = complement(meet(converse(X_72),converse(complement(X_72)))),
inference(subst,[],[refute_0_641:[bind(A,$fot(converse(X_72))),bind(B,$fot(converse(complement(X_72))))]]) ).
cnf(refute_0_643,plain,
converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))) = converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))),
introduced(tautology,[refl,[$fot(converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))))]]) ).
cnf(refute_0_644,plain,
( converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))) != converse(join(complement(converse(X_72)),complement(converse(complement(X_72)))))
| join(complement(converse(X_72)),complement(converse(complement(X_72)))) != complement(meet(converse(X_72),converse(complement(X_72))))
| converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))) = converse(complement(meet(converse(X_72),converse(complement(X_72))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))),converse(join(complement(converse(X_72)),complement(converse(complement(X_72)))))) ),[1,0],$fot(complement(meet(converse(X_72),converse(complement(X_72)))))]]) ).
cnf(refute_0_645,plain,
( join(complement(converse(X_72)),complement(converse(complement(X_72)))) != complement(meet(converse(X_72),converse(complement(X_72))))
| converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))) = converse(complement(meet(converse(X_72),converse(complement(X_72))))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))),converse(join(complement(converse(X_72)),complement(converse(complement(X_72)))))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))) = converse(complement(meet(converse(X_72),converse(complement(X_72))))),
inference(resolve,[$cnf( $equal(join(complement(converse(X_72)),complement(converse(complement(X_72)))),complement(meet(converse(X_72),converse(complement(X_72))))) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_648,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_647]) ).
cnf(refute_0_649,plain,
join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) = converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))),
inference(subst,[],[refute_0_648:[bind(A,$fot(complement(converse(X_72)))),bind(B,$fot(complement(converse(complement(X_72)))))]]) ).
cnf(refute_0_650,plain,
( converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))) != converse(complement(meet(converse(X_72),converse(complement(X_72)))))
| join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) != converse(join(complement(converse(X_72)),complement(converse(complement(X_72)))))
| join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) = converse(complement(meet(converse(X_72),converse(complement(X_72))))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))))),bind(Y,$fot(converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))))),bind(Z,$fot(converse(complement(meet(converse(X_72),converse(complement(X_72)))))))]]) ).
cnf(refute_0_651,plain,
( converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))) != converse(complement(meet(converse(X_72),converse(complement(X_72)))))
| join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) = converse(complement(meet(converse(X_72),converse(complement(X_72))))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))),converse(join(complement(converse(X_72)),complement(converse(complement(X_72)))))) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) = converse(complement(meet(converse(X_72),converse(complement(X_72))))),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(X_72)),complement(converse(complement(X_72))))),converse(complement(meet(converse(X_72),converse(complement(X_72)))))) )],[refute_0_646,refute_0_651]) ).
cnf(refute_0_653,plain,
( join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))) != converse(complement(meet(converse(X_72),converse(complement(X_72)))))
| top != join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72)))))
| top = converse(complement(meet(converse(X_72),converse(complement(X_72))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72)))))) ),[1],$fot(converse(complement(meet(converse(X_72),converse(complement(X_72))))))]]) ).
cnf(refute_0_654,plain,
( top != join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72)))))
| top = converse(complement(meet(converse(X_72),converse(complement(X_72))))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72))))),converse(complement(meet(converse(X_72),converse(complement(X_72)))))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
top = converse(complement(meet(converse(X_72),converse(complement(X_72))))),
inference(resolve,[$cnf( $equal(top,join(converse(complement(converse(X_72))),converse(complement(converse(complement(X_72)))))) )],[refute_0_635,refute_0_654]) ).
cnf(refute_0_656,plain,
top = converse(complement(meet(converse(X_374),converse(complement(X_374))))),
inference(subst,[],[refute_0_655:[bind(X_72,$fot(X_374))]]) ).
cnf(refute_0_657,plain,
( top != converse(complement(meet(converse(X_374),converse(complement(X_374)))))
| converse(complement(meet(converse(X_374),converse(complement(X_374))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(complement(meet(converse(X_374),converse(complement(X_374)))))))]]) ).
cnf(refute_0_658,plain,
converse(complement(meet(converse(X_374),converse(complement(X_374))))) = top,
inference(resolve,[$cnf( $equal(top,converse(complement(meet(converse(X_374),converse(complement(X_374)))))) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
( complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(converse(complement(meet(converse(X_374),converse(complement(X_374))))))))
| converse(complement(meet(converse(X_374),converse(complement(X_374))))) != top
| complement(complement(meet(converse(X_374),converse(complement(X_374))))) = meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(meet(converse(X_374),converse(complement(X_374))))),meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(converse(complement(meet(converse(X_374),converse(complement(X_374))))))))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_660,plain,
( complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(converse(complement(meet(converse(X_374),converse(complement(X_374))))))))
| complement(complement(meet(converse(X_374),converse(complement(X_374))))) = meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) ),
inference(resolve,[$cnf( $equal(converse(complement(meet(converse(X_374),converse(complement(X_374))))),top) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
complement(complement(meet(converse(X_374),converse(complement(X_374))))) = meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))),
inference(resolve,[$cnf( $equal(complement(complement(meet(converse(X_374),converse(complement(X_374))))),meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(converse(complement(meet(converse(X_374),converse(complement(X_374))))))))) )],[refute_0_596,refute_0_660]) ).
cnf(refute_0_662,plain,
complement(complement(meet(converse(X_374),converse(complement(X_374))))) = meet(converse(X_374),converse(complement(X_374))),
inference(subst,[],[refute_0_135:[bind(X_69,$fot(meet(converse(X_374),converse(complement(X_374)))))]]) ).
cnf(refute_0_663,plain,
( complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))
| complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(converse(X_374),converse(complement(X_374)))
| meet(converse(X_374),converse(complement(X_374))) = meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(meet(converse(X_374),converse(complement(X_374))))),meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))) ),[0],$fot(meet(converse(X_374),converse(complement(X_374))))]]) ).
cnf(refute_0_664,plain,
( complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))
| meet(converse(X_374),converse(complement(X_374))) = meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) ),
inference(resolve,[$cnf( $equal(complement(complement(meet(converse(X_374),converse(complement(X_374))))),meet(converse(X_374),converse(complement(X_374)))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
zero = join(meet(zero,B),complement(join(complement(zero),B))),
inference(subst,[],[refute_0_41:[bind(A,$fot(zero))]]) ).
cnf(refute_0_666,plain,
( complement(zero) != top
| zero != join(meet(zero,B),complement(join(complement(zero),B)))
| zero = join(meet(zero,B),complement(join(top,B))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(zero,B),complement(join(complement(zero),B)))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_667,plain,
( zero != join(meet(zero,B),complement(join(complement(zero),B)))
| zero = join(meet(zero,B),complement(join(top,B))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_429,refute_0_666]) ).
cnf(refute_0_668,plain,
zero = join(meet(zero,B),complement(join(top,B))),
inference(resolve,[$cnf( $equal(zero,join(meet(zero,B),complement(join(complement(zero),B)))) )],[refute_0_665,refute_0_667]) ).
cnf(refute_0_669,plain,
join(zero,join(zero,X_83)) = join(zero,X_83),
inference(subst,[],[refute_0_290:[bind(X_82,$fot(X_83))]]) ).
cnf(refute_0_670,plain,
join(X_83,zero) = join(zero,X_83),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_83)),bind(B,$fot(zero))]]) ).
cnf(refute_0_671,plain,
( join(X_83,zero) != join(zero,X_83)
| join(zero,X_83) = join(X_83,zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_83,zero))),bind(Y,$fot(join(zero,X_83)))]]) ).
cnf(refute_0_672,plain,
join(zero,X_83) = join(X_83,zero),
inference(resolve,[$cnf( $equal(join(X_83,zero),join(zero,X_83)) )],[refute_0_670,refute_0_671]) ).
cnf(refute_0_673,plain,
( join(zero,X_83) != join(X_83,zero)
| join(zero,join(zero,X_83)) != join(zero,X_83)
| join(zero,join(zero,X_83)) = join(X_83,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_83)),join(zero,X_83)) ),[1],$fot(join(X_83,zero))]]) ).
cnf(refute_0_674,plain,
( join(zero,join(zero,X_83)) != join(zero,X_83)
| join(zero,join(zero,X_83)) = join(X_83,zero) ),
inference(resolve,[$cnf( $equal(join(zero,X_83),join(X_83,zero)) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
join(zero,join(zero,X_83)) = join(X_83,zero),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_83)),join(zero,X_83)) )],[refute_0_669,refute_0_674]) ).
cnf(refute_0_676,plain,
join(zero,X_83) = X_83,
inference(subst,[],[refute_0_327:[bind(X_34,$fot(X_83))]]) ).
cnf(refute_0_677,plain,
( join(zero,X_83) != X_83
| join(zero,join(zero,X_83)) != join(zero,X_83)
| join(zero,join(zero,X_83)) = X_83 ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(zero,join(zero,X_83)))),bind(Y,$fot(join(zero,X_83))),bind(Z,$fot(X_83))]]) ).
cnf(refute_0_678,plain,
( join(zero,X_83) != X_83
| join(zero,join(zero,X_83)) = X_83 ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_83)),join(zero,X_83)) )],[refute_0_669,refute_0_677]) ).
cnf(refute_0_679,plain,
join(zero,join(zero,X_83)) = X_83,
inference(resolve,[$cnf( $equal(join(zero,X_83),X_83) )],[refute_0_676,refute_0_678]) ).
cnf(refute_0_680,plain,
( join(zero,join(zero,X_83)) != X_83
| join(zero,join(zero,X_83)) != join(X_83,zero)
| X_83 = join(X_83,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_83)),join(X_83,zero)) ),[0],$fot(X_83)]]) ).
cnf(refute_0_681,plain,
( join(zero,join(zero,X_83)) != join(X_83,zero)
| X_83 = join(X_83,zero) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_83)),X_83) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
X_83 = join(X_83,zero),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_83)),join(X_83,zero)) )],[refute_0_675,refute_0_681]) ).
cnf(refute_0_683,plain,
( X_83 != join(X_83,zero)
| join(X_83,zero) = X_83 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_83)),bind(Y,$fot(join(X_83,zero)))]]) ).
cnf(refute_0_684,plain,
join(X_83,zero) = X_83,
inference(resolve,[$cnf( $equal(X_83,join(X_83,zero)) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
join(meet(zero,B),zero) = meet(zero,B),
inference(subst,[],[refute_0_684:[bind(X_83,$fot(meet(zero,B)))]]) ).
cnf(refute_0_686,plain,
join(top,B) = top,
inference(subst,[],[refute_0_574:[bind(X_69,$fot(B))]]) ).
cnf(refute_0_687,plain,
complement(join(top,B)) = complement(join(top,B)),
introduced(tautology,[refl,[$fot(complement(join(top,B)))]]) ).
cnf(refute_0_688,plain,
( complement(join(top,B)) != complement(join(top,B))
| join(top,B) != top
| complement(join(top,B)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,B)),complement(join(top,B))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_689,plain,
( join(top,B) != top
| complement(join(top,B)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(top,B)),complement(join(top,B))) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
complement(join(top,B)) = complement(top),
inference(resolve,[$cnf( $equal(join(top,B),top) )],[refute_0_686,refute_0_689]) ).
cnf(refute_0_691,plain,
( complement(join(top,B)) != complement(top)
| complement(top) != zero
| complement(join(top,B)) = zero ),
inference(subst,[],[refute_0_35:[bind(X,$fot(complement(join(top,B)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_692,plain,
( complement(top) != zero
| complement(join(top,B)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,B)),complement(top)) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
complement(join(top,B)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_692]) ).
cnf(refute_0_694,plain,
join(meet(zero,B),complement(join(top,B))) = join(meet(zero,B),complement(join(top,B))),
introduced(tautology,[refl,[$fot(join(meet(zero,B),complement(join(top,B))))]]) ).
cnf(refute_0_695,plain,
( complement(join(top,B)) != zero
| join(meet(zero,B),complement(join(top,B))) != join(meet(zero,B),complement(join(top,B)))
| join(meet(zero,B),complement(join(top,B))) = join(meet(zero,B),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(zero,B),complement(join(top,B))),join(meet(zero,B),complement(join(top,B)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_696,plain,
( complement(join(top,B)) != zero
| join(meet(zero,B),complement(join(top,B))) = join(meet(zero,B),zero) ),
inference(resolve,[$cnf( $equal(join(meet(zero,B),complement(join(top,B))),join(meet(zero,B),complement(join(top,B)))) )],[refute_0_694,refute_0_695]) ).
cnf(refute_0_697,plain,
join(meet(zero,B),complement(join(top,B))) = join(meet(zero,B),zero),
inference(resolve,[$cnf( $equal(complement(join(top,B)),zero) )],[refute_0_693,refute_0_696]) ).
cnf(refute_0_698,plain,
( join(meet(zero,B),complement(join(top,B))) != join(meet(zero,B),zero)
| join(meet(zero,B),zero) != meet(zero,B)
| join(meet(zero,B),complement(join(top,B))) = meet(zero,B) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(zero,B),complement(join(top,B))))),bind(Y,$fot(join(meet(zero,B),zero))),bind(Z,$fot(meet(zero,B)))]]) ).
cnf(refute_0_699,plain,
( join(meet(zero,B),zero) != meet(zero,B)
| join(meet(zero,B),complement(join(top,B))) = meet(zero,B) ),
inference(resolve,[$cnf( $equal(join(meet(zero,B),complement(join(top,B))),join(meet(zero,B),zero)) )],[refute_0_697,refute_0_698]) ).
cnf(refute_0_700,plain,
join(meet(zero,B),complement(join(top,B))) = meet(zero,B),
inference(resolve,[$cnf( $equal(join(meet(zero,B),zero),meet(zero,B)) )],[refute_0_685,refute_0_699]) ).
cnf(refute_0_701,plain,
( join(meet(zero,B),complement(join(top,B))) != meet(zero,B)
| zero != join(meet(zero,B),complement(join(top,B)))
| zero = meet(zero,B) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(zero,B),complement(join(top,B)))) ),[1],$fot(meet(zero,B))]]) ).
cnf(refute_0_702,plain,
( zero != join(meet(zero,B),complement(join(top,B)))
| zero = meet(zero,B) ),
inference(resolve,[$cnf( $equal(join(meet(zero,B),complement(join(top,B))),meet(zero,B)) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
zero = meet(zero,B),
inference(resolve,[$cnf( $equal(zero,join(meet(zero,B),complement(join(top,B)))) )],[refute_0_668,refute_0_702]) ).
cnf(refute_0_704,plain,
( zero != meet(zero,B)
| meet(zero,B) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(zero,B)))]]) ).
cnf(refute_0_705,plain,
meet(zero,B) = zero,
inference(resolve,[$cnf( $equal(zero,meet(zero,B)) )],[refute_0_703,refute_0_704]) ).
cnf(refute_0_706,plain,
meet(zero,meet(converse(X_374),converse(complement(X_374)))) = zero,
inference(subst,[],[refute_0_705:[bind(B,$fot(meet(converse(X_374),converse(complement(X_374)))))]]) ).
cnf(refute_0_707,plain,
meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))),
introduced(tautology,[refl,[$fot(meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))))]]) ).
cnf(refute_0_708,plain,
( complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(converse(X_374),converse(complement(X_374)))
| meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374))))))
| meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,meet(converse(X_374),converse(complement(X_374)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))),meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374))))))) ),[1,1],$fot(meet(converse(X_374),converse(complement(X_374))))]]) ).
cnf(refute_0_709,plain,
( complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(converse(X_374),converse(complement(X_374)))
| meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,meet(converse(X_374),converse(complement(X_374)))) ),
inference(resolve,[$cnf( $equal(meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))),meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374))))))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,meet(converse(X_374),converse(complement(X_374)))),
inference(resolve,[$cnf( $equal(complement(complement(meet(converse(X_374),converse(complement(X_374))))),meet(converse(X_374),converse(complement(X_374)))) )],[refute_0_662,refute_0_709]) ).
cnf(refute_0_711,plain,
complement(complement(converse(zero))) = converse(zero),
inference(subst,[],[refute_0_135:[bind(X_69,$fot(converse(zero)))]]) ).
cnf(refute_0_712,plain,
converse(converse(complement(converse(zero)))) = complement(converse(zero)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_713,plain,
join(zero,join(zero,converse(complement(converse(zero))))) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_290:[bind(X_82,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_714,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_235:[bind(X_14,$fot(zero))]]) ).
cnf(refute_0_715,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_716,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
( join(zero,converse(complement(converse(zero)))) != converse(top)
| join(zero,join(zero,converse(complement(converse(zero))))) != join(zero,converse(complement(converse(zero))))
| join(zero,join(zero,converse(complement(converse(zero))))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,converse(complement(converse(zero))))),join(zero,converse(complement(converse(zero))))) ),[1],$fot(converse(top))]]) ).
cnf(refute_0_718,plain,
( join(zero,join(zero,converse(complement(converse(zero))))) != join(zero,converse(complement(converse(zero))))
| join(zero,join(zero,converse(complement(converse(zero))))) = converse(top) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
join(zero,join(zero,converse(complement(converse(zero))))) = converse(top),
inference(resolve,[$cnf( $equal(join(zero,join(zero,converse(complement(converse(zero))))),join(zero,converse(complement(converse(zero))))) )],[refute_0_713,refute_0_718]) ).
cnf(refute_0_720,plain,
join(zero,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(subst,[],[refute_0_327:[bind(X_34,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_721,plain,
( join(zero,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| join(zero,join(zero,converse(complement(converse(zero))))) != join(zero,converse(complement(converse(zero))))
| join(zero,join(zero,converse(complement(converse(zero))))) = converse(complement(converse(zero))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(zero,join(zero,converse(complement(converse(zero))))))),bind(Y,$fot(join(zero,converse(complement(converse(zero)))))),bind(Z,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_722,plain,
( join(zero,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| join(zero,join(zero,converse(complement(converse(zero))))) = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,converse(complement(converse(zero))))),join(zero,converse(complement(converse(zero))))) )],[refute_0_713,refute_0_721]) ).
cnf(refute_0_723,plain,
join(zero,join(zero,converse(complement(converse(zero))))) = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_720,refute_0_722]) ).
cnf(refute_0_724,plain,
( join(zero,join(zero,converse(complement(converse(zero))))) != converse(complement(converse(zero)))
| join(zero,join(zero,converse(complement(converse(zero))))) != converse(top)
| converse(complement(converse(zero))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,converse(complement(converse(zero))))),converse(top)) ),[0],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_725,plain,
( join(zero,join(zero,converse(complement(converse(zero))))) != converse(top)
| converse(complement(converse(zero))) = converse(top) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,converse(complement(converse(zero))))),converse(complement(converse(zero)))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
converse(complement(converse(zero))) = converse(top),
inference(resolve,[$cnf( $equal(join(zero,join(zero,converse(complement(converse(zero))))),converse(top)) )],[refute_0_719,refute_0_725]) ).
cnf(refute_0_727,plain,
( converse(complement(converse(zero))) != converse(top)
| converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(converse(top)) = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) ),[0,0],$fot(converse(top))]]) ).
cnf(refute_0_728,plain,
( converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(converse(top)) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),converse(top)) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
converse(converse(top)) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) )],[refute_0_712,refute_0_728]) ).
cnf(refute_0_730,plain,
converse(converse(top)) = top,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(top))]]) ).
cnf(refute_0_731,plain,
( converse(converse(top)) != complement(converse(zero))
| converse(converse(top)) != top
| top = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(top)),complement(converse(zero))) ),[0],$fot(top)]]) ).
cnf(refute_0_732,plain,
( converse(converse(top)) != complement(converse(zero))
| top = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
top = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(converse(top)),complement(converse(zero))) )],[refute_0_729,refute_0_732]) ).
cnf(refute_0_734,plain,
( top != complement(converse(zero))
| complement(converse(zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_735,plain,
complement(converse(zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(converse(zero))) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
( complement(complement(converse(zero))) != converse(zero)
| complement(converse(zero)) != top
| complement(top) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(converse(zero))),converse(zero)) ),[0,0],$fot(top)]]) ).
cnf(refute_0_737,plain,
( complement(complement(converse(zero))) != converse(zero)
| complement(top) = converse(zero) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_0_735,refute_0_736]) ).
cnf(refute_0_738,plain,
complement(top) = converse(zero),
inference(resolve,[$cnf( $equal(complement(complement(converse(zero))),converse(zero)) )],[refute_0_711,refute_0_737]) ).
cnf(refute_0_739,plain,
( complement(top) != converse(zero)
| complement(top) != zero
| zero = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(top),converse(zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_740,plain,
( complement(top) != converse(zero)
| zero = converse(zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_739]) ).
cnf(refute_0_741,plain,
zero = converse(zero),
inference(resolve,[$cnf( $equal(complement(top),converse(zero)) )],[refute_0_738,refute_0_740]) ).
cnf(refute_0_742,plain,
( zero != converse(zero)
| converse(zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(converse(zero)))]]) ).
cnf(refute_0_743,plain,
converse(zero) = zero,
inference(resolve,[$cnf( $equal(zero,converse(zero)) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
converse(complement(top)) = converse(complement(top)),
introduced(tautology,[refl,[$fot(converse(complement(top)))]]) ).
cnf(refute_0_745,plain,
( complement(top) != zero
| converse(complement(top)) != converse(complement(top))
| converse(complement(top)) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(top)),converse(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_746,plain,
( complement(top) != zero
| converse(complement(top)) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(complement(top))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
converse(complement(top)) = converse(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_114,refute_0_746]) ).
cnf(refute_0_748,plain,
( converse(complement(top)) != converse(zero)
| converse(zero) != zero
| converse(complement(top)) = zero ),
inference(subst,[],[refute_0_35:[bind(X,$fot(converse(complement(top)))),bind(Y,$fot(converse(zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_749,plain,
( converse(zero) != zero
| converse(complement(top)) = zero ),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(zero)) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
converse(complement(top)) = zero,
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_743,refute_0_749]) ).
cnf(refute_0_751,plain,
meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))),
introduced(tautology,[refl,[$fot(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))))]]) ).
cnf(refute_0_752,plain,
( converse(complement(top)) != zero
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374))))))
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))),meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_753,plain,
( converse(complement(top)) != zero
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))),meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374))))))) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))),
inference(resolve,[$cnf( $equal(converse(complement(top)),zero) )],[refute_0_750,refute_0_753]) ).
cnf(refute_0_755,plain,
( meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374))))))
| meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != meet(zero,meet(converse(X_374),converse(complement(X_374))))
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,meet(converse(X_374),converse(complement(X_374)))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))))),bind(Y,$fot(meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))))),bind(Z,$fot(meet(zero,meet(converse(X_374),converse(complement(X_374))))))]]) ).
cnf(refute_0_756,plain,
( meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != meet(zero,meet(converse(X_374),converse(complement(X_374))))
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,meet(converse(X_374),converse(complement(X_374)))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))),meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374))))))) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = meet(zero,meet(converse(X_374),converse(complement(X_374)))),
inference(resolve,[$cnf( $equal(meet(zero,complement(complement(meet(converse(X_374),converse(complement(X_374)))))),meet(zero,meet(converse(X_374),converse(complement(X_374))))) )],[refute_0_710,refute_0_756]) ).
cnf(refute_0_758,plain,
( meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != meet(zero,meet(converse(X_374),converse(complement(X_374))))
| meet(zero,meet(converse(X_374),converse(complement(X_374)))) != zero
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = zero ),
inference(subst,[],[refute_0_35:[bind(X,$fot(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))))),bind(Y,$fot(meet(zero,meet(converse(X_374),converse(complement(X_374)))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_759,plain,
( meet(zero,meet(converse(X_374),converse(complement(X_374)))) != zero
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = zero ),
inference(resolve,[$cnf( $equal(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))),meet(zero,meet(converse(X_374),converse(complement(X_374))))) )],[refute_0_757,refute_0_758]) ).
cnf(refute_0_760,plain,
meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) = zero,
inference(resolve,[$cnf( $equal(meet(zero,meet(converse(X_374),converse(complement(X_374)))),zero) )],[refute_0_706,refute_0_759]) ).
cnf(refute_0_761,plain,
( meet(X_26,X_27) != meet(X_27,X_26)
| meet(X_27,X_26) = meet(X_26,X_27) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_26,X_27))),bind(Y,$fot(meet(X_27,X_26)))]]) ).
cnf(refute_0_762,plain,
meet(X_27,X_26) = meet(X_26,X_27),
inference(resolve,[$cnf( $equal(meet(X_26,X_27),meet(X_27,X_26)) )],[refute_0_63,refute_0_761]) ).
cnf(refute_0_763,plain,
meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) = meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))),
inference(subst,[],[refute_0_762:[bind(X_26,$fot(converse(complement(top)))),bind(X_27,$fot(complement(complement(meet(converse(X_374),converse(complement(X_374)))))))]]) ).
cnf(refute_0_764,plain,
( meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) != meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374))))))
| meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != zero
| meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) = zero ),
inference(subst,[],[refute_0_35:[bind(X,$fot(meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))))),bind(Y,$fot(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_765,plain,
( meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))) != zero
| meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) = zero ),
inference(resolve,[$cnf( $equal(meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))),meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374))))))) )],[refute_0_763,refute_0_764]) ).
cnf(refute_0_766,plain,
meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) = zero,
inference(resolve,[$cnf( $equal(meet(converse(complement(top)),complement(complement(meet(converse(X_374),converse(complement(X_374)))))),zero) )],[refute_0_760,refute_0_765]) ).
cnf(refute_0_767,plain,
( meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))) != zero
| meet(converse(X_374),converse(complement(X_374))) != meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))
| meet(converse(X_374),converse(complement(X_374))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(X_374),converse(complement(X_374))),meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))) ),[1],$fot(zero)]]) ).
cnf(refute_0_768,plain,
( meet(converse(X_374),converse(complement(X_374))) != meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))
| meet(converse(X_374),converse(complement(X_374))) = zero ),
inference(resolve,[$cnf( $equal(meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top))),zero) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
( complement(complement(meet(converse(X_374),converse(complement(X_374))))) != meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))
| meet(converse(X_374),converse(complement(X_374))) = zero ),
inference(resolve,[$cnf( $equal(meet(converse(X_374),converse(complement(X_374))),meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))) )],[refute_0_664,refute_0_768]) ).
cnf(refute_0_770,plain,
meet(converse(X_374),converse(complement(X_374))) = zero,
inference(resolve,[$cnf( $equal(complement(complement(meet(converse(X_374),converse(complement(X_374))))),meet(complement(complement(meet(converse(X_374),converse(complement(X_374))))),converse(complement(top)))) )],[refute_0_661,refute_0_769]) ).
cnf(refute_0_771,plain,
meet(converse(X_380),converse(complement(X_380))) = zero,
inference(subst,[],[refute_0_770:[bind(X_374,$fot(X_380))]]) ).
cnf(refute_0_772,plain,
( join(converse(complement(X_380)),meet(converse(X_380),converse(complement(X_380)))) != converse(complement(X_380))
| meet(converse(X_380),converse(complement(X_380))) != zero
| join(converse(complement(X_380)),zero) = converse(complement(X_380)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(X_380)),meet(converse(X_380),converse(complement(X_380)))),converse(complement(X_380))) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_773,plain,
( join(converse(complement(X_380)),meet(converse(X_380),converse(complement(X_380)))) != converse(complement(X_380))
| join(converse(complement(X_380)),zero) = converse(complement(X_380)) ),
inference(resolve,[$cnf( $equal(meet(converse(X_380),converse(complement(X_380))),zero) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
join(converse(complement(X_380)),zero) = converse(complement(X_380)),
inference(resolve,[$cnf( $equal(join(converse(complement(X_380)),meet(converse(X_380),converse(complement(X_380)))),converse(complement(X_380))) )],[refute_0_227,refute_0_773]) ).
cnf(refute_0_775,plain,
join(zero,complement(converse(X_380))) = complement(converse(X_380)),
inference(subst,[],[refute_0_327:[bind(X_34,$fot(complement(converse(X_380))))]]) ).
cnf(refute_0_776,plain,
join(X_205,X_58) = join(meet(X_58,join(X_205,X_58)),meet(complement(X_58),join(X_205,X_58))),
inference(subst,[],[refute_0_74:[bind(X_59,$fot(join(X_205,X_58)))]]) ).
cnf(refute_0_777,plain,
( join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != X_34
| join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) = X_34 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),X_34) ),[0],$fot(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_778,plain,
( join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) = X_34 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),X_34) )],[refute_0_321,refute_0_777]) ).
cnf(refute_0_779,plain,
join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) = X_34,
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_291,refute_0_778]) ).
cnf(refute_0_780,plain,
join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) = meet(X_34,join(complement(X_27),meet(X_34,X_27))),
inference(subst,[],[refute_0_327:[bind(X_34,$fot(meet(X_34,join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_781,plain,
( join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))
| join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != meet(X_34,join(complement(X_27),meet(X_34,X_27)))
| join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) = meet(X_34,join(complement(X_27),meet(X_34,X_27))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))))),bind(Y,$fot(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))))),bind(Z,$fot(meet(X_34,join(complement(X_27),meet(X_34,X_27)))))]]) ).
cnf(refute_0_782,plain,
( join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))) != meet(X_34,join(complement(X_27),meet(X_34,X_27)))
| join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) = meet(X_34,join(complement(X_27),meet(X_34,X_27))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) )],[refute_0_291,refute_0_781]) ).
cnf(refute_0_783,plain,
join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) = meet(X_34,join(complement(X_27),meet(X_34,X_27))),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27)))),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) )],[refute_0_780,refute_0_782]) ).
cnf(refute_0_784,plain,
( join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != X_34
| join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != meet(X_34,join(complement(X_27),meet(X_34,X_27)))
| meet(X_34,join(complement(X_27),meet(X_34,X_27))) = X_34 ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),X_34) ),[0],$fot(meet(X_34,join(complement(X_27),meet(X_34,X_27))))]]) ).
cnf(refute_0_785,plain,
( join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))) != X_34
| meet(X_34,join(complement(X_27),meet(X_34,X_27))) = X_34 ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
meet(X_34,join(complement(X_27),meet(X_34,X_27))) = X_34,
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_34,join(complement(X_27),meet(X_34,X_27))))),X_34) )],[refute_0_779,refute_0_785]) ).
cnf(refute_0_787,plain,
join(join(complement(X_169),meet(X_58,X_169)),meet(X_58,join(complement(X_169),meet(X_58,X_169)))) = join(complement(X_169),meet(X_58,X_169)),
inference(subst,[],[refute_0_226:[bind(X_59,$fot(join(complement(X_169),meet(X_58,X_169))))]]) ).
cnf(refute_0_788,plain,
meet(X_58,join(complement(X_169),meet(X_58,X_169))) = X_58,
inference(subst,[],[refute_0_786:[bind(X_27,$fot(X_169)),bind(X_34,$fot(X_58))]]) ).
cnf(refute_0_789,plain,
( join(join(complement(X_169),meet(X_58,X_169)),meet(X_58,join(complement(X_169),meet(X_58,X_169)))) != join(complement(X_169),meet(X_58,X_169))
| meet(X_58,join(complement(X_169),meet(X_58,X_169))) != X_58
| join(join(complement(X_169),meet(X_58,X_169)),X_58) = join(complement(X_169),meet(X_58,X_169)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_169),meet(X_58,X_169)),meet(X_58,join(complement(X_169),meet(X_58,X_169)))),join(complement(X_169),meet(X_58,X_169))) ),[0,1],$fot(X_58)]]) ).
cnf(refute_0_790,plain,
( join(join(complement(X_169),meet(X_58,X_169)),meet(X_58,join(complement(X_169),meet(X_58,X_169)))) != join(complement(X_169),meet(X_58,X_169))
| join(join(complement(X_169),meet(X_58,X_169)),X_58) = join(complement(X_169),meet(X_58,X_169)) ),
inference(resolve,[$cnf( $equal(meet(X_58,join(complement(X_169),meet(X_58,X_169))),X_58) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
join(join(complement(X_169),meet(X_58,X_169)),X_58) = join(complement(X_169),meet(X_58,X_169)),
inference(resolve,[$cnf( $equal(join(join(complement(X_169),meet(X_58,X_169)),meet(X_58,join(complement(X_169),meet(X_58,X_169)))),join(complement(X_169),meet(X_58,X_169))) )],[refute_0_787,refute_0_790]) ).
cnf(refute_0_792,plain,
join(join(complement(X_169),meet(X_58,X_169)),X_58) = join(X_58,join(complement(X_169),meet(X_58,X_169))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(complement(X_169),meet(X_58,X_169)))),bind(B,$fot(X_58))]]) ).
cnf(refute_0_793,plain,
( join(join(complement(X_169),meet(X_58,X_169)),X_58) != join(X_58,join(complement(X_169),meet(X_58,X_169)))
| join(join(complement(X_169),meet(X_58,X_169)),X_58) != join(complement(X_169),meet(X_58,X_169))
| join(X_58,join(complement(X_169),meet(X_58,X_169))) = join(complement(X_169),meet(X_58,X_169)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_169),meet(X_58,X_169)),X_58),join(complement(X_169),meet(X_58,X_169))) ),[0],$fot(join(X_58,join(complement(X_169),meet(X_58,X_169))))]]) ).
cnf(refute_0_794,plain,
( join(join(complement(X_169),meet(X_58,X_169)),X_58) != join(complement(X_169),meet(X_58,X_169))
| join(X_58,join(complement(X_169),meet(X_58,X_169))) = join(complement(X_169),meet(X_58,X_169)) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_169),meet(X_58,X_169)),X_58),join(X_58,join(complement(X_169),meet(X_58,X_169)))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
join(X_58,join(complement(X_169),meet(X_58,X_169))) = join(complement(X_169),meet(X_58,X_169)),
inference(resolve,[$cnf( $equal(join(join(complement(X_169),meet(X_58,X_169)),X_58),join(complement(X_169),meet(X_58,X_169))) )],[refute_0_791,refute_0_794]) ).
cnf(refute_0_796,plain,
join(A,join(X_80,X_81)) = join(join(X_80,X_81),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_80,X_81)))]]) ).
cnf(refute_0_797,plain,
join(X_80,join(X_81,A)) = join(join(X_80,X_81),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_80)),bind(B,$fot(X_81)),bind(C,$fot(A))]]) ).
cnf(refute_0_798,plain,
( join(X_80,join(X_81,A)) != join(join(X_80,X_81),A)
| join(join(X_80,X_81),A) = join(X_80,join(X_81,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_80,join(X_81,A)))),bind(Y,$fot(join(join(X_80,X_81),A)))]]) ).
cnf(refute_0_799,plain,
join(join(X_80,X_81),A) = join(X_80,join(X_81,A)),
inference(resolve,[$cnf( $equal(join(X_80,join(X_81,A)),join(join(X_80,X_81),A)) )],[refute_0_797,refute_0_798]) ).
cnf(refute_0_800,plain,
( join(A,join(X_80,X_81)) != join(join(X_80,X_81),A)
| join(join(X_80,X_81),A) != join(X_80,join(X_81,A))
| join(A,join(X_80,X_81)) = join(X_80,join(X_81,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_80,X_81)),join(X_80,join(X_81,A))) ),[0],$fot(join(join(X_80,X_81),A))]]) ).
cnf(refute_0_801,plain,
( join(A,join(X_80,X_81)) != join(join(X_80,X_81),A)
| join(A,join(X_80,X_81)) = join(X_80,join(X_81,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_80,X_81),A),join(X_80,join(X_81,A))) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
join(A,join(X_80,X_81)) = join(X_80,join(X_81,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_80,X_81)),join(join(X_80,X_81),A)) )],[refute_0_796,refute_0_801]) ).
cnf(refute_0_803,plain,
join(meet(X_199,B),join(X_198,X_199)) = join(X_198,join(X_199,meet(X_199,B))),
inference(subst,[],[refute_0_802:[bind(A,$fot(meet(X_199,B))),bind(X_80,$fot(X_198)),bind(X_81,$fot(X_199))]]) ).
cnf(refute_0_804,plain,
join(meet(X_34,B),join(meet(X_34,B),meet(X_34,complement(B)))) = join(meet(X_34,B),meet(X_34,complement(B))),
inference(subst,[],[refute_0_213:[bind(B,$fot(meet(X_34,B))),bind(C,$fot(meet(X_34,complement(B))))]]) ).
cnf(refute_0_805,plain,
( X_34 != join(meet(X_34,B),meet(X_34,complement(B)))
| join(meet(X_34,B),meet(X_34,complement(B))) = X_34 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_34)),bind(Y,$fot(join(meet(X_34,B),meet(X_34,complement(B)))))]]) ).
cnf(refute_0_806,plain,
join(meet(X_34,B),meet(X_34,complement(B))) = X_34,
inference(resolve,[$cnf( $equal(X_34,join(meet(X_34,B),meet(X_34,complement(B)))) )],[refute_0_52,refute_0_805]) ).
cnf(refute_0_807,plain,
( join(meet(X_34,B),join(meet(X_34,B),meet(X_34,complement(B)))) != join(meet(X_34,B),meet(X_34,complement(B)))
| join(meet(X_34,B),meet(X_34,complement(B))) != X_34
| join(meet(X_34,B),X_34) = join(meet(X_34,B),meet(X_34,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_34,B),join(meet(X_34,B),meet(X_34,complement(B)))),join(meet(X_34,B),meet(X_34,complement(B)))) ),[0,1],$fot(X_34)]]) ).
cnf(refute_0_808,plain,
( join(meet(X_34,B),join(meet(X_34,B),meet(X_34,complement(B)))) != join(meet(X_34,B),meet(X_34,complement(B)))
| join(meet(X_34,B),X_34) = join(meet(X_34,B),meet(X_34,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,B),meet(X_34,complement(B))),X_34) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
join(meet(X_34,B),X_34) = join(meet(X_34,B),meet(X_34,complement(B))),
inference(resolve,[$cnf( $equal(join(meet(X_34,B),join(meet(X_34,B),meet(X_34,complement(B)))),join(meet(X_34,B),meet(X_34,complement(B)))) )],[refute_0_804,refute_0_808]) ).
cnf(refute_0_810,plain,
join(meet(X_34,B),X_34) = join(X_34,meet(X_34,B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_34)),bind(B,$fot(meet(X_34,B)))]]) ).
cnf(refute_0_811,plain,
( join(meet(X_34,B),X_34) != join(X_34,meet(X_34,B))
| join(meet(X_34,B),X_34) != join(meet(X_34,B),meet(X_34,complement(B)))
| join(X_34,meet(X_34,B)) = join(meet(X_34,B),meet(X_34,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_34,B),X_34),join(meet(X_34,B),meet(X_34,complement(B)))) ),[0],$fot(join(X_34,meet(X_34,B)))]]) ).
cnf(refute_0_812,plain,
( join(meet(X_34,B),X_34) != join(meet(X_34,B),meet(X_34,complement(B)))
| join(X_34,meet(X_34,B)) = join(meet(X_34,B),meet(X_34,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_34,B),X_34),join(X_34,meet(X_34,B))) )],[refute_0_810,refute_0_811]) ).
cnf(refute_0_813,plain,
( join(X_34,meet(X_34,B)) != join(meet(X_34,B),meet(X_34,complement(B)))
| join(meet(X_34,B),meet(X_34,complement(B))) != X_34
| join(X_34,meet(X_34,B)) = X_34 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_34,meet(X_34,B)),X_34) ),[0],$fot(join(meet(X_34,B),meet(X_34,complement(B))))]]) ).
cnf(refute_0_814,plain,
( join(X_34,meet(X_34,B)) != join(meet(X_34,B),meet(X_34,complement(B)))
| join(X_34,meet(X_34,B)) = X_34 ),
inference(resolve,[$cnf( $equal(join(meet(X_34,B),meet(X_34,complement(B))),X_34) )],[refute_0_806,refute_0_813]) ).
cnf(refute_0_815,plain,
( join(meet(X_34,B),X_34) != join(meet(X_34,B),meet(X_34,complement(B)))
| join(X_34,meet(X_34,B)) = X_34 ),
inference(resolve,[$cnf( $equal(join(X_34,meet(X_34,B)),join(meet(X_34,B),meet(X_34,complement(B)))) )],[refute_0_812,refute_0_814]) ).
cnf(refute_0_816,plain,
join(X_34,meet(X_34,B)) = X_34,
inference(resolve,[$cnf( $equal(join(meet(X_34,B),X_34),join(meet(X_34,B),meet(X_34,complement(B)))) )],[refute_0_809,refute_0_815]) ).
cnf(refute_0_817,plain,
join(X_199,meet(X_199,B)) = X_199,
inference(subst,[],[refute_0_816:[bind(X_34,$fot(X_199))]]) ).
cnf(refute_0_818,plain,
( join(X_199,meet(X_199,B)) != X_199
| join(meet(X_199,B),join(X_198,X_199)) != join(X_198,join(X_199,meet(X_199,B)))
| join(meet(X_199,B),join(X_198,X_199)) = join(X_198,X_199) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_199,B),join(X_198,X_199)),join(X_198,join(X_199,meet(X_199,B)))) ),[1,1],$fot(X_199)]]) ).
cnf(refute_0_819,plain,
( join(meet(X_199,B),join(X_198,X_199)) != join(X_198,join(X_199,meet(X_199,B)))
| join(meet(X_199,B),join(X_198,X_199)) = join(X_198,X_199) ),
inference(resolve,[$cnf( $equal(join(X_199,meet(X_199,B)),X_199) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
join(meet(X_199,B),join(X_198,X_199)) = join(X_198,X_199),
inference(resolve,[$cnf( $equal(join(meet(X_199,B),join(X_198,X_199)),join(X_198,join(X_199,meet(X_199,B)))) )],[refute_0_803,refute_0_819]) ).
cnf(refute_0_821,plain,
join(X_197,join(X_198,join(X_141,X_198))) = join(X_198,join(join(X_141,X_198),X_197)),
inference(subst,[],[refute_0_802:[bind(A,$fot(X_197)),bind(X_80,$fot(X_198)),bind(X_81,$fot(join(X_141,X_198)))]]) ).
cnf(refute_0_822,plain,
join(join(B,X_141),B) = join(B,join(B,X_141)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(B,X_141)))]]) ).
cnf(refute_0_823,plain,
join(B,join(B,X_141)) = join(B,X_141),
inference(subst,[],[refute_0_213:[bind(C,$fot(X_141))]]) ).
cnf(refute_0_824,plain,
( join(B,join(B,X_141)) != join(B,X_141)
| join(join(B,X_141),B) != join(B,join(B,X_141))
| join(join(B,X_141),B) = join(B,X_141) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(B,X_141),B),join(B,join(B,X_141))) ),[1],$fot(join(B,X_141))]]) ).
cnf(refute_0_825,plain,
( join(join(B,X_141),B) != join(B,join(B,X_141))
| join(join(B,X_141),B) = join(B,X_141) ),
inference(resolve,[$cnf( $equal(join(B,join(B,X_141)),join(B,X_141)) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
join(join(B,X_141),B) = join(B,X_141),
inference(resolve,[$cnf( $equal(join(join(B,X_141),B),join(B,join(B,X_141))) )],[refute_0_822,refute_0_825]) ).
cnf(refute_0_827,plain,
join(join(B,X_141),B) = join(B,join(X_141,B)),
inference(subst,[],[refute_0_298:[bind(A,$fot(B)),bind(B,$fot(X_141)),bind(C,$fot(B))]]) ).
cnf(refute_0_828,plain,
( join(join(B,X_141),B) != join(B,X_141)
| join(join(B,X_141),B) != join(B,join(X_141,B))
| join(B,join(X_141,B)) = join(B,X_141) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(B,X_141),B),join(B,X_141)) ),[0],$fot(join(B,join(X_141,B)))]]) ).
cnf(refute_0_829,plain,
( join(join(B,X_141),B) != join(B,X_141)
| join(B,join(X_141,B)) = join(B,X_141) ),
inference(resolve,[$cnf( $equal(join(join(B,X_141),B),join(B,join(X_141,B))) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
join(B,join(X_141,B)) = join(B,X_141),
inference(resolve,[$cnf( $equal(join(join(B,X_141),B),join(B,X_141)) )],[refute_0_826,refute_0_829]) ).
cnf(refute_0_831,plain,
join(X_198,join(X_141,X_198)) = join(X_198,X_141),
inference(subst,[],[refute_0_830:[bind(B,$fot(X_198))]]) ).
cnf(refute_0_832,plain,
( join(X_197,join(X_198,join(X_141,X_198))) != join(X_198,join(join(X_141,X_198),X_197))
| join(X_198,join(X_141,X_198)) != join(X_198,X_141)
| join(X_197,join(X_198,X_141)) = join(X_198,join(join(X_141,X_198),X_197)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_197,join(X_198,join(X_141,X_198))),join(X_198,join(join(X_141,X_198),X_197))) ),[0,1],$fot(join(X_198,X_141))]]) ).
cnf(refute_0_833,plain,
( join(X_197,join(X_198,join(X_141,X_198))) != join(X_198,join(join(X_141,X_198),X_197))
| join(X_197,join(X_198,X_141)) = join(X_198,join(join(X_141,X_198),X_197)) ),
inference(resolve,[$cnf( $equal(join(X_198,join(X_141,X_198)),join(X_198,X_141)) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
join(X_197,join(X_198,X_141)) = join(X_198,join(join(X_141,X_198),X_197)),
inference(resolve,[$cnf( $equal(join(X_197,join(X_198,join(X_141,X_198))),join(X_198,join(join(X_141,X_198),X_197))) )],[refute_0_821,refute_0_833]) ).
cnf(refute_0_835,plain,
join(A,join(B,join(B,X_141))) = join(join(A,B),join(B,X_141)),
inference(subst,[],[maddux2_join_associativity_2:[bind(C,$fot(join(B,X_141)))]]) ).
cnf(refute_0_836,plain,
( join(A,join(B,join(B,X_141))) != join(join(A,B),join(B,X_141))
| join(B,join(B,X_141)) != join(B,X_141)
| join(A,join(B,X_141)) = join(join(A,B),join(B,X_141)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(B,join(B,X_141))),join(join(A,B),join(B,X_141))) ),[0,1],$fot(join(B,X_141))]]) ).
cnf(refute_0_837,plain,
( join(A,join(B,join(B,X_141))) != join(join(A,B),join(B,X_141))
| join(A,join(B,X_141)) = join(join(A,B),join(B,X_141)) ),
inference(resolve,[$cnf( $equal(join(B,join(B,X_141)),join(B,X_141)) )],[refute_0_823,refute_0_836]) ).
cnf(refute_0_838,plain,
join(A,join(B,X_141)) = join(join(A,B),join(B,X_141)),
inference(resolve,[$cnf( $equal(join(A,join(B,join(B,X_141))),join(join(A,B),join(B,X_141))) )],[refute_0_835,refute_0_837]) ).
cnf(refute_0_839,plain,
join(join(A,B),X_141) = join(A,join(B,X_141)),
inference(subst,[],[refute_0_298:[bind(C,$fot(X_141))]]) ).
cnf(refute_0_840,plain,
join(B,join(join(A,B),X_141)) = join(B,join(join(A,B),X_141)),
introduced(tautology,[refl,[$fot(join(B,join(join(A,B),X_141)))]]) ).
cnf(refute_0_841,plain,
( join(B,join(join(A,B),X_141)) != join(B,join(join(A,B),X_141))
| join(join(A,B),X_141) != join(A,join(B,X_141))
| join(B,join(join(A,B),X_141)) = join(B,join(A,join(B,X_141))) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(join(A,B),X_141)),join(B,join(join(A,B),X_141))) ),[1,1],$fot(join(A,join(B,X_141)))]]) ).
cnf(refute_0_842,plain,
( join(join(A,B),X_141) != join(A,join(B,X_141))
| join(B,join(join(A,B),X_141)) = join(B,join(A,join(B,X_141))) ),
inference(resolve,[$cnf( $equal(join(B,join(join(A,B),X_141)),join(B,join(join(A,B),X_141))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
join(B,join(join(A,B),X_141)) = join(B,join(A,join(B,X_141))),
inference(resolve,[$cnf( $equal(join(join(A,B),X_141),join(A,join(B,X_141))) )],[refute_0_839,refute_0_842]) ).
cnf(refute_0_844,plain,
join(join(A,B),join(B,X_141)) = join(B,join(join(A,B),X_141)),
inference(subst,[],[refute_0_545:[bind(X_80,$fot(B)),bind(X_81,$fot(join(A,B))),bind(X_82,$fot(X_141))]]) ).
cnf(refute_0_845,plain,
( join(B,join(join(A,B),X_141)) != join(B,join(A,join(B,X_141)))
| join(join(A,B),join(B,X_141)) != join(B,join(join(A,B),X_141))
| join(join(A,B),join(B,X_141)) = join(B,join(A,join(B,X_141))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(join(A,B),join(B,X_141)))),bind(Y,$fot(join(B,join(join(A,B),X_141)))),bind(Z,$fot(join(B,join(A,join(B,X_141)))))]]) ).
cnf(refute_0_846,plain,
( join(B,join(join(A,B),X_141)) != join(B,join(A,join(B,X_141)))
| join(join(A,B),join(B,X_141)) = join(B,join(A,join(B,X_141))) ),
inference(resolve,[$cnf( $equal(join(join(A,B),join(B,X_141)),join(B,join(join(A,B),X_141))) )],[refute_0_844,refute_0_845]) ).
cnf(refute_0_847,plain,
join(join(A,B),join(B,X_141)) = join(B,join(A,join(B,X_141))),
inference(resolve,[$cnf( $equal(join(B,join(join(A,B),X_141)),join(B,join(A,join(B,X_141)))) )],[refute_0_843,refute_0_846]) ).
cnf(refute_0_848,plain,
( join(A,join(B,X_141)) != join(join(A,B),join(B,X_141))
| join(join(A,B),join(B,X_141)) != join(B,join(A,join(B,X_141)))
| join(A,join(B,X_141)) = join(B,join(A,join(B,X_141))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(B,X_141)),join(B,join(A,join(B,X_141)))) ),[0],$fot(join(join(A,B),join(B,X_141)))]]) ).
cnf(refute_0_849,plain,
( join(A,join(B,X_141)) != join(join(A,B),join(B,X_141))
| join(A,join(B,X_141)) = join(B,join(A,join(B,X_141))) ),
inference(resolve,[$cnf( $equal(join(join(A,B),join(B,X_141)),join(B,join(A,join(B,X_141)))) )],[refute_0_847,refute_0_848]) ).
cnf(refute_0_850,plain,
join(A,join(B,X_141)) = join(B,join(A,join(B,X_141))),
inference(resolve,[$cnf( $equal(join(A,join(B,X_141)),join(join(A,B),join(B,X_141))) )],[refute_0_838,refute_0_849]) ).
cnf(refute_0_851,plain,
( join(A,join(B,X_141)) != join(B,join(A,join(B,X_141)))
| join(B,join(A,join(B,X_141))) = join(A,join(B,X_141)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,X_141)))),bind(Y,$fot(join(B,join(A,join(B,X_141)))))]]) ).
cnf(refute_0_852,plain,
join(B,join(A,join(B,X_141))) = join(A,join(B,X_141)),
inference(resolve,[$cnf( $equal(join(A,join(B,X_141)),join(B,join(A,join(B,X_141)))) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
join(X_198,join(X_141,join(X_198,X_197))) = join(X_141,join(X_198,X_197)),
inference(subst,[],[refute_0_852:[bind(A,$fot(X_141)),bind(B,$fot(X_198)),bind(X_141,$fot(X_197))]]) ).
cnf(refute_0_854,plain,
join(join(X_141,X_198),X_197) = join(X_141,join(X_198,X_197)),
inference(subst,[],[refute_0_298:[bind(A,$fot(X_141)),bind(B,$fot(X_198)),bind(C,$fot(X_197))]]) ).
cnf(refute_0_855,plain,
join(X_198,join(join(X_141,X_198),X_197)) = join(X_198,join(join(X_141,X_198),X_197)),
introduced(tautology,[refl,[$fot(join(X_198,join(join(X_141,X_198),X_197)))]]) ).
cnf(refute_0_856,plain,
( join(X_198,join(join(X_141,X_198),X_197)) != join(X_198,join(join(X_141,X_198),X_197))
| join(join(X_141,X_198),X_197) != join(X_141,join(X_198,X_197))
| join(X_198,join(join(X_141,X_198),X_197)) = join(X_198,join(X_141,join(X_198,X_197))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_198,join(join(X_141,X_198),X_197)),join(X_198,join(join(X_141,X_198),X_197))) ),[1,1],$fot(join(X_141,join(X_198,X_197)))]]) ).
cnf(refute_0_857,plain,
( join(join(X_141,X_198),X_197) != join(X_141,join(X_198,X_197))
| join(X_198,join(join(X_141,X_198),X_197)) = join(X_198,join(X_141,join(X_198,X_197))) ),
inference(resolve,[$cnf( $equal(join(X_198,join(join(X_141,X_198),X_197)),join(X_198,join(join(X_141,X_198),X_197))) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
join(X_198,join(join(X_141,X_198),X_197)) = join(X_198,join(X_141,join(X_198,X_197))),
inference(resolve,[$cnf( $equal(join(join(X_141,X_198),X_197),join(X_141,join(X_198,X_197))) )],[refute_0_854,refute_0_857]) ).
cnf(refute_0_859,plain,
( join(X_198,join(X_141,join(X_198,X_197))) != join(X_141,join(X_198,X_197))
| join(X_198,join(join(X_141,X_198),X_197)) != join(X_198,join(X_141,join(X_198,X_197)))
| join(X_198,join(join(X_141,X_198),X_197)) = join(X_141,join(X_198,X_197)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(X_198,join(join(X_141,X_198),X_197)))),bind(Y,$fot(join(X_198,join(X_141,join(X_198,X_197))))),bind(Z,$fot(join(X_141,join(X_198,X_197))))]]) ).
cnf(refute_0_860,plain,
( join(X_198,join(X_141,join(X_198,X_197))) != join(X_141,join(X_198,X_197))
| join(X_198,join(join(X_141,X_198),X_197)) = join(X_141,join(X_198,X_197)) ),
inference(resolve,[$cnf( $equal(join(X_198,join(join(X_141,X_198),X_197)),join(X_198,join(X_141,join(X_198,X_197)))) )],[refute_0_858,refute_0_859]) ).
cnf(refute_0_861,plain,
join(X_198,join(join(X_141,X_198),X_197)) = join(X_141,join(X_198,X_197)),
inference(resolve,[$cnf( $equal(join(X_198,join(X_141,join(X_198,X_197))),join(X_141,join(X_198,X_197))) )],[refute_0_853,refute_0_860]) ).
cnf(refute_0_862,plain,
( join(X_197,join(X_198,X_141)) != join(X_198,join(join(X_141,X_198),X_197))
| join(X_198,join(join(X_141,X_198),X_197)) != join(X_141,join(X_198,X_197))
| join(X_197,join(X_198,X_141)) = join(X_141,join(X_198,X_197)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_197,join(X_198,X_141)),join(X_141,join(X_198,X_197))) ),[0],$fot(join(X_198,join(join(X_141,X_198),X_197)))]]) ).
cnf(refute_0_863,plain,
( join(X_197,join(X_198,X_141)) != join(X_198,join(join(X_141,X_198),X_197))
| join(X_197,join(X_198,X_141)) = join(X_141,join(X_198,X_197)) ),
inference(resolve,[$cnf( $equal(join(X_198,join(join(X_141,X_198),X_197)),join(X_141,join(X_198,X_197))) )],[refute_0_861,refute_0_862]) ).
cnf(refute_0_864,plain,
join(X_197,join(X_198,X_141)) = join(X_141,join(X_198,X_197)),
inference(resolve,[$cnf( $equal(join(X_197,join(X_198,X_141)),join(X_198,join(join(X_141,X_198),X_197))) )],[refute_0_834,refute_0_863]) ).
cnf(refute_0_865,plain,
( join(X_197,join(X_198,X_141)) != join(X_141,join(X_198,X_197))
| join(X_141,join(X_198,X_197)) = join(X_197,join(X_198,X_141)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_197,join(X_198,X_141)))),bind(Y,$fot(join(X_141,join(X_198,X_197))))]]) ).
cnf(refute_0_866,plain,
join(X_141,join(X_198,X_197)) = join(X_197,join(X_198,X_141)),
inference(resolve,[$cnf( $equal(join(X_197,join(X_198,X_141)),join(X_141,join(X_198,X_197))) )],[refute_0_864,refute_0_865]) ).
cnf(refute_0_867,plain,
join(meet(X_199,B),join(X_198,X_199)) = join(X_199,join(X_198,meet(X_199,B))),
inference(subst,[],[refute_0_866:[bind(X_141,$fot(meet(X_199,B))),bind(X_197,$fot(X_199))]]) ).
cnf(refute_0_868,plain,
( join(meet(X_199,B),join(X_198,X_199)) != join(X_198,X_199)
| join(meet(X_199,B),join(X_198,X_199)) != join(X_199,join(X_198,meet(X_199,B)))
| join(X_199,join(X_198,meet(X_199,B))) = join(X_198,X_199) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_199,B),join(X_198,X_199)),join(X_198,X_199)) ),[0],$fot(join(X_199,join(X_198,meet(X_199,B))))]]) ).
cnf(refute_0_869,plain,
( join(meet(X_199,B),join(X_198,X_199)) != join(X_198,X_199)
| join(X_199,join(X_198,meet(X_199,B))) = join(X_198,X_199) ),
inference(resolve,[$cnf( $equal(join(meet(X_199,B),join(X_198,X_199)),join(X_199,join(X_198,meet(X_199,B)))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
join(X_199,join(X_198,meet(X_199,B))) = join(X_198,X_199),
inference(resolve,[$cnf( $equal(join(meet(X_199,B),join(X_198,X_199)),join(X_198,X_199)) )],[refute_0_820,refute_0_869]) ).
cnf(refute_0_871,plain,
join(X_58,join(complement(X_169),meet(X_58,X_169))) = join(complement(X_169),X_58),
inference(subst,[],[refute_0_870:[bind(B,$fot(X_169)),bind(X_198,$fot(complement(X_169))),bind(X_199,$fot(X_58))]]) ).
cnf(refute_0_872,plain,
( join(X_58,join(complement(X_169),meet(X_58,X_169))) != join(complement(X_169),X_58)
| join(X_58,join(complement(X_169),meet(X_58,X_169))) != join(complement(X_169),meet(X_58,X_169))
| join(complement(X_169),X_58) = join(complement(X_169),meet(X_58,X_169)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_58,join(complement(X_169),meet(X_58,X_169))),join(complement(X_169),meet(X_58,X_169))) ),[0],$fot(join(complement(X_169),X_58))]]) ).
cnf(refute_0_873,plain,
( join(X_58,join(complement(X_169),meet(X_58,X_169))) != join(complement(X_169),meet(X_58,X_169))
| join(complement(X_169),X_58) = join(complement(X_169),meet(X_58,X_169)) ),
inference(resolve,[$cnf( $equal(join(X_58,join(complement(X_169),meet(X_58,X_169))),join(complement(X_169),X_58)) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
join(complement(X_169),X_58) = join(complement(X_169),meet(X_58,X_169)),
inference(resolve,[$cnf( $equal(join(X_58,join(complement(X_169),meet(X_58,X_169))),join(complement(X_169),meet(X_58,X_169))) )],[refute_0_795,refute_0_873]) ).
cnf(refute_0_875,plain,
( join(complement(X_169),X_58) != join(complement(X_169),meet(X_58,X_169))
| join(complement(X_169),meet(X_58,X_169)) = join(complement(X_169),X_58) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_169),X_58))),bind(Y,$fot(join(complement(X_169),meet(X_58,X_169))))]]) ).
cnf(refute_0_876,plain,
join(complement(X_169),meet(X_58,X_169)) = join(complement(X_169),X_58),
inference(resolve,[$cnf( $equal(join(complement(X_169),X_58),join(complement(X_169),meet(X_58,X_169))) )],[refute_0_874,refute_0_875]) ).
cnf(refute_0_877,plain,
join(complement(X_27),meet(X_34,X_27)) = join(complement(X_27),X_34),
inference(subst,[],[refute_0_876:[bind(X_169,$fot(X_27)),bind(X_58,$fot(X_34))]]) ).
cnf(refute_0_878,plain,
meet(X_34,join(complement(X_27),meet(X_34,X_27))) = meet(X_34,join(complement(X_27),meet(X_34,X_27))),
introduced(tautology,[refl,[$fot(meet(X_34,join(complement(X_27),meet(X_34,X_27))))]]) ).
cnf(refute_0_879,plain,
( join(complement(X_27),meet(X_34,X_27)) != join(complement(X_27),X_34)
| meet(X_34,join(complement(X_27),meet(X_34,X_27))) != meet(X_34,join(complement(X_27),meet(X_34,X_27)))
| meet(X_34,join(complement(X_27),meet(X_34,X_27))) = meet(X_34,join(complement(X_27),X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_34,join(complement(X_27),meet(X_34,X_27))),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) ),[1,1],$fot(join(complement(X_27),X_34))]]) ).
cnf(refute_0_880,plain,
( join(complement(X_27),meet(X_34,X_27)) != join(complement(X_27),X_34)
| meet(X_34,join(complement(X_27),meet(X_34,X_27))) = meet(X_34,join(complement(X_27),X_34)) ),
inference(resolve,[$cnf( $equal(meet(X_34,join(complement(X_27),meet(X_34,X_27))),meet(X_34,join(complement(X_27),meet(X_34,X_27)))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
meet(X_34,join(complement(X_27),meet(X_34,X_27))) = meet(X_34,join(complement(X_27),X_34)),
inference(resolve,[$cnf( $equal(join(complement(X_27),meet(X_34,X_27)),join(complement(X_27),X_34)) )],[refute_0_877,refute_0_880]) ).
cnf(refute_0_882,plain,
( meet(X_34,join(complement(X_27),meet(X_34,X_27))) != X_34
| meet(X_34,join(complement(X_27),meet(X_34,X_27))) != meet(X_34,join(complement(X_27),X_34))
| meet(X_34,join(complement(X_27),X_34)) = X_34 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_34,join(complement(X_27),meet(X_34,X_27))),X_34) ),[0],$fot(meet(X_34,join(complement(X_27),X_34)))]]) ).
cnf(refute_0_883,plain,
( meet(X_34,join(complement(X_27),meet(X_34,X_27))) != X_34
| meet(X_34,join(complement(X_27),X_34)) = X_34 ),
inference(resolve,[$cnf( $equal(meet(X_34,join(complement(X_27),meet(X_34,X_27))),meet(X_34,join(complement(X_27),X_34))) )],[refute_0_881,refute_0_882]) ).
cnf(refute_0_884,plain,
meet(X_34,join(complement(X_27),X_34)) = X_34,
inference(resolve,[$cnf( $equal(meet(X_34,join(complement(X_27),meet(X_34,X_27))),X_34) )],[refute_0_786,refute_0_883]) ).
cnf(refute_0_885,plain,
meet(X_203,join(complement(complement(X_69)),X_203)) = X_203,
inference(subst,[],[refute_0_884:[bind(X_27,$fot(complement(X_69))),bind(X_34,$fot(X_203))]]) ).
cnf(refute_0_886,plain,
( complement(complement(X_69)) != X_69
| meet(X_203,join(complement(complement(X_69)),X_203)) != X_203
| meet(X_203,join(X_69,X_203)) = X_203 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_203,join(complement(complement(X_69)),X_203)),X_203) ),[0,1,0],$fot(X_69)]]) ).
cnf(refute_0_887,plain,
( meet(X_203,join(complement(complement(X_69)),X_203)) != X_203
| meet(X_203,join(X_69,X_203)) = X_203 ),
inference(resolve,[$cnf( $equal(complement(complement(X_69)),X_69) )],[refute_0_135,refute_0_886]) ).
cnf(refute_0_888,plain,
meet(X_203,join(X_69,X_203)) = X_203,
inference(resolve,[$cnf( $equal(meet(X_203,join(complement(complement(X_69)),X_203)),X_203) )],[refute_0_885,refute_0_887]) ).
cnf(refute_0_889,plain,
meet(X_58,join(X_205,X_58)) = X_58,
inference(subst,[],[refute_0_888:[bind(X_203,$fot(X_58)),bind(X_69,$fot(X_205))]]) ).
cnf(refute_0_890,plain,
( join(X_205,X_58) != join(meet(X_58,join(X_205,X_58)),meet(complement(X_58),join(X_205,X_58)))
| meet(X_58,join(X_205,X_58)) != X_58
| join(X_205,X_58) = join(X_58,meet(complement(X_58),join(X_205,X_58))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_205,X_58),join(meet(X_58,join(X_205,X_58)),meet(complement(X_58),join(X_205,X_58)))) ),[1,0],$fot(X_58)]]) ).
cnf(refute_0_891,plain,
( join(X_205,X_58) != join(meet(X_58,join(X_205,X_58)),meet(complement(X_58),join(X_205,X_58)))
| join(X_205,X_58) = join(X_58,meet(complement(X_58),join(X_205,X_58))) ),
inference(resolve,[$cnf( $equal(meet(X_58,join(X_205,X_58)),X_58) )],[refute_0_889,refute_0_890]) ).
cnf(refute_0_892,plain,
join(X_205,X_58) = join(X_58,meet(complement(X_58),join(X_205,X_58))),
inference(resolve,[$cnf( $equal(join(X_205,X_58),join(meet(X_58,join(X_205,X_58)),meet(complement(X_58),join(X_205,X_58)))) )],[refute_0_776,refute_0_891]) ).
cnf(refute_0_893,plain,
join(X_58,join(X_205,X_58)) = join(X_58,X_205),
inference(subst,[],[refute_0_830:[bind(B,$fot(X_58)),bind(X_141,$fot(X_205))]]) ).
cnf(refute_0_894,plain,
join(join(X_328,meet(complement(X_328),X_58)),meet(X_58,join(X_328,meet(complement(X_328),X_58)))) = join(X_328,meet(complement(X_328),X_58)),
inference(subst,[],[refute_0_226:[bind(X_59,$fot(join(X_328,meet(complement(X_328),X_58))))]]) ).
cnf(refute_0_895,plain,
X_62 = join(zero,meet(X_62,join(complement(X_61),meet(X_62,X_61)))),
inference(subst,[],[refute_0_319:[bind(X_27,$fot(X_61)),bind(X_34,$fot(X_62))]]) ).
cnf(refute_0_896,plain,
meet(X_61,X_62) = meet(X_62,X_61),
inference(subst,[],[refute_0_63:[bind(X_26,$fot(X_61)),bind(X_27,$fot(X_62))]]) ).
cnf(refute_0_897,plain,
( meet(X_61,X_62) != meet(X_62,X_61)
| meet(X_62,X_61) = meet(X_61,X_62) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_61,X_62))),bind(Y,$fot(meet(X_62,X_61)))]]) ).
cnf(refute_0_898,plain,
meet(X_62,X_61) = meet(X_61,X_62),
inference(resolve,[$cnf( $equal(meet(X_61,X_62),meet(X_62,X_61)) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
( X_62 != join(zero,meet(X_62,join(complement(X_61),meet(X_62,X_61))))
| meet(X_62,X_61) != meet(X_61,X_62)
| X_62 = join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_62,join(zero,meet(X_62,join(complement(X_61),meet(X_62,X_61))))) ),[1,1,1,1],$fot(meet(X_61,X_62))]]) ).
cnf(refute_0_900,plain,
( X_62 != join(zero,meet(X_62,join(complement(X_61),meet(X_62,X_61))))
| X_62 = join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62)))) ),
inference(resolve,[$cnf( $equal(meet(X_62,X_61),meet(X_61,X_62)) )],[refute_0_898,refute_0_899]) ).
cnf(refute_0_901,plain,
X_62 = join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62)))),
inference(resolve,[$cnf( $equal(X_62,join(zero,meet(X_62,join(complement(X_61),meet(X_62,X_61))))) )],[refute_0_895,refute_0_900]) ).
cnf(refute_0_902,plain,
join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62)))) = meet(X_62,join(complement(X_61),meet(X_61,X_62))),
inference(subst,[],[refute_0_327:[bind(X_34,$fot(meet(X_62,join(complement(X_61),meet(X_61,X_62)))))]]) ).
cnf(refute_0_903,plain,
( X_62 != join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62))))
| join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62)))) != meet(X_62,join(complement(X_61),meet(X_61,X_62)))
| X_62 = meet(X_62,join(complement(X_61),meet(X_61,X_62))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_62,meet(X_62,join(complement(X_61),meet(X_61,X_62)))) ),[0],$fot(join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62)))))]]) ).
cnf(refute_0_904,plain,
( X_62 != join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62))))
| X_62 = meet(X_62,join(complement(X_61),meet(X_61,X_62))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62)))),meet(X_62,join(complement(X_61),meet(X_61,X_62)))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
X_62 = meet(X_62,join(complement(X_61),meet(X_61,X_62))),
inference(resolve,[$cnf( $equal(X_62,join(zero,meet(X_62,join(complement(X_61),meet(X_61,X_62))))) )],[refute_0_901,refute_0_904]) ).
cnf(refute_0_906,plain,
X_132 = meet(X_132,join(complement(complement(X_69)),meet(complement(X_69),X_132))),
inference(subst,[],[refute_0_905:[bind(X_61,$fot(complement(X_69))),bind(X_62,$fot(X_132))]]) ).
cnf(refute_0_907,plain,
( X_132 != meet(X_132,join(complement(complement(X_69)),meet(complement(X_69),X_132)))
| complement(complement(X_69)) != X_69
| X_132 = meet(X_132,join(X_69,meet(complement(X_69),X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(X_132,meet(X_132,join(complement(complement(X_69)),meet(complement(X_69),X_132)))) ),[1,1,0],$fot(X_69)]]) ).
cnf(refute_0_908,plain,
( X_132 != meet(X_132,join(complement(complement(X_69)),meet(complement(X_69),X_132)))
| X_132 = meet(X_132,join(X_69,meet(complement(X_69),X_132))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_69)),X_69) )],[refute_0_135,refute_0_907]) ).
cnf(refute_0_909,plain,
X_132 = meet(X_132,join(X_69,meet(complement(X_69),X_132))),
inference(resolve,[$cnf( $equal(X_132,meet(X_132,join(complement(complement(X_69)),meet(complement(X_69),X_132)))) )],[refute_0_906,refute_0_908]) ).
cnf(refute_0_910,plain,
X_58 = meet(X_58,join(X_328,meet(complement(X_328),X_58))),
inference(subst,[],[refute_0_909:[bind(X_132,$fot(X_58)),bind(X_69,$fot(X_328))]]) ).
cnf(refute_0_911,plain,
( X_58 != meet(X_58,join(X_328,meet(complement(X_328),X_58)))
| meet(X_58,join(X_328,meet(complement(X_328),X_58))) = X_58 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_58)),bind(Y,$fot(meet(X_58,join(X_328,meet(complement(X_328),X_58)))))]]) ).
cnf(refute_0_912,plain,
meet(X_58,join(X_328,meet(complement(X_328),X_58))) = X_58,
inference(resolve,[$cnf( $equal(X_58,meet(X_58,join(X_328,meet(complement(X_328),X_58)))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
( join(join(X_328,meet(complement(X_328),X_58)),meet(X_58,join(X_328,meet(complement(X_328),X_58)))) != join(X_328,meet(complement(X_328),X_58))
| meet(X_58,join(X_328,meet(complement(X_328),X_58))) != X_58
| join(join(X_328,meet(complement(X_328),X_58)),X_58) = join(X_328,meet(complement(X_328),X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_328,meet(complement(X_328),X_58)),meet(X_58,join(X_328,meet(complement(X_328),X_58)))),join(X_328,meet(complement(X_328),X_58))) ),[0,1],$fot(X_58)]]) ).
cnf(refute_0_914,plain,
( join(join(X_328,meet(complement(X_328),X_58)),meet(X_58,join(X_328,meet(complement(X_328),X_58)))) != join(X_328,meet(complement(X_328),X_58))
| join(join(X_328,meet(complement(X_328),X_58)),X_58) = join(X_328,meet(complement(X_328),X_58)) ),
inference(resolve,[$cnf( $equal(meet(X_58,join(X_328,meet(complement(X_328),X_58))),X_58) )],[refute_0_912,refute_0_913]) ).
cnf(refute_0_915,plain,
join(join(X_328,meet(complement(X_328),X_58)),X_58) = join(X_328,meet(complement(X_328),X_58)),
inference(resolve,[$cnf( $equal(join(join(X_328,meet(complement(X_328),X_58)),meet(X_58,join(X_328,meet(complement(X_328),X_58)))),join(X_328,meet(complement(X_328),X_58))) )],[refute_0_894,refute_0_914]) ).
cnf(refute_0_916,plain,
join(meet(X_58,X_199),join(X_198,X_199)) = join(X_198,join(X_199,meet(X_58,X_199))),
inference(subst,[],[refute_0_802:[bind(A,$fot(meet(X_58,X_199))),bind(X_80,$fot(X_198)),bind(X_81,$fot(X_199))]]) ).
cnf(refute_0_917,plain,
join(X_199,meet(X_58,X_199)) = X_199,
inference(subst,[],[refute_0_226:[bind(X_59,$fot(X_199))]]) ).
cnf(refute_0_918,plain,
( join(X_199,meet(X_58,X_199)) != X_199
| join(meet(X_58,X_199),join(X_198,X_199)) != join(X_198,join(X_199,meet(X_58,X_199)))
| join(meet(X_58,X_199),join(X_198,X_199)) = join(X_198,X_199) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_58,X_199),join(X_198,X_199)),join(X_198,join(X_199,meet(X_58,X_199)))) ),[1,1],$fot(X_199)]]) ).
cnf(refute_0_919,plain,
( join(meet(X_58,X_199),join(X_198,X_199)) != join(X_198,join(X_199,meet(X_58,X_199)))
| join(meet(X_58,X_199),join(X_198,X_199)) = join(X_198,X_199) ),
inference(resolve,[$cnf( $equal(join(X_199,meet(X_58,X_199)),X_199) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
join(meet(X_58,X_199),join(X_198,X_199)) = join(X_198,X_199),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_199),join(X_198,X_199)),join(X_198,join(X_199,meet(X_58,X_199)))) )],[refute_0_916,refute_0_919]) ).
cnf(refute_0_921,plain,
join(meet(X_58,X_199),join(X_198,X_199)) = join(X_199,join(X_198,meet(X_58,X_199))),
inference(subst,[],[refute_0_866:[bind(X_141,$fot(meet(X_58,X_199))),bind(X_197,$fot(X_199))]]) ).
cnf(refute_0_922,plain,
( join(meet(X_58,X_199),join(X_198,X_199)) != join(X_198,X_199)
| join(meet(X_58,X_199),join(X_198,X_199)) != join(X_199,join(X_198,meet(X_58,X_199)))
| join(X_199,join(X_198,meet(X_58,X_199))) = join(X_198,X_199) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_58,X_199),join(X_198,X_199)),join(X_198,X_199)) ),[0],$fot(join(X_199,join(X_198,meet(X_58,X_199))))]]) ).
cnf(refute_0_923,plain,
( join(meet(X_58,X_199),join(X_198,X_199)) != join(X_198,X_199)
| join(X_199,join(X_198,meet(X_58,X_199))) = join(X_198,X_199) ),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_199),join(X_198,X_199)),join(X_199,join(X_198,meet(X_58,X_199)))) )],[refute_0_921,refute_0_922]) ).
cnf(refute_0_924,plain,
join(X_199,join(X_198,meet(X_58,X_199))) = join(X_198,X_199),
inference(resolve,[$cnf( $equal(join(meet(X_58,X_199),join(X_198,X_199)),join(X_198,X_199)) )],[refute_0_920,refute_0_923]) ).
cnf(refute_0_925,plain,
join(X_58,join(X_328,meet(complement(X_328),X_58))) = join(X_328,X_58),
inference(subst,[],[refute_0_924:[bind(X_198,$fot(X_328)),bind(X_199,$fot(X_58)),bind(X_58,$fot(complement(X_328)))]]) ).
cnf(refute_0_926,plain,
join(join(X_328,meet(complement(X_328),X_58)),X_58) = join(X_58,join(X_328,meet(complement(X_328),X_58))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(X_328,meet(complement(X_328),X_58)))),bind(B,$fot(X_58))]]) ).
cnf(refute_0_927,plain,
( join(X_58,join(X_328,meet(complement(X_328),X_58))) != join(X_328,X_58)
| join(join(X_328,meet(complement(X_328),X_58)),X_58) != join(X_58,join(X_328,meet(complement(X_328),X_58)))
| join(join(X_328,meet(complement(X_328),X_58)),X_58) = join(X_328,X_58) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(join(X_328,meet(complement(X_328),X_58)),X_58))),bind(Y,$fot(join(X_58,join(X_328,meet(complement(X_328),X_58))))),bind(Z,$fot(join(X_328,X_58)))]]) ).
cnf(refute_0_928,plain,
( join(X_58,join(X_328,meet(complement(X_328),X_58))) != join(X_328,X_58)
| join(join(X_328,meet(complement(X_328),X_58)),X_58) = join(X_328,X_58) ),
inference(resolve,[$cnf( $equal(join(join(X_328,meet(complement(X_328),X_58)),X_58),join(X_58,join(X_328,meet(complement(X_328),X_58)))) )],[refute_0_926,refute_0_927]) ).
cnf(refute_0_929,plain,
join(join(X_328,meet(complement(X_328),X_58)),X_58) = join(X_328,X_58),
inference(resolve,[$cnf( $equal(join(X_58,join(X_328,meet(complement(X_328),X_58))),join(X_328,X_58)) )],[refute_0_925,refute_0_928]) ).
cnf(refute_0_930,plain,
( join(join(X_328,meet(complement(X_328),X_58)),X_58) != join(X_328,X_58)
| join(join(X_328,meet(complement(X_328),X_58)),X_58) != join(X_328,meet(complement(X_328),X_58))
| join(X_328,X_58) = join(X_328,meet(complement(X_328),X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_328,meet(complement(X_328),X_58)),X_58),join(X_328,meet(complement(X_328),X_58))) ),[0],$fot(join(X_328,X_58))]]) ).
cnf(refute_0_931,plain,
( join(join(X_328,meet(complement(X_328),X_58)),X_58) != join(X_328,meet(complement(X_328),X_58))
| join(X_328,X_58) = join(X_328,meet(complement(X_328),X_58)) ),
inference(resolve,[$cnf( $equal(join(join(X_328,meet(complement(X_328),X_58)),X_58),join(X_328,X_58)) )],[refute_0_929,refute_0_930]) ).
cnf(refute_0_932,plain,
join(X_328,X_58) = join(X_328,meet(complement(X_328),X_58)),
inference(resolve,[$cnf( $equal(join(join(X_328,meet(complement(X_328),X_58)),X_58),join(X_328,meet(complement(X_328),X_58))) )],[refute_0_915,refute_0_931]) ).
cnf(refute_0_933,plain,
( join(X_328,X_58) != join(X_328,meet(complement(X_328),X_58))
| join(X_328,meet(complement(X_328),X_58)) = join(X_328,X_58) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_328,X_58))),bind(Y,$fot(join(X_328,meet(complement(X_328),X_58))))]]) ).
cnf(refute_0_934,plain,
join(X_328,meet(complement(X_328),X_58)) = join(X_328,X_58),
inference(resolve,[$cnf( $equal(join(X_328,X_58),join(X_328,meet(complement(X_328),X_58))) )],[refute_0_932,refute_0_933]) ).
cnf(refute_0_935,plain,
join(X_58,meet(complement(X_58),join(X_205,X_58))) = join(X_58,join(X_205,X_58)),
inference(subst,[],[refute_0_934:[bind(X_328,$fot(X_58)),bind(X_58,$fot(join(X_205,X_58)))]]) ).
cnf(refute_0_936,plain,
( join(X_58,join(X_205,X_58)) != join(X_58,X_205)
| join(X_58,meet(complement(X_58),join(X_205,X_58))) != join(X_58,join(X_205,X_58))
| join(X_58,meet(complement(X_58),join(X_205,X_58))) = join(X_58,X_205) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(X_58,meet(complement(X_58),join(X_205,X_58))))),bind(Y,$fot(join(X_58,join(X_205,X_58)))),bind(Z,$fot(join(X_58,X_205)))]]) ).
cnf(refute_0_937,plain,
( join(X_58,join(X_205,X_58)) != join(X_58,X_205)
| join(X_58,meet(complement(X_58),join(X_205,X_58))) = join(X_58,X_205) ),
inference(resolve,[$cnf( $equal(join(X_58,meet(complement(X_58),join(X_205,X_58))),join(X_58,join(X_205,X_58))) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
join(X_58,meet(complement(X_58),join(X_205,X_58))) = join(X_58,X_205),
inference(resolve,[$cnf( $equal(join(X_58,join(X_205,X_58)),join(X_58,X_205)) )],[refute_0_893,refute_0_937]) ).
cnf(refute_0_939,plain,
( join(X_205,X_58) != join(X_58,meet(complement(X_58),join(X_205,X_58)))
| join(X_58,meet(complement(X_58),join(X_205,X_58))) != join(X_58,X_205)
| join(X_205,X_58) = join(X_58,X_205) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_205,X_58),join(X_58,X_205)) ),[0],$fot(join(X_58,meet(complement(X_58),join(X_205,X_58))))]]) ).
cnf(refute_0_940,plain,
( join(X_205,X_58) != join(X_58,meet(complement(X_58),join(X_205,X_58)))
| join(X_205,X_58) = join(X_58,X_205) ),
inference(resolve,[$cnf( $equal(join(X_58,meet(complement(X_58),join(X_205,X_58))),join(X_58,X_205)) )],[refute_0_938,refute_0_939]) ).
cnf(refute_0_941,plain,
join(X_205,X_58) = join(X_58,X_205),
inference(resolve,[$cnf( $equal(join(X_205,X_58),join(X_58,meet(complement(X_58),join(X_205,X_58)))) )],[refute_0_892,refute_0_940]) ).
cnf(refute_0_942,plain,
( join(X_205,X_58) != join(X_58,X_205)
| join(X_58,X_205) = join(X_205,X_58) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_205,X_58))),bind(Y,$fot(join(X_58,X_205)))]]) ).
cnf(refute_0_943,plain,
join(X_58,X_205) = join(X_205,X_58),
inference(resolve,[$cnf( $equal(join(X_205,X_58),join(X_58,X_205)) )],[refute_0_941,refute_0_942]) ).
cnf(refute_0_944,plain,
join(complement(converse(X_380)),zero) = join(zero,complement(converse(X_380))),
inference(subst,[],[refute_0_943:[bind(X_205,$fot(zero)),bind(X_58,$fot(complement(converse(X_380))))]]) ).
cnf(refute_0_945,plain,
( join(complement(converse(X_380)),zero) != join(zero,complement(converse(X_380)))
| join(zero,complement(converse(X_380))) != complement(converse(X_380))
| join(complement(converse(X_380)),zero) = complement(converse(X_380)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(converse(X_380)),zero))),bind(Y,$fot(join(zero,complement(converse(X_380))))),bind(Z,$fot(complement(converse(X_380))))]]) ).
cnf(refute_0_946,plain,
( join(zero,complement(converse(X_380))) != complement(converse(X_380))
| join(complement(converse(X_380)),zero) = complement(converse(X_380)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X_380)),zero),join(zero,complement(converse(X_380)))) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
join(complement(converse(X_380)),zero) = complement(converse(X_380)),
inference(resolve,[$cnf( $equal(join(zero,complement(converse(X_380))),complement(converse(X_380))) )],[refute_0_775,refute_0_946]) ).
cnf(refute_0_948,plain,
join(meet(converse(X_380),converse(complement(X_380))),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(converse(complement(X_380)),X_82),
inference(subst,[],[refute_0_625:[bind(X_58,$fot(converse(X_380))),bind(X_59,$fot(converse(complement(X_380))))]]) ).
cnf(refute_0_949,plain,
( join(meet(converse(X_380),converse(complement(X_380))),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) != join(converse(complement(X_380)),X_82)
| meet(converse(X_380),converse(complement(X_380))) != zero
| join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(converse(complement(X_380)),X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(converse(X_380),converse(complement(X_380))),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)),join(converse(complement(X_380)),X_82)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_950,plain,
( join(meet(converse(X_380),converse(complement(X_380))),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) != join(converse(complement(X_380)),X_82)
| join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(converse(complement(X_380)),X_82) ),
inference(resolve,[$cnf( $equal(meet(converse(X_380),converse(complement(X_380))),zero) )],[refute_0_771,refute_0_949]) ).
cnf(refute_0_951,plain,
join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(converse(complement(X_380)),X_82),
inference(resolve,[$cnf( $equal(join(meet(converse(X_380),converse(complement(X_380))),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)),join(converse(complement(X_380)),X_82)) )],[refute_0_948,refute_0_950]) ).
cnf(refute_0_952,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(converse(converse(A))))),
inference(subst,[],[refute_0_595:[bind(X_72,$fot(converse(A)))]]) ).
cnf(refute_0_953,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_954,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( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_953]) ).
cnf(refute_0_955,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(converse(converse(A)))))) )],[refute_0_952,refute_0_954]) ).
cnf(refute_0_956,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(A)))
| meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(converse(A)))),bind(Y,$fot(meet(complement(converse(A)),converse(complement(A)))))]]) ).
cnf(refute_0_957,plain,
meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(A)))) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
meet(complement(converse(X_380)),converse(complement(X_380))) = complement(converse(X_380)),
inference(subst,[],[refute_0_957:[bind(A,$fot(X_380))]]) ).
cnf(refute_0_959,plain,
join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82) = join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82),
introduced(tautology,[refl,[$fot(join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82))]]) ).
cnf(refute_0_960,plain,
( join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82) != join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)
| meet(complement(converse(X_380)),converse(complement(X_380))) != complement(converse(X_380))
| join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82) = join(complement(converse(X_380)),X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) ),[1,0],$fot(complement(converse(X_380)))]]) ).
cnf(refute_0_961,plain,
( meet(complement(converse(X_380)),converse(complement(X_380))) != complement(converse(X_380))
| join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82) = join(complement(converse(X_380)),X_82) ),
inference(resolve,[$cnf( $equal(join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82) = join(complement(converse(X_380)),X_82),
inference(resolve,[$cnf( $equal(meet(complement(converse(X_380)),converse(complement(X_380))),complement(converse(X_380))) )],[refute_0_958,refute_0_961]) ).
cnf(refute_0_963,plain,
join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82),
inference(subst,[],[refute_0_327:[bind(X_34,$fot(join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)))]]) ).
cnf(refute_0_964,plain,
( join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82) != join(complement(converse(X_380)),X_82)
| join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) != join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)
| join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(complement(converse(X_380)),X_82) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)))),bind(Y,$fot(join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82))),bind(Z,$fot(join(complement(converse(X_380)),X_82)))]]) ).
cnf(refute_0_965,plain,
( join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82) != join(complement(converse(X_380)),X_82)
| join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(complement(converse(X_380)),X_82) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)),join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) = join(complement(converse(X_380)),X_82),
inference(resolve,[$cnf( $equal(join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82),join(complement(converse(X_380)),X_82)) )],[refute_0_962,refute_0_965]) ).
cnf(refute_0_967,plain,
( join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) != join(complement(converse(X_380)),X_82)
| join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) != join(converse(complement(X_380)),X_82)
| join(complement(converse(X_380)),X_82) = join(converse(complement(X_380)),X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)),join(converse(complement(X_380)),X_82)) ),[0],$fot(join(complement(converse(X_380)),X_82))]]) ).
cnf(refute_0_968,plain,
( join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)) != join(converse(complement(X_380)),X_82)
| join(complement(converse(X_380)),X_82) = join(converse(complement(X_380)),X_82) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)),join(complement(converse(X_380)),X_82)) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
join(complement(converse(X_380)),X_82) = join(converse(complement(X_380)),X_82),
inference(resolve,[$cnf( $equal(join(zero,join(meet(complement(converse(X_380)),converse(complement(X_380))),X_82)),join(converse(complement(X_380)),X_82)) )],[refute_0_951,refute_0_968]) ).
cnf(refute_0_970,plain,
( join(complement(converse(X_380)),X_82) != join(converse(complement(X_380)),X_82)
| join(converse(complement(X_380)),X_82) = join(complement(converse(X_380)),X_82) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(converse(X_380)),X_82))),bind(Y,$fot(join(converse(complement(X_380)),X_82)))]]) ).
cnf(refute_0_971,plain,
join(converse(complement(X_380)),X_82) = join(complement(converse(X_380)),X_82),
inference(resolve,[$cnf( $equal(join(complement(converse(X_380)),X_82),join(converse(complement(X_380)),X_82)) )],[refute_0_969,refute_0_970]) ).
cnf(refute_0_972,plain,
join(converse(complement(X_380)),zero) = join(complement(converse(X_380)),zero),
inference(subst,[],[refute_0_971:[bind(X_82,$fot(zero))]]) ).
cnf(refute_0_973,plain,
( join(complement(converse(X_380)),zero) != complement(converse(X_380))
| join(converse(complement(X_380)),zero) != join(complement(converse(X_380)),zero)
| join(converse(complement(X_380)),zero) = complement(converse(X_380)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(converse(complement(X_380)),zero))),bind(Y,$fot(join(complement(converse(X_380)),zero))),bind(Z,$fot(complement(converse(X_380))))]]) ).
cnf(refute_0_974,plain,
( join(complement(converse(X_380)),zero) != complement(converse(X_380))
| join(converse(complement(X_380)),zero) = complement(converse(X_380)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_380)),zero),join(complement(converse(X_380)),zero)) )],[refute_0_972,refute_0_973]) ).
cnf(refute_0_975,plain,
join(converse(complement(X_380)),zero) = complement(converse(X_380)),
inference(resolve,[$cnf( $equal(join(complement(converse(X_380)),zero),complement(converse(X_380))) )],[refute_0_947,refute_0_974]) ).
cnf(refute_0_976,plain,
( join(converse(complement(X_380)),zero) != complement(converse(X_380))
| join(converse(complement(X_380)),zero) != converse(complement(X_380))
| complement(converse(X_380)) = converse(complement(X_380)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(X_380)),zero),converse(complement(X_380))) ),[0],$fot(complement(converse(X_380)))]]) ).
cnf(refute_0_977,plain,
( join(converse(complement(X_380)),zero) != converse(complement(X_380))
| complement(converse(X_380)) = converse(complement(X_380)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_380)),zero),complement(converse(X_380))) )],[refute_0_975,refute_0_976]) ).
cnf(refute_0_978,plain,
complement(converse(X_380)) = converse(complement(X_380)),
inference(resolve,[$cnf( $equal(join(converse(complement(X_380)),zero),converse(complement(X_380))) )],[refute_0_774,refute_0_977]) ).
cnf(refute_0_979,plain,
complement(converse(X_381)) = converse(complement(X_381)),
inference(subst,[],[refute_0_978:[bind(X_380,$fot(X_381))]]) ).
cnf(refute_0_980,plain,
( complement(converse(X_381)) != converse(complement(X_381))
| converse(complement(X_381)) = complement(converse(X_381)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(converse(X_381)))),bind(Y,$fot(converse(complement(X_381))))]]) ).
cnf(refute_0_981,plain,
converse(complement(X_381)) = complement(converse(X_381)),
inference(resolve,[$cnf( $equal(complement(converse(X_381)),converse(complement(X_381))) )],[refute_0_979,refute_0_980]) ).
cnf(refute_0_982,plain,
( converse(complement(X_381)) != complement(converse(X_381))
| converse(composition(X_17,converse(complement(X_381)))) != composition(complement(X_381),converse(X_17))
| converse(composition(X_17,complement(converse(X_381)))) = composition(complement(X_381),converse(X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_17,converse(complement(X_381)))),composition(complement(X_381),converse(X_17))) ),[0,0,1],$fot(complement(converse(X_381)))]]) ).
cnf(refute_0_983,plain,
( converse(composition(X_17,converse(complement(X_381)))) != composition(complement(X_381),converse(X_17))
| converse(composition(X_17,complement(converse(X_381)))) = composition(complement(X_381),converse(X_17)) ),
inference(resolve,[$cnf( $equal(converse(complement(X_381)),complement(converse(X_381))) )],[refute_0_981,refute_0_982]) ).
cnf(refute_0_984,plain,
converse(composition(X_17,complement(converse(X_381)))) = composition(complement(X_381),converse(X_17)),
inference(resolve,[$cnf( $equal(converse(composition(X_17,converse(complement(X_381)))),composition(complement(X_381),converse(X_17))) )],[refute_0_153,refute_0_983]) ).
cnf(refute_0_985,plain,
converse(composition(X_136,complement(converse(composition(complement(A),X_136))))) = composition(complement(composition(complement(A),X_136)),converse(X_136)),
inference(subst,[],[refute_0_984:[bind(X_17,$fot(X_136)),bind(X_381,$fot(composition(complement(A),X_136)))]]) ).
cnf(refute_0_986,plain,
converse(composition(complement(X_381),B)) = composition(converse(B),converse(complement(X_381))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(complement(X_381)))]]) ).
cnf(refute_0_987,plain,
( converse(complement(X_381)) != complement(converse(X_381))
| converse(composition(complement(X_381),B)) != composition(converse(B),converse(complement(X_381)))
| converse(composition(complement(X_381),B)) = composition(converse(B),complement(converse(X_381))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(complement(X_381),B)),composition(converse(B),converse(complement(X_381)))) ),[1,1],$fot(complement(converse(X_381)))]]) ).
cnf(refute_0_988,plain,
( converse(composition(complement(X_381),B)) != composition(converse(B),converse(complement(X_381)))
| converse(composition(complement(X_381),B)) = composition(converse(B),complement(converse(X_381))) ),
inference(resolve,[$cnf( $equal(converse(complement(X_381)),complement(converse(X_381))) )],[refute_0_981,refute_0_987]) ).
cnf(refute_0_989,plain,
converse(composition(complement(X_381),B)) = composition(converse(B),complement(converse(X_381))),
inference(resolve,[$cnf( $equal(converse(composition(complement(X_381),B)),composition(converse(B),converse(complement(X_381)))) )],[refute_0_986,refute_0_988]) ).
cnf(refute_0_990,plain,
( converse(composition(complement(X_381),B)) != composition(converse(B),complement(converse(X_381)))
| composition(converse(B),complement(converse(X_381))) = converse(composition(complement(X_381),B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(complement(X_381),B)))),bind(Y,$fot(composition(converse(B),complement(converse(X_381)))))]]) ).
cnf(refute_0_991,plain,
composition(converse(B),complement(converse(X_381))) = converse(composition(complement(X_381),B)),
inference(resolve,[$cnf( $equal(converse(composition(complement(X_381),B)),composition(converse(B),complement(converse(X_381)))) )],[refute_0_989,refute_0_990]) ).
cnf(refute_0_992,plain,
composition(converse(X_136),complement(converse(A))) = converse(composition(complement(A),X_136)),
inference(subst,[],[refute_0_991:[bind(B,$fot(X_136)),bind(X_381,$fot(A))]]) ).
cnf(refute_0_993,plain,
complement(composition(converse(X_136),complement(converse(A)))) = complement(composition(converse(X_136),complement(converse(A)))),
introduced(tautology,[refl,[$fot(complement(composition(converse(X_136),complement(converse(A)))))]]) ).
cnf(refute_0_994,plain,
( complement(composition(converse(X_136),complement(converse(A)))) != complement(composition(converse(X_136),complement(converse(A))))
| composition(converse(X_136),complement(converse(A))) != converse(composition(complement(A),X_136))
| complement(composition(converse(X_136),complement(converse(A)))) = complement(converse(composition(complement(A),X_136))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(converse(X_136),complement(converse(A)))),complement(composition(converse(X_136),complement(converse(A))))) ),[1,0],$fot(converse(composition(complement(A),X_136)))]]) ).
cnf(refute_0_995,plain,
( composition(converse(X_136),complement(converse(A))) != converse(composition(complement(A),X_136))
| complement(composition(converse(X_136),complement(converse(A)))) = complement(converse(composition(complement(A),X_136))) ),
inference(resolve,[$cnf( $equal(complement(composition(converse(X_136),complement(converse(A)))),complement(composition(converse(X_136),complement(converse(A))))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
complement(composition(converse(X_136),complement(converse(A)))) = complement(converse(composition(complement(A),X_136))),
inference(resolve,[$cnf( $equal(composition(converse(X_136),complement(converse(A))),converse(composition(complement(A),X_136))) )],[refute_0_992,refute_0_995]) ).
cnf(refute_0_997,plain,
composition(X_136,complement(composition(converse(X_136),complement(converse(A))))) = composition(X_136,complement(composition(converse(X_136),complement(converse(A))))),
introduced(tautology,[refl,[$fot(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))]]) ).
cnf(refute_0_998,plain,
( complement(composition(converse(X_136),complement(converse(A)))) != complement(converse(composition(complement(A),X_136)))
| composition(X_136,complement(composition(converse(X_136),complement(converse(A))))) != composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))
| composition(X_136,complement(composition(converse(X_136),complement(converse(A))))) = composition(X_136,complement(converse(composition(complement(A),X_136)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))),composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) ),[1,1],$fot(complement(converse(composition(complement(A),X_136))))]]) ).
cnf(refute_0_999,plain,
( complement(composition(converse(X_136),complement(converse(A)))) != complement(converse(composition(complement(A),X_136)))
| composition(X_136,complement(composition(converse(X_136),complement(converse(A))))) = composition(X_136,complement(converse(composition(complement(A),X_136)))) ),
inference(resolve,[$cnf( $equal(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))),composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) )],[refute_0_997,refute_0_998]) ).
cnf(refute_0_1000,plain,
composition(X_136,complement(composition(converse(X_136),complement(converse(A))))) = composition(X_136,complement(converse(composition(complement(A),X_136)))),
inference(resolve,[$cnf( $equal(complement(composition(converse(X_136),complement(converse(A)))),complement(converse(composition(complement(A),X_136)))) )],[refute_0_996,refute_0_999]) ).
cnf(refute_0_1001,plain,
converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))),
introduced(tautology,[refl,[$fot(converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))]]) ).
cnf(refute_0_1002,plain,
( composition(X_136,complement(composition(converse(X_136),complement(converse(A))))) != composition(X_136,complement(converse(composition(complement(A),X_136))))
| converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) != converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))
| converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = converse(composition(X_136,complement(converse(composition(complement(A),X_136))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))),converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) ),[1,0],$fot(composition(X_136,complement(converse(composition(complement(A),X_136)))))]]) ).
cnf(refute_0_1003,plain,
( composition(X_136,complement(composition(converse(X_136),complement(converse(A))))) != composition(X_136,complement(converse(composition(complement(A),X_136))))
| converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = converse(composition(X_136,complement(converse(composition(complement(A),X_136))))) ),
inference(resolve,[$cnf( $equal(converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))),converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = converse(composition(X_136,complement(converse(composition(complement(A),X_136))))),
inference(resolve,[$cnf( $equal(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))),composition(X_136,complement(converse(composition(complement(A),X_136))))) )],[refute_0_1000,refute_0_1003]) ).
cnf(refute_0_1005,plain,
( converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) != converse(composition(X_136,complement(converse(composition(complement(A),X_136)))))
| converse(composition(X_136,complement(converse(composition(complement(A),X_136))))) != composition(complement(composition(complement(A),X_136)),converse(X_136))
| converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = composition(complement(composition(complement(A),X_136)),converse(X_136)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))),bind(Y,$fot(converse(composition(X_136,complement(converse(composition(complement(A),X_136))))))),bind(Z,$fot(composition(complement(composition(complement(A),X_136)),converse(X_136))))]]) ).
cnf(refute_0_1006,plain,
( converse(composition(X_136,complement(converse(composition(complement(A),X_136))))) != composition(complement(composition(complement(A),X_136)),converse(X_136))
| converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = composition(complement(composition(complement(A),X_136)),converse(X_136)) ),
inference(resolve,[$cnf( $equal(converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))),converse(composition(X_136,complement(converse(composition(complement(A),X_136)))))) )],[refute_0_1004,refute_0_1005]) ).
cnf(refute_0_1007,plain,
converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) = composition(complement(composition(complement(A),X_136)),converse(X_136)),
inference(resolve,[$cnf( $equal(converse(composition(X_136,complement(converse(composition(complement(A),X_136))))),composition(complement(composition(complement(A),X_136)),converse(X_136))) )],[refute_0_985,refute_0_1006]) ).
cnf(refute_0_1008,plain,
join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) = join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),
introduced(tautology,[refl,[$fot(join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))))]]) ).
cnf(refute_0_1009,plain,
( converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) != composition(complement(composition(complement(A),X_136)),converse(X_136))
| join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) != join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))
| join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) = join(A,composition(complement(composition(complement(A),X_136)),converse(X_136))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))) ),[1,1],$fot(composition(complement(composition(complement(A),X_136)),converse(X_136)))]]) ).
cnf(refute_0_1010,plain,
( converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))) != composition(complement(composition(complement(A),X_136)),converse(X_136))
| join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) = join(A,composition(complement(composition(complement(A),X_136)),converse(X_136))) ),
inference(resolve,[$cnf( $equal(join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))) )],[refute_0_1008,refute_0_1009]) ).
cnf(refute_0_1011,plain,
join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) = join(A,composition(complement(composition(complement(A),X_136)),converse(X_136))),
inference(resolve,[$cnf( $equal(converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))),composition(complement(composition(complement(A),X_136)),converse(X_136))) )],[refute_0_1007,refute_0_1010]) ).
cnf(refute_0_1012,plain,
( A != join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))
| join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))) != join(A,composition(complement(composition(complement(A),X_136)),converse(X_136)))
| A = join(A,composition(complement(composition(complement(A),X_136)),converse(X_136))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(A,composition(complement(composition(complement(A),X_136)),converse(X_136)))) ),[0],$fot(join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))))]]) ).
cnf(refute_0_1013,plain,
( A != join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))
| A = join(A,composition(complement(composition(complement(A),X_136)),converse(X_136))) ),
inference(resolve,[$cnf( $equal(join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A))))))),join(A,composition(complement(composition(complement(A),X_136)),converse(X_136)))) )],[refute_0_1011,refute_0_1012]) ).
cnf(refute_0_1014,plain,
A = join(A,composition(complement(composition(complement(A),X_136)),converse(X_136))),
inference(resolve,[$cnf( $equal(A,join(A,converse(composition(X_136,complement(composition(converse(X_136),complement(converse(A)))))))) )],[refute_0_148,refute_0_1013]) ).
cnf(refute_0_1015,plain,
complement(X_69) = join(complement(X_69),composition(complement(composition(complement(complement(X_69)),X_1126)),converse(X_1126))),
inference(subst,[],[refute_0_1014:[bind(A,$fot(complement(X_69))),bind(X_136,$fot(X_1126))]]) ).
cnf(refute_0_1016,plain,
( complement(X_69) != join(complement(X_69),composition(complement(composition(complement(complement(X_69)),X_1126)),converse(X_1126)))
| complement(complement(X_69)) != X_69
| complement(X_69) = join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_69),join(complement(X_69),composition(complement(composition(complement(complement(X_69)),X_1126)),converse(X_1126)))) ),[1,1,0,0,0],$fot(X_69)]]) ).
cnf(refute_0_1017,plain,
( complement(X_69) != join(complement(X_69),composition(complement(composition(complement(complement(X_69)),X_1126)),converse(X_1126)))
| complement(X_69) = join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_69)),X_69) )],[refute_0_135,refute_0_1016]) ).
cnf(refute_0_1018,plain,
complement(X_69) = join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126))),
inference(resolve,[$cnf( $equal(complement(X_69),join(complement(X_69),composition(complement(composition(complement(complement(X_69)),X_1126)),converse(X_1126)))) )],[refute_0_1015,refute_0_1017]) ).
cnf(refute_0_1019,plain,
( complement(X_69) != join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126)))
| join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126))) = complement(X_69) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_69))),bind(Y,$fot(join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126)))))]]) ).
cnf(refute_0_1020,plain,
join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126))) = complement(X_69),
inference(resolve,[$cnf( $equal(complement(X_69),join(complement(X_69),composition(complement(composition(X_69,X_1126)),converse(X_1126)))) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) = complement(sk1),
inference(subst,[],[refute_0_1020:[bind(X_1126,$fot(sk2)),bind(X_69,$fot(sk1))]]) ).
cnf(refute_0_1022,plain,
( complement(sk1) != complement(sk1)
| join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) != complement(sk1)
| join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))),complement(sk1)) ),[0,0],$fot(complement(sk1))]]) ).
cnf(refute_0_1023,plain,
( complement(sk1) != complement(sk1)
| join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) = complement(sk1) ),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))),complement(sk1)) )],[refute_0_1021,refute_0_1022]) ).
cnf(refute_0_1024,plain,
complement(sk1) != complement(sk1),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))),complement(sk1)) )],[refute_0_1023,refute_0_8]) ).
cnf(refute_0_1025,plain,
complement(sk1) = complement(sk1),
introduced(tautology,[refl,[$fot(complement(sk1))]]) ).
cnf(refute_0_1026,plain,
$false,
inference(resolve,[$cnf( $equal(complement(sk1),complement(sk1)) )],[refute_0_1025,refute_0_1024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL012-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.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 15:40:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 123.13/123.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 123.13/123.31
% 123.13/123.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 123.24/123.39
%------------------------------------------------------------------------------