TSTP Solution File: REL023-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL023-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:43:53 EDT 2022
% Result : Unsatisfiable 4.19s 4.36s
% Output : CNFRefutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 206
% Number of leaves : 614
% Syntax : Number of clauses : 2559 (1255 unt; 0 nHn;1605 RR)
% Number of literals : 4448 (4447 equ;1892 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 2650 ( 56 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_associativity_5,axiom,
composition(A,composition(B,C)) = composition(composition(A,B),C) ).
cnf(composition_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_17,negated_conjecture,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_4,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(meet(sk1,converse(sk2)),sk1) = join(sk1,meet(sk1,converse(sk2))),
inference(subst,[],[refute_0_4:[bind(A,$fot(sk1)),bind(B,$fot(meet(sk1,converse(sk2))))]]) ).
cnf(refute_0_6,plain,
composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),
introduced(tautology,[refl,[$fot(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)))]]) ).
cnf(refute_0_7,plain,
( composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) != composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))
| join(meet(sk1,converse(sk2)),sk1) != join(sk1,meet(sk1,converse(sk2)))
| composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))) ),[1,0],$fot(join(sk1,meet(sk1,converse(sk2))))]]) ).
cnf(refute_0_8,plain,
( join(meet(sk1,converse(sk2)),sk1) != join(sk1,meet(sk1,converse(sk2)))
| composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(meet(sk1,converse(sk2)),sk1),join(sk1,meet(sk1,converse(sk2)))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( composition(join(A,B),C) != join(composition(A,C),composition(B,C))
| join(composition(A,C),composition(B,C)) = composition(join(A,B),C) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(A,B),C))),bind(Y,$fot(join(composition(A,C),composition(B,C))))]]) ).
cnf(refute_0_11,plain,
join(composition(A,C),composition(B,C)) = composition(join(A,B),C),
inference(resolve,[$cnf( $equal(composition(join(A,B),C),join(composition(A,C),composition(B,C))) )],[composition_distributivity_7,refute_0_10]) ).
cnf(refute_0_12,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),
inference(subst,[],[refute_0_11:[bind(A,$fot(meet(sk1,converse(sk2)))),bind(B,$fot(sk1)),bind(C,$fot(meet(sk2,sk3)))]]) ).
cnf(refute_0_13,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))))),bind(Y,$fot(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)))),bind(Z,$fot(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))))]]) ).
cnf(refute_0_16,plain,
( composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(composition(join(meet(sk1,converse(sk2)),sk1),meet(sk2,sk3)),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(sk1,meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) ),[1],$fot(composition(sk1,meet(sk2,sk3)))]]) ).
cnf(refute_0_19,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) = composition(sk1,meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))),composition(sk1,meet(sk2,sk3))) )],[refute_0_19,goals_17]) ).
cnf(refute_0_21,plain,
join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)) = join(join(meet(X_33,X_34),meet(X_33,complement(X_34))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(meet(X_33,X_34))),bind(B,$fot(meet(X_33,complement(X_34))))]]) ).
cnf(refute_0_22,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_23,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[0],$fot(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))))]]) ).
cnf(refute_0_24,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_24]) ).
cnf(refute_0_26,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_27,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_28,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_27]) ).
cnf(refute_0_29,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_30,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[1,1],$fot(meet(A,B))]]) ).
cnf(refute_0_31,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))),bind(Y,$fot(join(complement(join(complement(A),B)),meet(A,B)))),bind(Z,$fot(join(meet(A,B),complement(join(complement(A),B)))))]]) ).
cnf(refute_0_34,plain,
( join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_26,refute_0_34]) ).
cnf(refute_0_36,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(meet(A,B),complement(join(complement(A),B)))) ),[0],$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_37,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_25,refute_0_37]) ).
cnf(refute_0_39,plain,
A = join(meet(A,complement(X_18)),complement(join(complement(A),complement(X_18)))),
inference(subst,[],[refute_0_38:[bind(B,$fot(complement(X_18)))]]) ).
cnf(refute_0_40,plain,
meet(A,X_18) = complement(join(complement(A),complement(X_18))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(X_18))]]) ).
cnf(refute_0_41,plain,
( meet(A,X_18) != complement(join(complement(A),complement(X_18)))
| complement(join(complement(A),complement(X_18))) = meet(A,X_18) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,X_18))),bind(Y,$fot(complement(join(complement(A),complement(X_18)))))]]) ).
cnf(refute_0_42,plain,
complement(join(complement(A),complement(X_18))) = meet(A,X_18),
inference(resolve,[$cnf( $equal(meet(A,X_18),complement(join(complement(A),complement(X_18)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( A != join(meet(A,complement(X_18)),complement(join(complement(A),complement(X_18))))
| complement(join(complement(A),complement(X_18))) != meet(A,X_18)
| A = join(meet(A,complement(X_18)),meet(A,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(A,join(meet(A,complement(X_18)),complement(join(complement(A),complement(X_18))))) ),[1,1],$fot(meet(A,X_18))]]) ).
cnf(refute_0_44,plain,
( A != join(meet(A,complement(X_18)),complement(join(complement(A),complement(X_18))))
| A = join(meet(A,complement(X_18)),meet(A,X_18)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(X_18))),meet(A,X_18)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
A = join(meet(A,complement(X_18)),meet(A,X_18)),
inference(resolve,[$cnf( $equal(A,join(meet(A,complement(X_18)),complement(join(complement(A),complement(X_18))))) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
join(meet(A,complement(X_18)),meet(A,X_18)) = join(meet(A,X_18),meet(A,complement(X_18))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,X_18))),bind(B,$fot(meet(A,complement(X_18))))]]) ).
cnf(refute_0_47,plain,
( A != join(meet(A,complement(X_18)),meet(A,X_18))
| join(meet(A,complement(X_18)),meet(A,X_18)) != join(meet(A,X_18),meet(A,complement(X_18)))
| A = join(meet(A,X_18),meet(A,complement(X_18))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(meet(A,X_18),meet(A,complement(X_18)))) ),[0],$fot(join(meet(A,complement(X_18)),meet(A,X_18)))]]) ).
cnf(refute_0_48,plain,
( A != join(meet(A,complement(X_18)),meet(A,X_18))
| A = join(meet(A,X_18),meet(A,complement(X_18))) ),
inference(resolve,[$cnf( $equal(join(meet(A,complement(X_18)),meet(A,X_18)),join(meet(A,X_18),meet(A,complement(X_18)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
A = join(meet(A,X_18),meet(A,complement(X_18))),
inference(resolve,[$cnf( $equal(A,join(meet(A,complement(X_18)),meet(A,X_18))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
X_33 = join(meet(X_33,X_34),meet(X_33,complement(X_34))),
inference(subst,[],[refute_0_49:[bind(A,$fot(X_33)),bind(X_18,$fot(X_34))]]) ).
cnf(refute_0_51,plain,
( X_33 != join(meet(X_33,X_34),meet(X_33,complement(X_34)))
| join(meet(X_33,X_34),meet(X_33,complement(X_34))) = X_33 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_33)),bind(Y,$fot(join(meet(X_33,X_34),meet(X_33,complement(X_34)))))]]) ).
cnf(refute_0_52,plain,
join(meet(X_33,X_34),meet(X_33,complement(X_34))) = X_33,
inference(resolve,[$cnf( $equal(X_33,join(meet(X_33,X_34),meet(X_33,complement(X_34)))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)) != join(join(meet(X_33,X_34),meet(X_33,complement(X_34))),C)
| join(meet(X_33,X_34),meet(X_33,complement(X_34))) != X_33
| join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)) = join(X_33,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)),join(join(meet(X_33,X_34),meet(X_33,complement(X_34))),C)) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_54,plain,
( join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)) != join(join(meet(X_33,X_34),meet(X_33,complement(X_34))),C)
| join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)) = join(X_33,C) ),
inference(resolve,[$cnf( $equal(join(meet(X_33,X_34),meet(X_33,complement(X_34))),X_33) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)) = join(X_33,C),
inference(resolve,[$cnf( $equal(join(meet(X_33,X_34),join(meet(X_33,complement(X_34)),C)),join(join(meet(X_33,X_34),meet(X_33,complement(X_34))),C)) )],[refute_0_21,refute_0_54]) ).
cnf(refute_0_56,plain,
join(meet(X_315,X_316),join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))) = join(X_315,meet(complement(complement(X_316)),X_315)),
inference(subst,[],[refute_0_55:[bind(C,$fot(meet(complement(complement(X_316)),X_315))),bind(X_33,$fot(X_315)),bind(X_34,$fot(X_316))]]) ).
cnf(refute_0_57,plain,
meet(X_17,X_18) = complement(join(complement(X_17),complement(X_18))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_17)),bind(B,$fot(X_18))]]) ).
cnf(refute_0_58,plain,
join(complement(X_18),complement(X_17)) = join(complement(X_17),complement(X_18)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_18))),bind(B,$fot(complement(X_17)))]]) ).
cnf(refute_0_59,plain,
( join(complement(X_18),complement(X_17)) != join(complement(X_17),complement(X_18))
| join(complement(X_17),complement(X_18)) = join(complement(X_18),complement(X_17)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_18),complement(X_17)))),bind(Y,$fot(join(complement(X_17),complement(X_18))))]]) ).
cnf(refute_0_60,plain,
join(complement(X_17),complement(X_18)) = join(complement(X_18),complement(X_17)),
inference(resolve,[$cnf( $equal(join(complement(X_18),complement(X_17)),join(complement(X_17),complement(X_18))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( join(complement(X_17),complement(X_18)) != join(complement(X_18),complement(X_17))
| meet(X_17,X_18) != complement(join(complement(X_17),complement(X_18)))
| meet(X_17,X_18) = complement(join(complement(X_18),complement(X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_17,X_18),complement(join(complement(X_17),complement(X_18)))) ),[1,0],$fot(join(complement(X_18),complement(X_17)))]]) ).
cnf(refute_0_62,plain,
( meet(X_17,X_18) != complement(join(complement(X_17),complement(X_18)))
| meet(X_17,X_18) = complement(join(complement(X_18),complement(X_17))) ),
inference(resolve,[$cnf( $equal(join(complement(X_17),complement(X_18)),join(complement(X_18),complement(X_17))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
meet(X_17,X_18) = complement(join(complement(X_18),complement(X_17))),
inference(resolve,[$cnf( $equal(meet(X_17,X_18),complement(join(complement(X_17),complement(X_18)))) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
complement(join(complement(X_18),complement(X_17))) = meet(X_18,X_17),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_18)),bind(B,$fot(X_17))]]) ).
cnf(refute_0_65,plain,
( complement(join(complement(X_18),complement(X_17))) != meet(X_18,X_17)
| meet(X_17,X_18) != complement(join(complement(X_18),complement(X_17)))
| meet(X_17,X_18) = meet(X_18,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_17,X_18),complement(join(complement(X_18),complement(X_17)))) ),[1],$fot(meet(X_18,X_17))]]) ).
cnf(refute_0_66,plain,
( meet(X_17,X_18) != complement(join(complement(X_18),complement(X_17)))
| meet(X_17,X_18) = meet(X_18,X_17) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_18),complement(X_17))),meet(X_18,X_17)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
meet(X_17,X_18) = meet(X_18,X_17),
inference(resolve,[$cnf( $equal(meet(X_17,X_18),complement(join(complement(X_18),complement(X_17)))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
meet(A,complement(X_18)) = meet(complement(X_18),A),
inference(subst,[],[refute_0_67:[bind(X_17,$fot(A)),bind(X_18,$fot(complement(X_18)))]]) ).
cnf(refute_0_69,plain,
( A != join(meet(A,X_18),meet(A,complement(X_18)))
| meet(A,complement(X_18)) != meet(complement(X_18),A)
| A = join(meet(A,X_18),meet(complement(X_18),A)) ),
introduced(tautology,[equality,[$cnf( $equal(A,join(meet(A,X_18),meet(A,complement(X_18)))) ),[1,1],$fot(meet(complement(X_18),A))]]) ).
cnf(refute_0_70,plain,
( A != join(meet(A,X_18),meet(A,complement(X_18)))
| A = join(meet(A,X_18),meet(complement(X_18),A)) ),
inference(resolve,[$cnf( $equal(meet(A,complement(X_18)),meet(complement(X_18),A)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
A = join(meet(A,X_18),meet(complement(X_18),A)),
inference(resolve,[$cnf( $equal(A,join(meet(A,X_18),meet(A,complement(X_18)))) )],[refute_0_49,refute_0_70]) ).
cnf(refute_0_72,plain,
X_315 = join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315)),
inference(subst,[],[refute_0_71:[bind(A,$fot(X_315)),bind(X_18,$fot(complement(X_316)))]]) ).
cnf(refute_0_73,plain,
( X_315 != join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))
| join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315)) = X_315 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_315)),bind(Y,$fot(join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))))]]) ).
cnf(refute_0_74,plain,
join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315)) = X_315,
inference(resolve,[$cnf( $equal(X_315,join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( join(meet(X_315,X_316),join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))) != join(X_315,meet(complement(complement(X_316)),X_315))
| join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315)) != X_315
| join(meet(X_315,X_316),X_315) = join(X_315,meet(complement(complement(X_316)),X_315)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_315,X_316),join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))),join(X_315,meet(complement(complement(X_316)),X_315))) ),[0,1],$fot(X_315)]]) ).
cnf(refute_0_76,plain,
( join(meet(X_315,X_316),join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))) != join(X_315,meet(complement(complement(X_316)),X_315))
| join(meet(X_315,X_316),X_315) = join(X_315,meet(complement(complement(X_316)),X_315)) ),
inference(resolve,[$cnf( $equal(join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315)),X_315) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
join(meet(X_315,X_316),X_315) = join(X_315,meet(complement(complement(X_316)),X_315)),
inference(resolve,[$cnf( $equal(join(meet(X_315,X_316),join(meet(X_315,complement(X_316)),meet(complement(complement(X_316)),X_315))),join(X_315,meet(complement(complement(X_316)),X_315))) )],[refute_0_56,refute_0_76]) ).
cnf(refute_0_78,plain,
join(X_14,join(X_15,X_16)) = join(join(X_14,X_15),X_16),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_79,plain,
join(X_15,X_14) = join(X_14,X_15),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_15)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_80,plain,
( join(X_15,X_14) != join(X_14,X_15)
| join(X_14,X_15) = join(X_15,X_14) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_15,X_14))),bind(Y,$fot(join(X_14,X_15)))]]) ).
cnf(refute_0_81,plain,
join(X_14,X_15) = join(X_15,X_14),
inference(resolve,[$cnf( $equal(join(X_15,X_14),join(X_14,X_15)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( join(X_14,X_15) != join(X_15,X_14)
| join(X_14,join(X_15,X_16)) != join(join(X_14,X_15),X_16)
| join(X_14,join(X_15,X_16)) = join(join(X_15,X_14),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(join(X_14,X_15),X_16)) ),[1,0],$fot(join(X_15,X_14))]]) ).
cnf(refute_0_83,plain,
( join(X_14,join(X_15,X_16)) != join(join(X_14,X_15),X_16)
| join(X_14,join(X_15,X_16)) = join(join(X_15,X_14),X_16) ),
inference(resolve,[$cnf( $equal(join(X_14,X_15),join(X_15,X_14)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
join(X_14,join(X_15,X_16)) = join(join(X_15,X_14),X_16),
inference(resolve,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(join(X_14,X_15),X_16)) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_86,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_85]) ).
cnf(refute_0_87,plain,
join(join(X_15,X_14),X_16) = join(X_15,join(X_14,X_16)),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_15)),bind(B,$fot(X_14)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_88,plain,
( join(X_14,join(X_15,X_16)) != join(join(X_15,X_14),X_16)
| join(join(X_15,X_14),X_16) != join(X_15,join(X_14,X_16))
| join(X_14,join(X_15,X_16)) = join(X_15,join(X_14,X_16)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_14,join(X_15,X_16)),join(X_15,join(X_14,X_16))) ),[0],$fot(join(join(X_15,X_14),X_16))]]) ).
cnf(refute_0_89,plain,
( join(X_14,join(X_15,X_16)) != join(join(X_15,X_14),X_16)
| join(X_14,join(X_15,X_16)) = join(X_15,join(X_14,X_16)) ),
inference(resolve,[$cnf( $equal(join(join(X_15,X_14),X_16),join(X_15,join(X_14,X_16))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
join(X_14,join(X_15,X_16)) = join(X_15,join(X_14,X_16)),
inference(resolve,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(join(X_15,X_14),X_16)) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
join(X_118,join(X_119,meet(X_119,zero))) = join(X_119,join(X_118,meet(X_119,zero))),
inference(subst,[],[refute_0_90:[bind(X_14,$fot(X_118)),bind(X_15,$fot(X_119)),bind(X_16,$fot(meet(X_119,zero)))]]) ).
cnf(refute_0_92,plain,
X_33 = join(meet(X_33,top),meet(X_33,complement(top))),
inference(subst,[],[refute_0_49:[bind(A,$fot(X_33)),bind(X_18,$fot(top))]]) ).
cnf(refute_0_93,plain,
zero = meet(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_17),complement(X_18))))]]) ).
cnf(refute_0_94,plain,
( meet(X_17,X_18) != complement(join(complement(X_17),complement(X_18)))
| complement(join(complement(X_17),complement(X_18))) = meet(X_17,X_18) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_17,X_18))),bind(Y,$fot(complement(join(complement(X_17),complement(X_18)))))]]) ).
cnf(refute_0_95,plain,
complement(join(complement(X_17),complement(X_18))) = meet(X_17,X_18),
inference(resolve,[$cnf( $equal(meet(X_17,X_18),complement(join(complement(X_17),complement(X_18)))) )],[refute_0_57,refute_0_94]) ).
cnf(refute_0_96,plain,
( complement(join(complement(X_17),complement(X_18))) != meet(X_17,X_18)
| zero != meet(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))
| zero = meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))) ),[1,1],$fot(meet(X_17,X_18))]]) ).
cnf(refute_0_97,plain,
( zero != meet(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))
| zero = meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_17),complement(X_18))),meet(X_17,X_18)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
zero = meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))) )],[refute_0_93,refute_0_97]) ).
cnf(refute_0_99,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_100,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_99]) ).
cnf(refute_0_101,plain,
join(meet(X_17,X_18),complement(meet(X_17,X_18))) = top,
inference(subst,[],[refute_0_100:[bind(A,$fot(meet(X_17,X_18)))]]) ).
cnf(refute_0_102,plain,
complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))) = complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))))]]) ).
cnf(refute_0_103,plain,
( complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))) != complement(join(meet(X_17,X_18),complement(meet(X_17,X_18))))
| join(meet(X_17,X_18),complement(meet(X_17,X_18))) != top
| complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))),complement(join(meet(X_17,X_18),complement(meet(X_17,X_18))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_104,plain,
( join(meet(X_17,X_18),complement(meet(X_17,X_18))) != top
| complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))),complement(join(meet(X_17,X_18),complement(meet(X_17,X_18))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_17,X_18),complement(meet(X_17,X_18))),top) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
meet(join(complement(X_17),complement(X_18)),B) = complement(join(complement(join(complement(X_17),complement(X_18))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_17),complement(X_18))))]]) ).
cnf(refute_0_107,plain,
( complement(join(complement(X_17),complement(X_18))) != meet(X_17,X_18)
| meet(join(complement(X_17),complement(X_18)),B) != complement(join(complement(join(complement(X_17),complement(X_18))),complement(B)))
| meet(join(complement(X_17),complement(X_18)),B) = complement(join(meet(X_17,X_18),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),B),complement(join(complement(join(complement(X_17),complement(X_18))),complement(B)))) ),[1,0,0],$fot(meet(X_17,X_18))]]) ).
cnf(refute_0_108,plain,
( meet(join(complement(X_17),complement(X_18)),B) != complement(join(complement(join(complement(X_17),complement(X_18))),complement(B)))
| meet(join(complement(X_17),complement(X_18)),B) = complement(join(meet(X_17,X_18),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_17),complement(X_18))),meet(X_17,X_18)) )],[refute_0_95,refute_0_107]) ).
cnf(refute_0_109,plain,
meet(join(complement(X_17),complement(X_18)),B) = complement(join(meet(X_17,X_18),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),B),complement(join(complement(join(complement(X_17),complement(X_18))),complement(B)))) )],[refute_0_106,refute_0_108]) ).
cnf(refute_0_110,plain,
meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) = complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))),
inference(subst,[],[refute_0_109:[bind(B,$fot(meet(X_17,X_18)))]]) ).
cnf(refute_0_111,plain,
( complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))) != complement(top)
| meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) != complement(join(meet(X_17,X_18),complement(meet(X_17,X_18))))
| meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) = complement(top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)))),bind(Y,$fot(complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_112,plain,
( complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))) != complement(top)
| meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)),complement(join(meet(X_17,X_18),complement(meet(X_17,X_18))))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_17,X_18),complement(meet(X_17,X_18)))),complement(top)) )],[refute_0_105,refute_0_112]) ).
cnf(refute_0_114,plain,
( meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) != complement(top)
| zero != meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_115,plain,
( zero != meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18)),complement(top)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_17),complement(X_18)),meet(X_17,X_18))) )],[refute_0_98,refute_0_115]) ).
cnf(refute_0_117,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_118,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( X_33 != join(meet(X_33,top),meet(X_33,complement(top)))
| complement(top) != zero
| X_33 = join(meet(X_33,top),meet(X_33,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(X_33,join(meet(X_33,top),meet(X_33,complement(top)))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_120,plain,
( X_33 != join(meet(X_33,top),meet(X_33,complement(top)))
| X_33 = join(meet(X_33,top),meet(X_33,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
X_33 = join(meet(X_33,top),meet(X_33,zero)),
inference(resolve,[$cnf( $equal(X_33,join(meet(X_33,top),meet(X_33,complement(top)))) )],[refute_0_92,refute_0_120]) ).
cnf(refute_0_122,plain,
X_35 = join(meet(X_35,top),meet(X_35,zero)),
inference(subst,[],[refute_0_121:[bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_123,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_124,plain,
( complement(top) != zero
| meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_125,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_124]) ).
cnf(refute_0_126,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_123,refute_0_125]) ).
cnf(refute_0_127,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_128,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_129,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_128]) ).
cnf(refute_0_130,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_127,refute_0_129]) ).
cnf(refute_0_131,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_132,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_132:[bind(B,$fot(A))]]) ).
cnf(refute_0_134,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_135,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_136,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_137,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_140,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_133,refute_0_140]) ).
cnf(refute_0_142,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_143,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_126,refute_0_143]) ).
cnf(refute_0_145,plain,
meet(X_35,top) = meet(top,X_35),
inference(subst,[],[refute_0_144:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_146,plain,
( X_35 != join(meet(X_35,top),meet(X_35,zero))
| meet(X_35,top) != meet(top,X_35)
| X_35 = join(meet(top,X_35),meet(X_35,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(X_35,top),meet(X_35,zero))) ),[1,0],$fot(meet(top,X_35))]]) ).
cnf(refute_0_147,plain,
( X_35 != join(meet(X_35,top),meet(X_35,zero))
| X_35 = join(meet(top,X_35),meet(X_35,zero)) ),
inference(resolve,[$cnf( $equal(meet(X_35,top),meet(top,X_35)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
X_35 = join(meet(top,X_35),meet(X_35,zero)),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,top),meet(X_35,zero))) )],[refute_0_122,refute_0_147]) ).
cnf(refute_0_149,plain,
X_10 = join(meet(X_10,X_11),complement(join(complement(X_10),X_11))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_150,plain,
join(X_11,complement(X_10)) = join(complement(X_10),X_11),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_11)),bind(B,$fot(complement(X_10)))]]) ).
cnf(refute_0_151,plain,
( join(X_11,complement(X_10)) != join(complement(X_10),X_11)
| join(complement(X_10),X_11) = join(X_11,complement(X_10)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_11,complement(X_10)))),bind(Y,$fot(join(complement(X_10),X_11)))]]) ).
cnf(refute_0_152,plain,
join(complement(X_10),X_11) = join(X_11,complement(X_10)),
inference(resolve,[$cnf( $equal(join(X_11,complement(X_10)),join(complement(X_10),X_11)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
( X_10 != join(meet(X_10,X_11),complement(join(complement(X_10),X_11)))
| join(complement(X_10),X_11) != join(X_11,complement(X_10))
| X_10 = join(meet(X_10,X_11),complement(join(X_11,complement(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_10,join(meet(X_10,X_11),complement(join(complement(X_10),X_11)))) ),[1,1,0],$fot(join(X_11,complement(X_10)))]]) ).
cnf(refute_0_154,plain,
( X_10 != join(meet(X_10,X_11),complement(join(complement(X_10),X_11)))
| X_10 = join(meet(X_10,X_11),complement(join(X_11,complement(X_10)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_10),X_11),join(X_11,complement(X_10))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
X_10 = join(meet(X_10,X_11),complement(join(X_11,complement(X_10)))),
inference(resolve,[$cnf( $equal(X_10,join(meet(X_10,X_11),complement(join(complement(X_10),X_11)))) )],[refute_0_149,refute_0_154]) ).
cnf(refute_0_156,plain,
X_10 = join(meet(X_10,complement(X_10)),complement(join(complement(X_10),complement(X_10)))),
inference(subst,[],[refute_0_155:[bind(X_11,$fot(complement(X_10)))]]) ).
cnf(refute_0_157,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_158,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_159,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_159]) ).
cnf(refute_0_161,plain,
join(complement(X_46),composition(converse(one),complement(composition(one,X_46)))) = complement(X_46),
inference(subst,[],[refute_0_160:[bind(A,$fot(one)),bind(B,$fot(X_46))]]) ).
cnf(refute_0_162,plain,
converse(composition(converse(A),X_23)) = composition(converse(X_23),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_23))]]) ).
cnf(refute_0_163,plain,
( converse(composition(converse(A),X_23)) != composition(converse(X_23),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_23)) = composition(converse(X_23),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_23)),composition(converse(X_23),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_164,plain,
( converse(composition(converse(A),X_23)) != composition(converse(X_23),converse(converse(A)))
| converse(composition(converse(A),X_23)) = composition(converse(X_23),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_163]) ).
cnf(refute_0_165,plain,
converse(composition(converse(A),X_23)) = composition(converse(X_23),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_23)),composition(converse(X_23),converse(converse(A)))) )],[refute_0_162,refute_0_164]) ).
cnf(refute_0_166,plain,
converse(composition(converse(X_24),one)) = composition(converse(one),X_24),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_24)),bind(X_23,$fot(one))]]) ).
cnf(refute_0_167,plain,
composition(converse(X_24),one) = converse(X_24),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_24)))]]) ).
cnf(refute_0_168,plain,
( composition(converse(X_24),one) != converse(X_24)
| converse(composition(converse(X_24),one)) != composition(converse(one),X_24)
| converse(converse(X_24)) = composition(converse(one),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_24),one)),composition(converse(one),X_24)) ),[0,0],$fot(converse(X_24))]]) ).
cnf(refute_0_169,plain,
( converse(composition(converse(X_24),one)) != composition(converse(one),X_24)
| converse(converse(X_24)) = composition(converse(one),X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(X_24),one),converse(X_24)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
converse(converse(X_24)) = composition(converse(one),X_24),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_24),one)),composition(converse(one),X_24)) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
converse(converse(X_24)) = X_24,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_172,plain,
( converse(converse(X_24)) != X_24
| converse(converse(X_24)) != composition(converse(one),X_24)
| X_24 = composition(converse(one),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_24)),composition(converse(one),X_24)) ),[0],$fot(X_24)]]) ).
cnf(refute_0_173,plain,
( converse(converse(X_24)) != composition(converse(one),X_24)
| X_24 = composition(converse(one),X_24) ),
inference(resolve,[$cnf( $equal(converse(converse(X_24)),X_24) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
X_24 = composition(converse(one),X_24),
inference(resolve,[$cnf( $equal(converse(converse(X_24)),composition(converse(one),X_24)) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_176,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_174:[bind(X_24,$fot(one))]]) ).
cnf(refute_0_177,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_178,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_180,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_175,refute_0_180]) ).
cnf(refute_0_182,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_183,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
composition(converse(one),X_24) = composition(converse(one),X_24),
introduced(tautology,[refl,[$fot(composition(converse(one),X_24))]]) ).
cnf(refute_0_185,plain,
( composition(converse(one),X_24) != composition(converse(one),X_24)
| converse(one) != one
| composition(converse(one),X_24) = composition(one,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_24),composition(converse(one),X_24)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_186,plain,
( converse(one) != one
| composition(converse(one),X_24) = composition(one,X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_24),composition(converse(one),X_24)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
composition(converse(one),X_24) = composition(one,X_24),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
( X_24 != composition(converse(one),X_24)
| composition(converse(one),X_24) != composition(one,X_24)
| X_24 = composition(one,X_24) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,composition(one,X_24)) ),[0],$fot(composition(converse(one),X_24))]]) ).
cnf(refute_0_189,plain,
( X_24 != composition(converse(one),X_24)
| X_24 = composition(one,X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_24),composition(one,X_24)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
X_24 = composition(one,X_24),
inference(resolve,[$cnf( $equal(X_24,composition(converse(one),X_24)) )],[refute_0_174,refute_0_189]) ).
cnf(refute_0_191,plain,
X_46 = composition(one,X_46),
inference(subst,[],[refute_0_190:[bind(X_24,$fot(X_46))]]) ).
cnf(refute_0_192,plain,
( X_46 != composition(one,X_46)
| composition(one,X_46) = X_46 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_46)),bind(Y,$fot(composition(one,X_46)))]]) ).
cnf(refute_0_193,plain,
composition(one,X_46) = X_46,
inference(resolve,[$cnf( $equal(X_46,composition(one,X_46)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
( composition(one,X_46) != X_46
| join(complement(X_46),composition(converse(one),complement(composition(one,X_46)))) != complement(X_46)
| join(complement(X_46),composition(converse(one),complement(X_46))) = complement(X_46) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_46),composition(converse(one),complement(composition(one,X_46)))),complement(X_46)) ),[0,1,1,0],$fot(X_46)]]) ).
cnf(refute_0_195,plain,
( join(complement(X_46),composition(converse(one),complement(composition(one,X_46)))) != complement(X_46)
| join(complement(X_46),composition(converse(one),complement(X_46))) = complement(X_46) ),
inference(resolve,[$cnf( $equal(composition(one,X_46),X_46) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
join(complement(X_46),composition(converse(one),complement(X_46))) = complement(X_46),
inference(resolve,[$cnf( $equal(join(complement(X_46),composition(converse(one),complement(composition(one,X_46)))),complement(X_46)) )],[refute_0_161,refute_0_195]) ).
cnf(refute_0_197,plain,
( X_24 != composition(one,X_24)
| composition(one,X_24) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(composition(one,X_24)))]]) ).
cnf(refute_0_198,plain,
composition(one,X_24) = X_24,
inference(resolve,[$cnf( $equal(X_24,composition(one,X_24)) )],[refute_0_190,refute_0_197]) ).
cnf(refute_0_199,plain,
composition(one,complement(X_46)) = complement(X_46),
inference(subst,[],[refute_0_198:[bind(X_24,$fot(complement(X_46)))]]) ).
cnf(refute_0_200,plain,
composition(converse(one),complement(X_46)) = composition(converse(one),complement(X_46)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_46)))]]) ).
cnf(refute_0_201,plain,
( composition(converse(one),complement(X_46)) != composition(converse(one),complement(X_46))
| converse(one) != one
| composition(converse(one),complement(X_46)) = composition(one,complement(X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_46)),composition(converse(one),complement(X_46))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_202,plain,
( converse(one) != one
| composition(converse(one),complement(X_46)) = composition(one,complement(X_46)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_46)),composition(converse(one),complement(X_46))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
composition(converse(one),complement(X_46)) = composition(one,complement(X_46)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_202]) ).
cnf(refute_0_204,plain,
( composition(converse(one),complement(X_46)) != composition(one,complement(X_46))
| composition(one,complement(X_46)) != complement(X_46)
| composition(converse(one),complement(X_46)) = complement(X_46) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(converse(one),complement(X_46)))),bind(Y,$fot(composition(one,complement(X_46)))),bind(Z,$fot(complement(X_46)))]]) ).
cnf(refute_0_205,plain,
( composition(one,complement(X_46)) != complement(X_46)
| composition(converse(one),complement(X_46)) = complement(X_46) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_46)),composition(one,complement(X_46))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
composition(converse(one),complement(X_46)) = complement(X_46),
inference(resolve,[$cnf( $equal(composition(one,complement(X_46)),complement(X_46)) )],[refute_0_199,refute_0_205]) ).
cnf(refute_0_207,plain,
join(complement(X_46),composition(converse(one),complement(X_46))) = join(complement(X_46),composition(converse(one),complement(X_46))),
introduced(tautology,[refl,[$fot(join(complement(X_46),composition(converse(one),complement(X_46))))]]) ).
cnf(refute_0_208,plain,
( composition(converse(one),complement(X_46)) != complement(X_46)
| join(complement(X_46),composition(converse(one),complement(X_46))) != join(complement(X_46),composition(converse(one),complement(X_46)))
| join(complement(X_46),composition(converse(one),complement(X_46))) = join(complement(X_46),complement(X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_46),composition(converse(one),complement(X_46))),join(complement(X_46),composition(converse(one),complement(X_46)))) ),[1,1],$fot(complement(X_46))]]) ).
cnf(refute_0_209,plain,
( composition(converse(one),complement(X_46)) != complement(X_46)
| join(complement(X_46),composition(converse(one),complement(X_46))) = join(complement(X_46),complement(X_46)) ),
inference(resolve,[$cnf( $equal(join(complement(X_46),composition(converse(one),complement(X_46))),join(complement(X_46),composition(converse(one),complement(X_46)))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
join(complement(X_46),composition(converse(one),complement(X_46))) = join(complement(X_46),complement(X_46)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_46)),complement(X_46)) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
( join(complement(X_46),composition(converse(one),complement(X_46))) != complement(X_46)
| join(complement(X_46),composition(converse(one),complement(X_46))) != join(complement(X_46),complement(X_46))
| join(complement(X_46),complement(X_46)) = complement(X_46) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_46),composition(converse(one),complement(X_46))),complement(X_46)) ),[0],$fot(join(complement(X_46),complement(X_46)))]]) ).
cnf(refute_0_212,plain,
( join(complement(X_46),composition(converse(one),complement(X_46))) != complement(X_46)
| join(complement(X_46),complement(X_46)) = complement(X_46) ),
inference(resolve,[$cnf( $equal(join(complement(X_46),composition(converse(one),complement(X_46))),join(complement(X_46),complement(X_46))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
join(complement(X_46),complement(X_46)) = complement(X_46),
inference(resolve,[$cnf( $equal(join(complement(X_46),composition(converse(one),complement(X_46))),complement(X_46)) )],[refute_0_196,refute_0_212]) ).
cnf(refute_0_214,plain,
join(complement(X_10),complement(X_10)) = complement(X_10),
inference(subst,[],[refute_0_213:[bind(X_46,$fot(X_10))]]) ).
cnf(refute_0_215,plain,
( X_10 != join(meet(X_10,complement(X_10)),complement(join(complement(X_10),complement(X_10))))
| join(complement(X_10),complement(X_10)) != complement(X_10)
| X_10 = join(meet(X_10,complement(X_10)),complement(complement(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(X_10,join(meet(X_10,complement(X_10)),complement(join(complement(X_10),complement(X_10))))) ),[1,1,0],$fot(complement(X_10))]]) ).
cnf(refute_0_216,plain,
( X_10 != join(meet(X_10,complement(X_10)),complement(join(complement(X_10),complement(X_10))))
| X_10 = join(meet(X_10,complement(X_10)),complement(complement(X_10))) ),
inference(resolve,[$cnf( $equal(join(complement(X_10),complement(X_10)),complement(X_10)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
X_10 = join(meet(X_10,complement(X_10)),complement(complement(X_10))),
inference(resolve,[$cnf( $equal(X_10,join(meet(X_10,complement(X_10)),complement(join(complement(X_10),complement(X_10))))) )],[refute_0_156,refute_0_216]) ).
cnf(refute_0_218,plain,
join(complement(complement(X_10)),zero) = join(zero,complement(complement(X_10))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_10))))]]) ).
cnf(refute_0_219,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_220,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_219]) ).
cnf(refute_0_221,plain,
meet(X_10,complement(X_10)) = zero,
inference(subst,[],[refute_0_220:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_222,plain,
join(complement(complement(X_10)),meet(X_10,complement(X_10))) = join(complement(complement(X_10)),meet(X_10,complement(X_10))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_10)),meet(X_10,complement(X_10))))]]) ).
cnf(refute_0_223,plain,
( join(complement(complement(X_10)),meet(X_10,complement(X_10))) != join(complement(complement(X_10)),meet(X_10,complement(X_10)))
| meet(X_10,complement(X_10)) != zero
| join(complement(complement(X_10)),meet(X_10,complement(X_10))) = join(complement(complement(X_10)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_10)),meet(X_10,complement(X_10))),join(complement(complement(X_10)),meet(X_10,complement(X_10)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_224,plain,
( meet(X_10,complement(X_10)) != zero
| join(complement(complement(X_10)),meet(X_10,complement(X_10))) = join(complement(complement(X_10)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_10)),meet(X_10,complement(X_10))),join(complement(complement(X_10)),meet(X_10,complement(X_10)))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
join(complement(complement(X_10)),meet(X_10,complement(X_10))) = join(complement(complement(X_10)),zero),
inference(resolve,[$cnf( $equal(meet(X_10,complement(X_10)),zero) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( join(complement(complement(X_10)),meet(X_10,complement(X_10))) != join(complement(complement(X_10)),zero)
| join(complement(complement(X_10)),zero) != join(zero,complement(complement(X_10)))
| join(complement(complement(X_10)),meet(X_10,complement(X_10))) = join(zero,complement(complement(X_10))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(complement(X_10)),meet(X_10,complement(X_10))))),bind(Y,$fot(join(complement(complement(X_10)),zero))),bind(Z,$fot(join(zero,complement(complement(X_10)))))]]) ).
cnf(refute_0_227,plain,
( join(complement(complement(X_10)),zero) != join(zero,complement(complement(X_10)))
| join(complement(complement(X_10)),meet(X_10,complement(X_10))) = join(zero,complement(complement(X_10))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_10)),meet(X_10,complement(X_10))),join(complement(complement(X_10)),zero)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
join(complement(complement(X_10)),meet(X_10,complement(X_10))) = join(zero,complement(complement(X_10))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_10)),zero),join(zero,complement(complement(X_10)))) )],[refute_0_218,refute_0_227]) ).
cnf(refute_0_229,plain,
join(meet(X_10,complement(X_10)),complement(complement(X_10))) = join(complement(complement(X_10)),meet(X_10,complement(X_10))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(complement(X_10)))),bind(B,$fot(meet(X_10,complement(X_10))))]]) ).
cnf(refute_0_230,plain,
( join(complement(complement(X_10)),meet(X_10,complement(X_10))) != join(zero,complement(complement(X_10)))
| join(meet(X_10,complement(X_10)),complement(complement(X_10))) != join(complement(complement(X_10)),meet(X_10,complement(X_10)))
| join(meet(X_10,complement(X_10)),complement(complement(X_10))) = join(zero,complement(complement(X_10))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(X_10,complement(X_10)),complement(complement(X_10))))),bind(Y,$fot(join(complement(complement(X_10)),meet(X_10,complement(X_10))))),bind(Z,$fot(join(zero,complement(complement(X_10)))))]]) ).
cnf(refute_0_231,plain,
( join(complement(complement(X_10)),meet(X_10,complement(X_10))) != join(zero,complement(complement(X_10)))
| join(meet(X_10,complement(X_10)),complement(complement(X_10))) = join(zero,complement(complement(X_10))) ),
inference(resolve,[$cnf( $equal(join(meet(X_10,complement(X_10)),complement(complement(X_10))),join(complement(complement(X_10)),meet(X_10,complement(X_10)))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
join(meet(X_10,complement(X_10)),complement(complement(X_10))) = join(zero,complement(complement(X_10))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_10)),meet(X_10,complement(X_10))),join(zero,complement(complement(X_10)))) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( X_10 != join(meet(X_10,complement(X_10)),complement(complement(X_10)))
| join(meet(X_10,complement(X_10)),complement(complement(X_10))) != join(zero,complement(complement(X_10)))
| X_10 = join(zero,complement(complement(X_10))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_10,join(zero,complement(complement(X_10)))) ),[0],$fot(join(meet(X_10,complement(X_10)),complement(complement(X_10))))]]) ).
cnf(refute_0_234,plain,
( X_10 != join(meet(X_10,complement(X_10)),complement(complement(X_10)))
| X_10 = join(zero,complement(complement(X_10))) ),
inference(resolve,[$cnf( $equal(join(meet(X_10,complement(X_10)),complement(complement(X_10))),join(zero,complement(complement(X_10)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
X_10 = join(zero,complement(complement(X_10))),
inference(resolve,[$cnf( $equal(X_10,join(meet(X_10,complement(X_10)),complement(complement(X_10)))) )],[refute_0_217,refute_0_234]) ).
cnf(refute_0_236,plain,
meet(top,complement(X_51)) = complement(join(zero,complement(complement(X_51)))),
inference(subst,[],[refute_0_130:[bind(B,$fot(complement(X_51)))]]) ).
cnf(refute_0_237,plain,
X_51 = join(zero,complement(complement(X_51))),
inference(subst,[],[refute_0_235:[bind(X_10,$fot(X_51))]]) ).
cnf(refute_0_238,plain,
( X_51 != join(zero,complement(complement(X_51)))
| join(zero,complement(complement(X_51))) = X_51 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_51)),bind(Y,$fot(join(zero,complement(complement(X_51)))))]]) ).
cnf(refute_0_239,plain,
join(zero,complement(complement(X_51))) = X_51,
inference(resolve,[$cnf( $equal(X_51,join(zero,complement(complement(X_51)))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
( join(zero,complement(complement(X_51))) != X_51
| meet(top,complement(X_51)) != complement(join(zero,complement(complement(X_51))))
| meet(top,complement(X_51)) = complement(X_51) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(X_51)),complement(join(zero,complement(complement(X_51))))) ),[1,0],$fot(X_51)]]) ).
cnf(refute_0_241,plain,
( meet(top,complement(X_51)) != complement(join(zero,complement(complement(X_51))))
| meet(top,complement(X_51)) = complement(X_51) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_51))),X_51) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
meet(top,complement(X_51)) = complement(X_51),
inference(resolve,[$cnf( $equal(meet(top,complement(X_51)),complement(join(zero,complement(complement(X_51))))) )],[refute_0_236,refute_0_241]) ).
cnf(refute_0_243,plain,
meet(top,complement(X_10)) = complement(X_10),
inference(subst,[],[refute_0_242:[bind(X_51,$fot(X_10))]]) ).
cnf(refute_0_244,plain,
complement(meet(top,complement(X_10))) = complement(meet(top,complement(X_10))),
introduced(tautology,[refl,[$fot(complement(meet(top,complement(X_10))))]]) ).
cnf(refute_0_245,plain,
( complement(meet(top,complement(X_10))) != complement(meet(top,complement(X_10)))
| meet(top,complement(X_10)) != complement(X_10)
| complement(meet(top,complement(X_10))) = complement(complement(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,complement(X_10))),complement(meet(top,complement(X_10)))) ),[1,0],$fot(complement(X_10))]]) ).
cnf(refute_0_246,plain,
( meet(top,complement(X_10)) != complement(X_10)
| complement(meet(top,complement(X_10))) = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_10))),complement(meet(top,complement(X_10)))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
complement(meet(top,complement(X_10))) = complement(complement(X_10)),
inference(resolve,[$cnf( $equal(meet(top,complement(X_10)),complement(X_10)) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
X_10 = join(meet(X_10,complement(complement(X_10))),complement(join(complement(X_10),complement(complement(X_10))))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_10)),bind(B,$fot(complement(complement(X_10))))]]) ).
cnf(refute_0_249,plain,
top = join(complement(X_10),complement(complement(X_10))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_10)))]]) ).
cnf(refute_0_250,plain,
( top != join(complement(X_10),complement(complement(X_10)))
| join(complement(X_10),complement(complement(X_10))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_10),complement(complement(X_10)))))]]) ).
cnf(refute_0_251,plain,
join(complement(X_10),complement(complement(X_10))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_10),complement(complement(X_10)))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
( X_10 != join(meet(X_10,complement(complement(X_10))),complement(join(complement(X_10),complement(complement(X_10)))))
| join(complement(X_10),complement(complement(X_10))) != top
| X_10 = join(meet(X_10,complement(complement(X_10))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_10,join(meet(X_10,complement(complement(X_10))),complement(join(complement(X_10),complement(complement(X_10)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_253,plain,
( X_10 != join(meet(X_10,complement(complement(X_10))),complement(join(complement(X_10),complement(complement(X_10)))))
| X_10 = join(meet(X_10,complement(complement(X_10))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_10),complement(complement(X_10))),top) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
X_10 = join(meet(X_10,complement(complement(X_10))),complement(top)),
inference(resolve,[$cnf( $equal(X_10,join(meet(X_10,complement(complement(X_10))),complement(join(complement(X_10),complement(complement(X_10)))))) )],[refute_0_248,refute_0_253]) ).
cnf(refute_0_255,plain,
join(meet(X_10,complement(complement(X_10))),complement(top)) = join(complement(top),meet(X_10,complement(complement(X_10)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_10,complement(complement(X_10)))))]]) ).
cnf(refute_0_256,plain,
( X_10 != join(meet(X_10,complement(complement(X_10))),complement(top))
| join(meet(X_10,complement(complement(X_10))),complement(top)) != join(complement(top),meet(X_10,complement(complement(X_10))))
| X_10 = join(complement(top),meet(X_10,complement(complement(X_10)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_10,join(complement(top),meet(X_10,complement(complement(X_10))))) ),[0],$fot(join(meet(X_10,complement(complement(X_10))),complement(top)))]]) ).
cnf(refute_0_257,plain,
( X_10 != join(meet(X_10,complement(complement(X_10))),complement(top))
| X_10 = join(complement(top),meet(X_10,complement(complement(X_10)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_10,complement(complement(X_10))),complement(top)),join(complement(top),meet(X_10,complement(complement(X_10))))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
X_10 = join(complement(top),meet(X_10,complement(complement(X_10)))),
inference(resolve,[$cnf( $equal(X_10,join(meet(X_10,complement(complement(X_10))),complement(top))) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
join(complement(top),meet(X_10,complement(complement(X_10)))) = join(complement(top),meet(X_10,complement(complement(X_10)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_10,complement(complement(X_10)))))]]) ).
cnf(refute_0_260,plain,
( complement(top) != zero
| join(complement(top),meet(X_10,complement(complement(X_10)))) != join(complement(top),meet(X_10,complement(complement(X_10))))
| join(complement(top),meet(X_10,complement(complement(X_10)))) = join(zero,meet(X_10,complement(complement(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_10,complement(complement(X_10)))),join(complement(top),meet(X_10,complement(complement(X_10))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_261,plain,
( complement(top) != zero
| join(complement(top),meet(X_10,complement(complement(X_10)))) = join(zero,meet(X_10,complement(complement(X_10)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_10,complement(complement(X_10)))),join(complement(top),meet(X_10,complement(complement(X_10))))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
join(complement(top),meet(X_10,complement(complement(X_10)))) = join(zero,meet(X_10,complement(complement(X_10)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_261]) ).
cnf(refute_0_263,plain,
( X_10 != join(complement(top),meet(X_10,complement(complement(X_10))))
| join(complement(top),meet(X_10,complement(complement(X_10)))) != join(zero,meet(X_10,complement(complement(X_10))))
| X_10 = join(zero,meet(X_10,complement(complement(X_10)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_10,join(zero,meet(X_10,complement(complement(X_10))))) ),[0],$fot(join(complement(top),meet(X_10,complement(complement(X_10)))))]]) ).
cnf(refute_0_264,plain,
( X_10 != join(complement(top),meet(X_10,complement(complement(X_10))))
| X_10 = join(zero,meet(X_10,complement(complement(X_10)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_10,complement(complement(X_10)))),join(zero,meet(X_10,complement(complement(X_10))))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
X_10 = join(zero,meet(X_10,complement(complement(X_10)))),
inference(resolve,[$cnf( $equal(X_10,join(complement(top),meet(X_10,complement(complement(X_10))))) )],[refute_0_258,refute_0_264]) ).
cnf(refute_0_266,plain,
join(zero,complement(X_44)) = join(zero,meet(join(zero,complement(X_44)),complement(complement(join(zero,complement(X_44)))))),
inference(subst,[],[refute_0_265:[bind(X_10,$fot(join(zero,complement(X_44))))]]) ).
cnf(refute_0_267,plain,
meet(top,X_44) = complement(join(zero,complement(X_44))),
inference(subst,[],[refute_0_130:[bind(B,$fot(X_44))]]) ).
cnf(refute_0_268,plain,
( meet(top,X_44) != complement(join(zero,complement(X_44)))
| complement(join(zero,complement(X_44))) = meet(top,X_44) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,X_44))),bind(Y,$fot(complement(join(zero,complement(X_44)))))]]) ).
cnf(refute_0_269,plain,
complement(join(zero,complement(X_44))) = meet(top,X_44),
inference(resolve,[$cnf( $equal(meet(top,X_44),complement(join(zero,complement(X_44)))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
( complement(join(zero,complement(X_44))) != meet(top,X_44)
| join(zero,complement(X_44)) != join(zero,meet(join(zero,complement(X_44)),complement(complement(join(zero,complement(X_44))))))
| join(zero,complement(X_44)) = join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(X_44)),join(zero,meet(join(zero,complement(X_44)),complement(complement(join(zero,complement(X_44))))))) ),[1,1,1,0],$fot(meet(top,X_44))]]) ).
cnf(refute_0_271,plain,
( join(zero,complement(X_44)) != join(zero,meet(join(zero,complement(X_44)),complement(complement(join(zero,complement(X_44))))))
| join(zero,complement(X_44)) = join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_44))),meet(top,X_44)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
join(zero,complement(X_44)) = join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))),
inference(resolve,[$cnf( $equal(join(zero,complement(X_44)),join(zero,meet(join(zero,complement(X_44)),complement(complement(join(zero,complement(X_44))))))) )],[refute_0_266,refute_0_271]) ).
cnf(refute_0_273,plain,
( meet(X_17,X_18) != meet(X_18,X_17)
| meet(X_18,X_17) = meet(X_17,X_18) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_17,X_18))),bind(Y,$fot(meet(X_18,X_17)))]]) ).
cnf(refute_0_274,plain,
meet(X_18,X_17) = meet(X_17,X_18),
inference(resolve,[$cnf( $equal(meet(X_17,X_18),meet(X_18,X_17)) )],[refute_0_67,refute_0_273]) ).
cnf(refute_0_275,plain,
meet(join(zero,complement(X_44)),complement(meet(top,X_44))) = meet(complement(meet(top,X_44)),join(zero,complement(X_44))),
inference(subst,[],[refute_0_274:[bind(X_17,$fot(complement(meet(top,X_44)))),bind(X_18,$fot(join(zero,complement(X_44))))]]) ).
cnf(refute_0_276,plain,
join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) = join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))))]]) ).
cnf(refute_0_277,plain,
( join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) != join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44))))
| meet(join(zero,complement(X_44)),complement(meet(top,X_44))) != meet(complement(meet(top,X_44)),join(zero,complement(X_44)))
| join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) = join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))),join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44))))) ),[1,1],$fot(meet(complement(meet(top,X_44)),join(zero,complement(X_44))))]]) ).
cnf(refute_0_278,plain,
( meet(join(zero,complement(X_44)),complement(meet(top,X_44))) != meet(complement(meet(top,X_44)),join(zero,complement(X_44)))
| join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) = join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))),join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44))))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) = join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_44)),complement(meet(top,X_44))),meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) )],[refute_0_275,refute_0_278]) ).
cnf(refute_0_280,plain,
( join(zero,complement(X_44)) != join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44))))
| join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))) != join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))
| join(zero,complement(X_44)) = join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(X_44)),join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))) ),[0],$fot(join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))))]]) ).
cnf(refute_0_281,plain,
( join(zero,complement(X_44)) != join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44))))
| join(zero,complement(X_44)) = join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44)))),join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
join(zero,complement(X_44)) = join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))),
inference(resolve,[$cnf( $equal(join(zero,complement(X_44)),join(zero,meet(join(zero,complement(X_44)),complement(meet(top,X_44))))) )],[refute_0_272,refute_0_281]) ).
cnf(refute_0_283,plain,
join(complement(X_17),complement(X_18)) = join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(complement(join(complement(X_17),complement(X_18)))))),
inference(subst,[],[refute_0_258:[bind(X_10,$fot(join(complement(X_17),complement(X_18))))]]) ).
cnf(refute_0_284,plain,
( complement(join(complement(X_17),complement(X_18))) != meet(X_17,X_18)
| join(complement(X_17),complement(X_18)) != join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(complement(join(complement(X_17),complement(X_18))))))
| join(complement(X_17),complement(X_18)) = join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_17),complement(X_18)),join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(complement(join(complement(X_17),complement(X_18))))))) ),[1,1,1,0],$fot(meet(X_17,X_18))]]) ).
cnf(refute_0_285,plain,
( join(complement(X_17),complement(X_18)) != join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(complement(join(complement(X_17),complement(X_18))))))
| join(complement(X_17),complement(X_18)) = join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_17),complement(X_18))),meet(X_17,X_18)) )],[refute_0_95,refute_0_284]) ).
cnf(refute_0_286,plain,
join(complement(X_17),complement(X_18)) = join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))),
inference(resolve,[$cnf( $equal(join(complement(X_17),complement(X_18)),join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(complement(join(complement(X_17),complement(X_18))))))) )],[refute_0_283,refute_0_285]) ).
cnf(refute_0_287,plain,
meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))) = complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))),
inference(subst,[],[refute_0_109:[bind(B,$fot(complement(meet(X_17,X_18))))]]) ).
cnf(refute_0_288,plain,
join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) = join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))))]]) ).
cnf(refute_0_289,plain,
( join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) != join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))))
| meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))) != complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))
| join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) = join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))),join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))))) ),[1,1],$fot(complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))]]) ).
cnf(refute_0_290,plain,
( meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))) != complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))
| join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) = join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))),join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) = join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) )],[refute_0_287,refute_0_290]) ).
cnf(refute_0_292,plain,
( join(complement(X_17),complement(X_18)) != join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))))
| join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))) != join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))
| join(complement(X_17),complement(X_18)) = join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(X_17),complement(X_18)),join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) ),[0],$fot(join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))))]]) ).
cnf(refute_0_293,plain,
( join(complement(X_17),complement(X_18)) != join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))))
| join(complement(X_17),complement(X_18)) = join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18)))),join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
join(complement(X_17),complement(X_18)) = join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),
inference(resolve,[$cnf( $equal(join(complement(X_17),complement(X_18)),join(complement(top),meet(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))))) )],[refute_0_286,refute_0_293]) ).
cnf(refute_0_295,plain,
join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) = join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),
introduced(tautology,[refl,[$fot(join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))))]]) ).
cnf(refute_0_296,plain,
( complement(top) != zero
| join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) != join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))
| join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) = join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_297,plain,
( complement(top) != zero
| join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) = join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) = join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_297]) ).
cnf(refute_0_299,plain,
( join(complement(X_17),complement(X_18)) != join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))
| join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) != join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))
| join(complement(X_17),complement(X_18)) = join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(X_17),complement(X_18)),join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) ),[0],$fot(join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))))]]) ).
cnf(refute_0_300,plain,
( join(complement(X_17),complement(X_18)) != join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))
| join(complement(X_17),complement(X_18)) = join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
join(complement(X_17),complement(X_18)) = join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),
inference(resolve,[$cnf( $equal(join(complement(X_17),complement(X_18)),join(complement(top),complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) )],[refute_0_294,refute_0_300]) ).
cnf(refute_0_302,plain,
meet(X_10,X_11) = meet(X_11,X_10),
inference(subst,[],[refute_0_67:[bind(X_17,$fot(X_10)),bind(X_18,$fot(X_11))]]) ).
cnf(refute_0_303,plain,
( X_10 != join(meet(X_10,X_11),complement(join(X_11,complement(X_10))))
| meet(X_10,X_11) != meet(X_11,X_10)
| X_10 = join(meet(X_11,X_10),complement(join(X_11,complement(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_10,join(meet(X_10,X_11),complement(join(X_11,complement(X_10))))) ),[1,0],$fot(meet(X_11,X_10))]]) ).
cnf(refute_0_304,plain,
( X_10 != join(meet(X_10,X_11),complement(join(X_11,complement(X_10))))
| X_10 = join(meet(X_11,X_10),complement(join(X_11,complement(X_10)))) ),
inference(resolve,[$cnf( $equal(meet(X_10,X_11),meet(X_11,X_10)) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
X_10 = join(meet(X_11,X_10),complement(join(X_11,complement(X_10)))),
inference(resolve,[$cnf( $equal(X_10,join(meet(X_10,X_11),complement(join(X_11,complement(X_10))))) )],[refute_0_155,refute_0_304]) ).
cnf(refute_0_306,plain,
complement(X_89) = join(meet(X_89,complement(X_89)),complement(join(X_89,complement(complement(X_89))))),
inference(subst,[],[refute_0_305:[bind(X_10,$fot(complement(X_89))),bind(X_11,$fot(X_89))]]) ).
cnf(refute_0_307,plain,
zero = meet(X_89,complement(X_89)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_89))]]) ).
cnf(refute_0_308,plain,
( zero != meet(X_89,complement(X_89))
| meet(X_89,complement(X_89)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_89,complement(X_89))))]]) ).
cnf(refute_0_309,plain,
meet(X_89,complement(X_89)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_89,complement(X_89))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
( complement(X_89) != join(meet(X_89,complement(X_89)),complement(join(X_89,complement(complement(X_89)))))
| meet(X_89,complement(X_89)) != zero
| complement(X_89) = join(zero,complement(join(X_89,complement(complement(X_89))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_89),join(meet(X_89,complement(X_89)),complement(join(X_89,complement(complement(X_89)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_311,plain,
( complement(X_89) != join(meet(X_89,complement(X_89)),complement(join(X_89,complement(complement(X_89)))))
| complement(X_89) = join(zero,complement(join(X_89,complement(complement(X_89))))) ),
inference(resolve,[$cnf( $equal(meet(X_89,complement(X_89)),zero) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
complement(X_89) = join(zero,complement(join(X_89,complement(complement(X_89))))),
inference(resolve,[$cnf( $equal(complement(X_89),join(meet(X_89,complement(X_89)),complement(join(X_89,complement(complement(X_89)))))) )],[refute_0_306,refute_0_311]) ).
cnf(refute_0_313,plain,
( complement(X_89) != join(zero,complement(join(X_89,complement(complement(X_89)))))
| join(zero,complement(join(X_89,complement(complement(X_89))))) = complement(X_89) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_89))),bind(Y,$fot(join(zero,complement(join(X_89,complement(complement(X_89)))))))]]) ).
cnf(refute_0_314,plain,
join(zero,complement(join(X_89,complement(complement(X_89))))) = complement(X_89),
inference(resolve,[$cnf( $equal(complement(X_89),join(zero,complement(join(X_89,complement(complement(X_89)))))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) = complement(meet(X_17,X_18)),
inference(subst,[],[refute_0_314:[bind(X_89,$fot(meet(X_17,X_18)))]]) ).
cnf(refute_0_316,plain,
( join(complement(X_17),complement(X_18)) != join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))
| join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))) != complement(meet(X_17,X_18))
| join(complement(X_17),complement(X_18)) = complement(meet(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))) ),[0],$fot(join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))))]]) ).
cnf(refute_0_317,plain,
( join(complement(X_17),complement(X_18)) != join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))
| join(complement(X_17),complement(X_18)) = complement(meet(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18)))))),complement(meet(X_17,X_18))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
join(complement(X_17),complement(X_18)) = complement(meet(X_17,X_18)),
inference(resolve,[$cnf( $equal(join(complement(X_17),complement(X_18)),join(zero,complement(join(meet(X_17,X_18),complement(complement(meet(X_17,X_18))))))) )],[refute_0_301,refute_0_317]) ).
cnf(refute_0_319,plain,
join(complement(top),complement(X_44)) = complement(meet(top,X_44)),
inference(subst,[],[refute_0_318:[bind(X_17,$fot(top)),bind(X_18,$fot(X_44))]]) ).
cnf(refute_0_320,plain,
join(complement(A),complement(B)) = join(zero,complement(complement(join(complement(A),complement(B))))),
inference(subst,[],[refute_0_235:[bind(X_10,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_321,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(A),complement(B)) != join(zero,complement(complement(join(complement(A),complement(B)))))
| join(complement(A),complement(B)) = join(zero,complement(meet(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(complement(join(complement(A),complement(B)))))) ),[1,1,0],$fot(meet(A,B))]]) ).
cnf(refute_0_322,plain,
( join(complement(A),complement(B)) != join(zero,complement(complement(join(complement(A),complement(B)))))
| join(complement(A),complement(B)) = join(zero,complement(meet(A,B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_28,refute_0_321]) ).
cnf(refute_0_323,plain,
join(complement(A),complement(B)) = join(zero,complement(meet(A,B))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(complement(join(complement(A),complement(B)))))) )],[refute_0_320,refute_0_322]) ).
cnf(refute_0_324,plain,
( join(complement(A),complement(B)) != join(zero,complement(meet(A,B)))
| join(zero,complement(meet(A,B))) = join(complement(A),complement(B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(A),complement(B)))),bind(Y,$fot(join(zero,complement(meet(A,B)))))]]) ).
cnf(refute_0_325,plain,
join(zero,complement(meet(A,B))) = join(complement(A),complement(B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(meet(A,B)))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
join(zero,complement(meet(top,X_44))) = join(complement(top),complement(X_44)),
inference(subst,[],[refute_0_325:[bind(A,$fot(top)),bind(B,$fot(X_44))]]) ).
cnf(refute_0_327,plain,
( join(complement(top),complement(X_44)) != complement(meet(top,X_44))
| join(zero,complement(meet(top,X_44))) != join(complement(top),complement(X_44))
| join(zero,complement(meet(top,X_44))) = complement(meet(top,X_44)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,complement(meet(top,X_44))))),bind(Y,$fot(join(complement(top),complement(X_44)))),bind(Z,$fot(complement(meet(top,X_44))))]]) ).
cnf(refute_0_328,plain,
( join(complement(top),complement(X_44)) != complement(meet(top,X_44))
| join(zero,complement(meet(top,X_44))) = complement(meet(top,X_44)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(top,X_44))),join(complement(top),complement(X_44))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
join(zero,complement(meet(top,X_44))) = complement(meet(top,X_44)),
inference(resolve,[$cnf( $equal(join(complement(top),complement(X_44)),complement(meet(top,X_44))) )],[refute_0_319,refute_0_328]) ).
cnf(refute_0_330,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(subst,[],[refute_0_318:[bind(X_17,$fot(A)),bind(X_18,$fot(B))]]) ).
cnf(refute_0_331,plain,
complement(join(complement(A),complement(B))) = complement(join(complement(A),complement(B))),
introduced(tautology,[refl,[$fot(complement(join(complement(A),complement(B))))]]) ).
cnf(refute_0_332,plain,
( complement(join(complement(A),complement(B))) != complement(join(complement(A),complement(B)))
| join(complement(A),complement(B)) != complement(meet(A,B))
| complement(join(complement(A),complement(B))) = complement(complement(meet(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(B)))) ),[1,0],$fot(complement(meet(A,B)))]]) ).
cnf(refute_0_333,plain,
( join(complement(A),complement(B)) != complement(meet(A,B))
| complement(join(complement(A),complement(B))) = complement(complement(meet(A,B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(B)))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
complement(join(complement(A),complement(B))) = complement(complement(meet(A,B))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),complement(meet(A,B))) )],[refute_0_330,refute_0_333]) ).
cnf(refute_0_335,plain,
( complement(join(complement(A),complement(B))) != complement(complement(meet(A,B)))
| meet(A,B) != complement(join(complement(A),complement(B)))
| meet(A,B) = complement(complement(meet(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) ),[1],$fot(complement(complement(meet(A,B))))]]) ).
cnf(refute_0_336,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| meet(A,B) = complement(complement(meet(A,B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),complement(complement(meet(A,B)))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
meet(A,B) = complement(complement(meet(A,B))),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_336]) ).
cnf(refute_0_338,plain,
( meet(A,B) != complement(complement(meet(A,B)))
| complement(complement(meet(A,B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_339,plain,
complement(complement(meet(A,B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(complement(meet(A,B)))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
complement(complement(meet(top,X_44))) = meet(top,X_44),
inference(subst,[],[refute_0_339:[bind(A,$fot(top)),bind(B,$fot(X_44))]]) ).
cnf(refute_0_341,plain,
complement(complement(complement(meet(top,X_44)))) = complement(complement(complement(meet(top,X_44)))),
introduced(tautology,[refl,[$fot(complement(complement(complement(meet(top,X_44)))))]]) ).
cnf(refute_0_342,plain,
( complement(complement(complement(meet(top,X_44)))) != complement(complement(complement(meet(top,X_44))))
| complement(complement(meet(top,X_44))) != meet(top,X_44)
| complement(complement(complement(meet(top,X_44)))) = complement(meet(top,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(complement(meet(top,X_44)))),complement(complement(complement(meet(top,X_44))))) ),[1,0],$fot(meet(top,X_44))]]) ).
cnf(refute_0_343,plain,
( complement(complement(meet(top,X_44))) != meet(top,X_44)
| complement(complement(complement(meet(top,X_44)))) = complement(meet(top,X_44)) ),
inference(resolve,[$cnf( $equal(complement(complement(complement(meet(top,X_44)))),complement(complement(complement(meet(top,X_44))))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
complement(complement(complement(meet(top,X_44)))) = complement(meet(top,X_44)),
inference(resolve,[$cnf( $equal(complement(complement(meet(top,X_44))),meet(top,X_44)) )],[refute_0_340,refute_0_343]) ).
cnf(refute_0_345,plain,
meet(B,B) = complement(join(complement(B),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_346,plain,
join(complement(B),complement(B)) = complement(B),
inference(subst,[],[refute_0_213:[bind(X_46,$fot(B))]]) ).
cnf(refute_0_347,plain,
( join(complement(B),complement(B)) != complement(B)
| meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_348,plain,
( meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(join(complement(B),complement(B)),complement(B)) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
meet(B,B) = complement(complement(B)),
inference(resolve,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) )],[refute_0_345,refute_0_348]) ).
cnf(refute_0_350,plain,
meet(complement(meet(top,X_44)),complement(meet(top,X_44))) = complement(complement(complement(meet(top,X_44)))),
inference(subst,[],[refute_0_349:[bind(B,$fot(complement(meet(top,X_44))))]]) ).
cnf(refute_0_351,plain,
meet(A,join(zero,complement(X_44))) = complement(join(complement(A),complement(join(zero,complement(X_44))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(zero,complement(X_44))))]]) ).
cnf(refute_0_352,plain,
( complement(join(zero,complement(X_44))) != meet(top,X_44)
| meet(A,join(zero,complement(X_44))) != complement(join(complement(A),complement(join(zero,complement(X_44)))))
| meet(A,join(zero,complement(X_44))) = complement(join(complement(A),meet(top,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_44))),complement(join(complement(A),complement(join(zero,complement(X_44)))))) ),[1,0,1],$fot(meet(top,X_44))]]) ).
cnf(refute_0_353,plain,
( meet(A,join(zero,complement(X_44))) != complement(join(complement(A),complement(join(zero,complement(X_44)))))
| meet(A,join(zero,complement(X_44))) = complement(join(complement(A),meet(top,X_44))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_44))),meet(top,X_44)) )],[refute_0_269,refute_0_352]) ).
cnf(refute_0_354,plain,
meet(A,join(zero,complement(X_44))) = complement(join(complement(A),meet(top,X_44))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_44))),complement(join(complement(A),complement(join(zero,complement(X_44)))))) )],[refute_0_351,refute_0_353]) ).
cnf(refute_0_355,plain,
meet(A,join(complement(X_17),complement(X_18))) = complement(join(complement(A),complement(join(complement(X_17),complement(X_18))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(complement(X_17),complement(X_18))))]]) ).
cnf(refute_0_356,plain,
( complement(join(complement(X_17),complement(X_18))) != meet(X_17,X_18)
| meet(A,join(complement(X_17),complement(X_18))) != complement(join(complement(A),complement(join(complement(X_17),complement(X_18)))))
| meet(A,join(complement(X_17),complement(X_18))) = complement(join(complement(A),meet(X_17,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_17),complement(X_18))),complement(join(complement(A),complement(join(complement(X_17),complement(X_18)))))) ),[1,0,1],$fot(meet(X_17,X_18))]]) ).
cnf(refute_0_357,plain,
( meet(A,join(complement(X_17),complement(X_18))) != complement(join(complement(A),complement(join(complement(X_17),complement(X_18)))))
| meet(A,join(complement(X_17),complement(X_18))) = complement(join(complement(A),meet(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_17),complement(X_18))),meet(X_17,X_18)) )],[refute_0_95,refute_0_356]) ).
cnf(refute_0_358,plain,
meet(A,join(complement(X_17),complement(X_18))) = complement(join(complement(A),meet(X_17,X_18))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_17),complement(X_18))),complement(join(complement(A),complement(join(complement(X_17),complement(X_18)))))) )],[refute_0_355,refute_0_357]) ).
cnf(refute_0_359,plain,
meet(A,join(complement(X_17),complement(X_18))) = meet(A,join(complement(X_17),complement(X_18))),
introduced(tautology,[refl,[$fot(meet(A,join(complement(X_17),complement(X_18))))]]) ).
cnf(refute_0_360,plain,
( join(complement(X_17),complement(X_18)) != complement(meet(X_17,X_18))
| meet(A,join(complement(X_17),complement(X_18))) != meet(A,join(complement(X_17),complement(X_18)))
| meet(A,join(complement(X_17),complement(X_18))) = meet(A,complement(meet(X_17,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_17),complement(X_18))),meet(A,join(complement(X_17),complement(X_18)))) ),[1,1],$fot(complement(meet(X_17,X_18)))]]) ).
cnf(refute_0_361,plain,
( join(complement(X_17),complement(X_18)) != complement(meet(X_17,X_18))
| meet(A,join(complement(X_17),complement(X_18))) = meet(A,complement(meet(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_17),complement(X_18))),meet(A,join(complement(X_17),complement(X_18)))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
meet(A,join(complement(X_17),complement(X_18))) = meet(A,complement(meet(X_17,X_18))),
inference(resolve,[$cnf( $equal(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))) )],[refute_0_318,refute_0_361]) ).
cnf(refute_0_363,plain,
( meet(A,join(complement(X_17),complement(X_18))) != complement(join(complement(A),meet(X_17,X_18)))
| meet(A,join(complement(X_17),complement(X_18))) != meet(A,complement(meet(X_17,X_18)))
| meet(A,complement(meet(X_17,X_18))) = complement(join(complement(A),meet(X_17,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_17),complement(X_18))),complement(join(complement(A),meet(X_17,X_18)))) ),[0],$fot(meet(A,complement(meet(X_17,X_18))))]]) ).
cnf(refute_0_364,plain,
( meet(A,join(complement(X_17),complement(X_18))) != complement(join(complement(A),meet(X_17,X_18)))
| meet(A,complement(meet(X_17,X_18))) = complement(join(complement(A),meet(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_17),complement(X_18))),meet(A,complement(meet(X_17,X_18)))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
meet(A,complement(meet(X_17,X_18))) = complement(join(complement(A),meet(X_17,X_18))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_17),complement(X_18))),complement(join(complement(A),meet(X_17,X_18)))) )],[refute_0_358,refute_0_364]) ).
cnf(refute_0_366,plain,
( meet(A,complement(meet(X_17,X_18))) != complement(join(complement(A),meet(X_17,X_18)))
| complement(join(complement(A),meet(X_17,X_18))) = meet(A,complement(meet(X_17,X_18))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,complement(meet(X_17,X_18))))),bind(Y,$fot(complement(join(complement(A),meet(X_17,X_18)))))]]) ).
cnf(refute_0_367,plain,
complement(join(complement(A),meet(X_17,X_18))) = meet(A,complement(meet(X_17,X_18))),
inference(resolve,[$cnf( $equal(meet(A,complement(meet(X_17,X_18))),complement(join(complement(A),meet(X_17,X_18)))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
complement(join(complement(A),meet(top,X_44))) = meet(A,complement(meet(top,X_44))),
inference(subst,[],[refute_0_367:[bind(X_17,$fot(top)),bind(X_18,$fot(X_44))]]) ).
cnf(refute_0_369,plain,
( complement(join(complement(A),meet(top,X_44))) != meet(A,complement(meet(top,X_44)))
| meet(A,join(zero,complement(X_44))) != complement(join(complement(A),meet(top,X_44)))
| meet(A,join(zero,complement(X_44))) = meet(A,complement(meet(top,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_44))),complement(join(complement(A),meet(top,X_44)))) ),[1],$fot(meet(A,complement(meet(top,X_44))))]]) ).
cnf(refute_0_370,plain,
( meet(A,join(zero,complement(X_44))) != complement(join(complement(A),meet(top,X_44)))
| meet(A,join(zero,complement(X_44))) = meet(A,complement(meet(top,X_44))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_44))),meet(A,complement(meet(top,X_44)))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
meet(A,join(zero,complement(X_44))) = meet(A,complement(meet(top,X_44))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_44))),complement(join(complement(A),meet(top,X_44)))) )],[refute_0_354,refute_0_370]) ).
cnf(refute_0_372,plain,
meet(complement(meet(top,X_44)),join(zero,complement(X_44))) = meet(complement(meet(top,X_44)),complement(meet(top,X_44))),
inference(subst,[],[refute_0_371:[bind(A,$fot(complement(meet(top,X_44))))]]) ).
cnf(refute_0_373,plain,
( meet(complement(meet(top,X_44)),complement(meet(top,X_44))) != complement(complement(complement(meet(top,X_44))))
| meet(complement(meet(top,X_44)),join(zero,complement(X_44))) != meet(complement(meet(top,X_44)),complement(meet(top,X_44)))
| meet(complement(meet(top,X_44)),join(zero,complement(X_44))) = complement(complement(complement(meet(top,X_44)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(complement(meet(top,X_44)),join(zero,complement(X_44))))),bind(Y,$fot(meet(complement(meet(top,X_44)),complement(meet(top,X_44))))),bind(Z,$fot(complement(complement(complement(meet(top,X_44))))))]]) ).
cnf(refute_0_374,plain,
( meet(complement(meet(top,X_44)),complement(meet(top,X_44))) != complement(complement(complement(meet(top,X_44))))
| meet(complement(meet(top,X_44)),join(zero,complement(X_44))) = complement(complement(complement(meet(top,X_44)))) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_44)),join(zero,complement(X_44))),meet(complement(meet(top,X_44)),complement(meet(top,X_44)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
meet(complement(meet(top,X_44)),join(zero,complement(X_44))) = complement(complement(complement(meet(top,X_44)))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_44)),complement(meet(top,X_44))),complement(complement(complement(meet(top,X_44))))) )],[refute_0_350,refute_0_374]) ).
cnf(refute_0_376,plain,
( complement(complement(complement(meet(top,X_44)))) != complement(meet(top,X_44))
| meet(complement(meet(top,X_44)),join(zero,complement(X_44))) != complement(complement(complement(meet(top,X_44))))
| meet(complement(meet(top,X_44)),join(zero,complement(X_44))) = complement(meet(top,X_44)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(complement(meet(top,X_44)),join(zero,complement(X_44))))),bind(Y,$fot(complement(complement(complement(meet(top,X_44)))))),bind(Z,$fot(complement(meet(top,X_44))))]]) ).
cnf(refute_0_377,plain,
( complement(complement(complement(meet(top,X_44)))) != complement(meet(top,X_44))
| meet(complement(meet(top,X_44)),join(zero,complement(X_44))) = complement(meet(top,X_44)) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_44)),join(zero,complement(X_44))),complement(complement(complement(meet(top,X_44))))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
meet(complement(meet(top,X_44)),join(zero,complement(X_44))) = complement(meet(top,X_44)),
inference(resolve,[$cnf( $equal(complement(complement(complement(meet(top,X_44)))),complement(meet(top,X_44))) )],[refute_0_344,refute_0_377]) ).
cnf(refute_0_379,plain,
join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) = join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))))]]) ).
cnf(refute_0_380,plain,
( join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) != join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))
| meet(complement(meet(top,X_44)),join(zero,complement(X_44))) != complement(meet(top,X_44))
| join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) = join(zero,complement(meet(top,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))),join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))) ),[1,1],$fot(complement(meet(top,X_44)))]]) ).
cnf(refute_0_381,plain,
( meet(complement(meet(top,X_44)),join(zero,complement(X_44))) != complement(meet(top,X_44))
| join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) = join(zero,complement(meet(top,X_44))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))),join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) = join(zero,complement(meet(top,X_44))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_44)),join(zero,complement(X_44))),complement(meet(top,X_44))) )],[refute_0_378,refute_0_381]) ).
cnf(refute_0_383,plain,
( join(zero,complement(meet(top,X_44))) != complement(meet(top,X_44))
| join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) != join(zero,complement(meet(top,X_44)))
| join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) = complement(meet(top,X_44)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))))),bind(Y,$fot(join(zero,complement(meet(top,X_44))))),bind(Z,$fot(complement(meet(top,X_44))))]]) ).
cnf(refute_0_384,plain,
( join(zero,complement(meet(top,X_44))) != complement(meet(top,X_44))
| join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) = complement(meet(top,X_44)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))),join(zero,complement(meet(top,X_44)))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) = complement(meet(top,X_44)),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(top,X_44))),complement(meet(top,X_44))) )],[refute_0_329,refute_0_384]) ).
cnf(refute_0_386,plain,
( join(zero,complement(X_44)) != join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))
| join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))) != complement(meet(top,X_44))
| join(zero,complement(X_44)) = complement(meet(top,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(X_44)),complement(meet(top,X_44))) ),[0],$fot(join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))))]]) ).
cnf(refute_0_387,plain,
( join(zero,complement(X_44)) != join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))
| join(zero,complement(X_44)) = complement(meet(top,X_44)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44)))),complement(meet(top,X_44))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
join(zero,complement(X_44)) = complement(meet(top,X_44)),
inference(resolve,[$cnf( $equal(join(zero,complement(X_44)),join(zero,meet(complement(meet(top,X_44)),join(zero,complement(X_44))))) )],[refute_0_282,refute_0_387]) ).
cnf(refute_0_389,plain,
join(zero,complement(complement(X_10))) = complement(meet(top,complement(X_10))),
inference(subst,[],[refute_0_388:[bind(X_44,$fot(complement(X_10)))]]) ).
cnf(refute_0_390,plain,
( complement(meet(top,complement(X_10))) != complement(complement(X_10))
| join(zero,complement(complement(X_10))) != complement(meet(top,complement(X_10)))
| join(zero,complement(complement(X_10))) = complement(complement(X_10)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,complement(complement(X_10))))),bind(Y,$fot(complement(meet(top,complement(X_10))))),bind(Z,$fot(complement(complement(X_10))))]]) ).
cnf(refute_0_391,plain,
( complement(meet(top,complement(X_10))) != complement(complement(X_10))
| join(zero,complement(complement(X_10))) = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_10))),complement(meet(top,complement(X_10)))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
join(zero,complement(complement(X_10))) = complement(complement(X_10)),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_10))),complement(complement(X_10))) )],[refute_0_247,refute_0_391]) ).
cnf(refute_0_393,plain,
( X_10 != join(zero,complement(complement(X_10)))
| join(zero,complement(complement(X_10))) != complement(complement(X_10))
| X_10 = complement(complement(X_10)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_10,complement(complement(X_10))) ),[0],$fot(join(zero,complement(complement(X_10))))]]) ).
cnf(refute_0_394,plain,
( X_10 != join(zero,complement(complement(X_10)))
| X_10 = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_10))),complement(complement(X_10))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
X_10 = complement(complement(X_10)),
inference(resolve,[$cnf( $equal(X_10,join(zero,complement(complement(X_10)))) )],[refute_0_235,refute_0_394]) ).
cnf(refute_0_396,plain,
( X_10 != complement(complement(X_10))
| complement(complement(X_10)) = X_10 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_10)),bind(Y,$fot(complement(complement(X_10))))]]) ).
cnf(refute_0_397,plain,
complement(complement(X_10)) = X_10,
inference(resolve,[$cnf( $equal(X_10,complement(complement(X_10))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
complement(complement(B)) = B,
inference(subst,[],[refute_0_397:[bind(X_10,$fot(B))]]) ).
cnf(refute_0_399,plain,
meet(X_10,X_10) = complement(complement(X_10)),
inference(subst,[],[refute_0_349:[bind(B,$fot(X_10))]]) ).
cnf(refute_0_400,plain,
( complement(complement(X_10)) != X_10
| meet(X_10,X_10) != complement(complement(X_10))
| meet(X_10,X_10) = X_10 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(X_10,X_10))),bind(Y,$fot(complement(complement(X_10)))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_401,plain,
( complement(complement(X_10)) != X_10
| meet(X_10,X_10) = X_10 ),
inference(resolve,[$cnf( $equal(meet(X_10,X_10),complement(complement(X_10))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
meet(X_10,X_10) = X_10,
inference(resolve,[$cnf( $equal(complement(complement(X_10)),X_10) )],[refute_0_397,refute_0_401]) ).
cnf(refute_0_403,plain,
meet(X_10,complement(complement(X_10))) = meet(X_10,complement(complement(X_10))),
introduced(tautology,[refl,[$fot(meet(X_10,complement(complement(X_10))))]]) ).
cnf(refute_0_404,plain,
( complement(complement(X_10)) != X_10
| meet(X_10,complement(complement(X_10))) != meet(X_10,complement(complement(X_10)))
| meet(X_10,complement(complement(X_10))) = meet(X_10,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_10,complement(complement(X_10))),meet(X_10,complement(complement(X_10)))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_405,plain,
( complement(complement(X_10)) != X_10
| meet(X_10,complement(complement(X_10))) = meet(X_10,X_10) ),
inference(resolve,[$cnf( $equal(meet(X_10,complement(complement(X_10))),meet(X_10,complement(complement(X_10)))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
meet(X_10,complement(complement(X_10))) = meet(X_10,X_10),
inference(resolve,[$cnf( $equal(complement(complement(X_10)),X_10) )],[refute_0_397,refute_0_405]) ).
cnf(refute_0_407,plain,
( meet(X_10,X_10) != X_10
| meet(X_10,complement(complement(X_10))) != meet(X_10,X_10)
| meet(X_10,complement(complement(X_10))) = X_10 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(X_10,complement(complement(X_10))))),bind(Y,$fot(meet(X_10,X_10))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_408,plain,
( meet(X_10,X_10) != X_10
| meet(X_10,complement(complement(X_10))) = X_10 ),
inference(resolve,[$cnf( $equal(meet(X_10,complement(complement(X_10))),meet(X_10,X_10)) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
meet(X_10,complement(complement(X_10))) = X_10,
inference(resolve,[$cnf( $equal(meet(X_10,X_10),X_10) )],[refute_0_402,refute_0_408]) ).
cnf(refute_0_410,plain,
join(zero,meet(X_10,complement(complement(X_10)))) = join(zero,meet(X_10,complement(complement(X_10)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_10,complement(complement(X_10)))))]]) ).
cnf(refute_0_411,plain,
( join(zero,meet(X_10,complement(complement(X_10)))) != join(zero,meet(X_10,complement(complement(X_10))))
| meet(X_10,complement(complement(X_10))) != X_10
| join(zero,meet(X_10,complement(complement(X_10)))) = join(zero,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_10,complement(complement(X_10)))),join(zero,meet(X_10,complement(complement(X_10))))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_412,plain,
( meet(X_10,complement(complement(X_10))) != X_10
| join(zero,meet(X_10,complement(complement(X_10)))) = join(zero,X_10) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_10,complement(complement(X_10)))),join(zero,meet(X_10,complement(complement(X_10))))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
join(zero,meet(X_10,complement(complement(X_10)))) = join(zero,X_10),
inference(resolve,[$cnf( $equal(meet(X_10,complement(complement(X_10))),X_10) )],[refute_0_409,refute_0_412]) ).
cnf(refute_0_414,plain,
( X_10 != join(zero,meet(X_10,complement(complement(X_10))))
| join(zero,meet(X_10,complement(complement(X_10)))) != join(zero,X_10)
| X_10 = join(zero,X_10) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_10,join(zero,X_10)) ),[0],$fot(join(zero,meet(X_10,complement(complement(X_10)))))]]) ).
cnf(refute_0_415,plain,
( X_10 != join(zero,meet(X_10,complement(complement(X_10))))
| X_10 = join(zero,X_10) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_10,complement(complement(X_10)))),join(zero,X_10)) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
X_10 = join(zero,X_10),
inference(resolve,[$cnf( $equal(X_10,join(zero,meet(X_10,complement(complement(X_10))))) )],[refute_0_265,refute_0_415]) ).
cnf(refute_0_417,plain,
( X_10 != join(zero,X_10)
| join(zero,X_10) = X_10 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_10)),bind(Y,$fot(join(zero,X_10)))]]) ).
cnf(refute_0_418,plain,
join(zero,X_10) = X_10,
inference(resolve,[$cnf( $equal(X_10,join(zero,X_10)) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
join(zero,complement(B)) = complement(B),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(complement(B)))]]) ).
cnf(refute_0_420,plain,
complement(join(zero,complement(B))) = complement(join(zero,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(zero,complement(B))))]]) ).
cnf(refute_0_421,plain,
( complement(join(zero,complement(B))) != complement(join(zero,complement(B)))
| join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_422,plain,
( join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
complement(join(zero,complement(B))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_419,refute_0_422]) ).
cnf(refute_0_424,plain,
( complement(complement(B)) != B
| complement(join(zero,complement(B))) != complement(complement(B))
| complement(join(zero,complement(B))) = B ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(join(zero,complement(B))))),bind(Y,$fot(complement(complement(B)))),bind(Z,$fot(B))]]) ).
cnf(refute_0_425,plain,
( complement(complement(B)) != B
| complement(join(zero,complement(B))) = B ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(complement(B))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
complement(join(zero,complement(B))) = B,
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_398,refute_0_425]) ).
cnf(refute_0_427,plain,
( complement(join(zero,complement(B))) != B
| meet(top,B) != complement(join(zero,complement(B)))
| meet(top,B) = B ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) ),[1],$fot(B)]]) ).
cnf(refute_0_428,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| meet(top,B) = B ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),B) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
meet(top,B) = B,
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_130,refute_0_428]) ).
cnf(refute_0_430,plain,
meet(top,X_35) = X_35,
inference(subst,[],[refute_0_429:[bind(B,$fot(X_35))]]) ).
cnf(refute_0_431,plain,
join(meet(top,X_35),meet(X_35,zero)) = join(meet(top,X_35),meet(X_35,zero)),
introduced(tautology,[refl,[$fot(join(meet(top,X_35),meet(X_35,zero)))]]) ).
cnf(refute_0_432,plain,
( join(meet(top,X_35),meet(X_35,zero)) != join(meet(top,X_35),meet(X_35,zero))
| meet(top,X_35) != X_35
| join(meet(top,X_35),meet(X_35,zero)) = join(X_35,meet(X_35,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_35),meet(X_35,zero)),join(meet(top,X_35),meet(X_35,zero))) ),[1,0],$fot(X_35)]]) ).
cnf(refute_0_433,plain,
( meet(top,X_35) != X_35
| join(meet(top,X_35),meet(X_35,zero)) = join(X_35,meet(X_35,zero)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_35),meet(X_35,zero)),join(meet(top,X_35),meet(X_35,zero))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
join(meet(top,X_35),meet(X_35,zero)) = join(X_35,meet(X_35,zero)),
inference(resolve,[$cnf( $equal(meet(top,X_35),X_35) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
( X_35 != join(meet(top,X_35),meet(X_35,zero))
| join(meet(top,X_35),meet(X_35,zero)) != join(X_35,meet(X_35,zero))
| X_35 = join(X_35,meet(X_35,zero)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,join(X_35,meet(X_35,zero))) ),[0],$fot(join(meet(top,X_35),meet(X_35,zero)))]]) ).
cnf(refute_0_436,plain,
( X_35 != join(meet(top,X_35),meet(X_35,zero))
| X_35 = join(X_35,meet(X_35,zero)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_35),meet(X_35,zero)),join(X_35,meet(X_35,zero))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
X_35 = join(X_35,meet(X_35,zero)),
inference(resolve,[$cnf( $equal(X_35,join(meet(top,X_35),meet(X_35,zero))) )],[refute_0_148,refute_0_436]) ).
cnf(refute_0_438,plain,
X_119 = join(X_119,meet(X_119,zero)),
inference(subst,[],[refute_0_437:[bind(X_35,$fot(X_119))]]) ).
cnf(refute_0_439,plain,
( X_119 != join(X_119,meet(X_119,zero))
| join(X_119,meet(X_119,zero)) = X_119 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_119)),bind(Y,$fot(join(X_119,meet(X_119,zero))))]]) ).
cnf(refute_0_440,plain,
join(X_119,meet(X_119,zero)) = X_119,
inference(resolve,[$cnf( $equal(X_119,join(X_119,meet(X_119,zero))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
( join(X_118,join(X_119,meet(X_119,zero))) != join(X_119,join(X_118,meet(X_119,zero)))
| join(X_119,meet(X_119,zero)) != X_119
| join(X_118,X_119) = join(X_119,join(X_118,meet(X_119,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_118,join(X_119,meet(X_119,zero))),join(X_119,join(X_118,meet(X_119,zero)))) ),[0,1],$fot(X_119)]]) ).
cnf(refute_0_442,plain,
( join(X_118,join(X_119,meet(X_119,zero))) != join(X_119,join(X_118,meet(X_119,zero)))
| join(X_118,X_119) = join(X_119,join(X_118,meet(X_119,zero))) ),
inference(resolve,[$cnf( $equal(join(X_119,meet(X_119,zero)),X_119) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
join(X_118,X_119) = join(X_119,join(X_118,meet(X_119,zero))),
inference(resolve,[$cnf( $equal(join(X_118,join(X_119,meet(X_119,zero))),join(X_119,join(X_118,meet(X_119,zero)))) )],[refute_0_91,refute_0_442]) ).
cnf(refute_0_444,plain,
X_10 = join(meet(X_10,X_10),complement(join(X_10,complement(X_10)))),
inference(subst,[],[refute_0_305:[bind(X_11,$fot(X_10))]]) ).
cnf(refute_0_445,plain,
( X_10 != join(meet(X_10,X_10),complement(join(X_10,complement(X_10))))
| meet(X_10,X_10) != X_10
| X_10 = join(X_10,complement(join(X_10,complement(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_10,join(meet(X_10,X_10),complement(join(X_10,complement(X_10))))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_446,plain,
( X_10 != join(meet(X_10,X_10),complement(join(X_10,complement(X_10))))
| X_10 = join(X_10,complement(join(X_10,complement(X_10)))) ),
inference(resolve,[$cnf( $equal(meet(X_10,X_10),X_10) )],[refute_0_402,refute_0_445]) ).
cnf(refute_0_447,plain,
X_10 = join(X_10,complement(join(X_10,complement(X_10)))),
inference(resolve,[$cnf( $equal(X_10,join(meet(X_10,X_10),complement(join(X_10,complement(X_10))))) )],[refute_0_444,refute_0_446]) ).
cnf(refute_0_448,plain,
join(X_10,complement(X_10)) = top,
inference(subst,[],[refute_0_100:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_449,plain,
complement(join(X_10,complement(X_10))) = complement(join(X_10,complement(X_10))),
introduced(tautology,[refl,[$fot(complement(join(X_10,complement(X_10))))]]) ).
cnf(refute_0_450,plain,
( complement(join(X_10,complement(X_10))) != complement(join(X_10,complement(X_10)))
| join(X_10,complement(X_10)) != top
| complement(join(X_10,complement(X_10))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(X_10,complement(X_10))),complement(join(X_10,complement(X_10)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_451,plain,
( join(X_10,complement(X_10)) != top
| complement(join(X_10,complement(X_10))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(X_10,complement(X_10))),complement(join(X_10,complement(X_10)))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
complement(join(X_10,complement(X_10))) = complement(top),
inference(resolve,[$cnf( $equal(join(X_10,complement(X_10)),top) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
( complement(join(X_10,complement(X_10))) != complement(top)
| complement(top) != zero
| complement(join(X_10,complement(X_10))) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(join(X_10,complement(X_10))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_454,plain,
( complement(top) != zero
| complement(join(X_10,complement(X_10))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(X_10,complement(X_10))),complement(top)) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
complement(join(X_10,complement(X_10))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_454]) ).
cnf(refute_0_456,plain,
join(X_10,complement(join(X_10,complement(X_10)))) = join(X_10,complement(join(X_10,complement(X_10)))),
introduced(tautology,[refl,[$fot(join(X_10,complement(join(X_10,complement(X_10)))))]]) ).
cnf(refute_0_457,plain,
( complement(join(X_10,complement(X_10))) != zero
| join(X_10,complement(join(X_10,complement(X_10)))) != join(X_10,complement(join(X_10,complement(X_10))))
| join(X_10,complement(join(X_10,complement(X_10)))) = join(X_10,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_10,complement(join(X_10,complement(X_10)))),join(X_10,complement(join(X_10,complement(X_10))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_458,plain,
( complement(join(X_10,complement(X_10))) != zero
| join(X_10,complement(join(X_10,complement(X_10)))) = join(X_10,zero) ),
inference(resolve,[$cnf( $equal(join(X_10,complement(join(X_10,complement(X_10)))),join(X_10,complement(join(X_10,complement(X_10))))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
join(X_10,complement(join(X_10,complement(X_10)))) = join(X_10,zero),
inference(resolve,[$cnf( $equal(complement(join(X_10,complement(X_10))),zero) )],[refute_0_455,refute_0_458]) ).
cnf(refute_0_460,plain,
( X_10 != join(X_10,complement(join(X_10,complement(X_10))))
| join(X_10,complement(join(X_10,complement(X_10)))) != join(X_10,zero)
| X_10 = join(X_10,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_10,join(X_10,zero)) ),[0],$fot(join(X_10,complement(join(X_10,complement(X_10)))))]]) ).
cnf(refute_0_461,plain,
( X_10 != join(X_10,complement(join(X_10,complement(X_10))))
| X_10 = join(X_10,zero) ),
inference(resolve,[$cnf( $equal(join(X_10,complement(join(X_10,complement(X_10)))),join(X_10,zero)) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
X_10 = join(X_10,zero),
inference(resolve,[$cnf( $equal(X_10,join(X_10,complement(join(X_10,complement(X_10))))) )],[refute_0_447,refute_0_461]) ).
cnf(refute_0_463,plain,
( X_10 != join(X_10,zero)
| join(X_10,zero) = X_10 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_10)),bind(Y,$fot(join(X_10,zero)))]]) ).
cnf(refute_0_464,plain,
join(X_10,zero) = X_10,
inference(resolve,[$cnf( $equal(X_10,join(X_10,zero)) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
join(X_118,zero) = X_118,
inference(subst,[],[refute_0_464:[bind(X_10,$fot(X_118))]]) ).
cnf(refute_0_466,plain,
meet(A,B) = meet(B,A),
inference(subst,[],[refute_0_67:[bind(X_17,$fot(A)),bind(X_18,$fot(B))]]) ).
cnf(refute_0_467,plain,
( A != join(meet(A,B),complement(join(complement(A),B)))
| meet(A,B) != meet(B,A)
| A = join(meet(B,A),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$cnf( $equal(A,join(meet(A,B),complement(join(complement(A),B)))) ),[1,0],$fot(meet(B,A))]]) ).
cnf(refute_0_468,plain,
( A != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(B,A),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(meet(A,B),meet(B,A)) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
A = join(meet(B,A),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_38,refute_0_468]) ).
cnf(refute_0_470,plain,
meet(zero,X_129) = join(meet(B,meet(zero,X_129)),complement(join(complement(meet(zero,X_129)),B))),
inference(subst,[],[refute_0_469:[bind(A,$fot(meet(zero,X_129)))]]) ).
cnf(refute_0_471,plain,
join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = join(complement(X_53),join(complement(X_54),meet(X_53,X_54))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(complement(X_54),meet(X_53,X_54)))),bind(B,$fot(complement(X_53)))]]) ).
cnf(refute_0_472,plain,
top = join(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_17),complement(X_18))))]]) ).
cnf(refute_0_473,plain,
( complement(join(complement(X_17),complement(X_18))) != meet(X_17,X_18)
| top != join(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))
| top = join(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))) ),[1,1],$fot(meet(X_17,X_18))]]) ).
cnf(refute_0_474,plain,
( top != join(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))
| top = join(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_17),complement(X_18))),meet(X_17,X_18)) )],[refute_0_95,refute_0_473]) ).
cnf(refute_0_475,plain,
top = join(join(complement(X_17),complement(X_18)),meet(X_17,X_18)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_17),complement(X_18)),complement(join(complement(X_17),complement(X_18))))) )],[refute_0_472,refute_0_474]) ).
cnf(refute_0_476,plain,
join(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) = join(complement(X_17),join(complement(X_18),meet(X_17,X_18))),
inference(subst,[],[refute_0_86:[bind(A,$fot(complement(X_17))),bind(B,$fot(complement(X_18))),bind(C,$fot(meet(X_17,X_18)))]]) ).
cnf(refute_0_477,plain,
( join(join(complement(X_17),complement(X_18)),meet(X_17,X_18)) != join(complement(X_17),join(complement(X_18),meet(X_17,X_18)))
| top != join(join(complement(X_17),complement(X_18)),meet(X_17,X_18))
| top = join(complement(X_17),join(complement(X_18),meet(X_17,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_17),complement(X_18)),meet(X_17,X_18))) ),[1],$fot(join(complement(X_17),join(complement(X_18),meet(X_17,X_18))))]]) ).
cnf(refute_0_478,plain,
( top != join(join(complement(X_17),complement(X_18)),meet(X_17,X_18))
| top = join(complement(X_17),join(complement(X_18),meet(X_17,X_18))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_17),complement(X_18)),meet(X_17,X_18)),join(complement(X_17),join(complement(X_18),meet(X_17,X_18)))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
top = join(complement(X_17),join(complement(X_18),meet(X_17,X_18))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_17),complement(X_18)),meet(X_17,X_18))) )],[refute_0_475,refute_0_478]) ).
cnf(refute_0_480,plain,
top = join(complement(X_53),join(complement(X_54),meet(X_53,X_54))),
inference(subst,[],[refute_0_479:[bind(X_17,$fot(X_53)),bind(X_18,$fot(X_54))]]) ).
cnf(refute_0_481,plain,
( top != join(complement(X_53),join(complement(X_54),meet(X_53,X_54)))
| join(complement(X_53),join(complement(X_54),meet(X_53,X_54))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_53),join(complement(X_54),meet(X_53,X_54)))))]]) ).
cnf(refute_0_482,plain,
join(complement(X_53),join(complement(X_54),meet(X_53,X_54))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_53),join(complement(X_54),meet(X_53,X_54)))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
( join(complement(X_53),join(complement(X_54),meet(X_53,X_54))) != top
| join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) != join(complement(X_53),join(complement(X_54),meet(X_53,X_54)))
| join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)),join(complement(X_53),join(complement(X_54),meet(X_53,X_54)))) ),[1],$fot(top)]]) ).
cnf(refute_0_484,plain,
( join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) != join(complement(X_53),join(complement(X_54),meet(X_53,X_54)))
| join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_53),join(complement(X_54),meet(X_53,X_54))),top) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)),join(complement(X_53),join(complement(X_54),meet(X_53,X_54)))) )],[refute_0_471,refute_0_484]) ).
cnf(refute_0_486,plain,
join(X_16,X_15) = join(X_15,X_16),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_16)),bind(B,$fot(X_15))]]) ).
cnf(refute_0_487,plain,
( join(X_16,X_15) != join(X_15,X_16)
| join(X_15,X_16) = join(X_16,X_15) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_16,X_15))),bind(Y,$fot(join(X_15,X_16)))]]) ).
cnf(refute_0_488,plain,
join(X_15,X_16) = join(X_16,X_15),
inference(resolve,[$cnf( $equal(join(X_16,X_15),join(X_15,X_16)) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
( join(X_14,join(X_15,X_16)) != join(join(X_14,X_15),X_16)
| join(X_15,X_16) != join(X_16,X_15)
| join(X_14,join(X_16,X_15)) = join(join(X_14,X_15),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(join(X_14,X_15),X_16)) ),[0,1],$fot(join(X_16,X_15))]]) ).
cnf(refute_0_490,plain,
( join(X_14,join(X_15,X_16)) != join(join(X_14,X_15),X_16)
| join(X_14,join(X_16,X_15)) = join(join(X_14,X_15),X_16) ),
inference(resolve,[$cnf( $equal(join(X_15,X_16),join(X_16,X_15)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
join(X_14,join(X_16,X_15)) = join(join(X_14,X_15),X_16),
inference(resolve,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(join(X_14,X_15),X_16)) )],[refute_0_78,refute_0_490]) ).
cnf(refute_0_492,plain,
join(join(X_14,X_15),X_16) = join(X_14,join(X_15,X_16)),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_493,plain,
( join(X_14,join(X_16,X_15)) != join(join(X_14,X_15),X_16)
| join(join(X_14,X_15),X_16) != join(X_14,join(X_15,X_16))
| join(X_14,join(X_16,X_15)) = join(X_14,join(X_15,X_16)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_14,join(X_16,X_15)),join(X_14,join(X_15,X_16))) ),[0],$fot(join(join(X_14,X_15),X_16))]]) ).
cnf(refute_0_494,plain,
( join(X_14,join(X_16,X_15)) != join(join(X_14,X_15),X_16)
| join(X_14,join(X_16,X_15)) = join(X_14,join(X_15,X_16)) ),
inference(resolve,[$cnf( $equal(join(join(X_14,X_15),X_16),join(X_14,join(X_15,X_16))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
join(X_14,join(X_16,X_15)) = join(X_14,join(X_15,X_16)),
inference(resolve,[$cnf( $equal(join(X_14,join(X_16,X_15)),join(join(X_14,X_15),X_16)) )],[refute_0_491,refute_0_494]) ).
cnf(refute_0_496,plain,
( join(X_14,join(X_16,X_15)) != join(X_14,join(X_15,X_16))
| join(X_14,join(X_15,X_16)) = join(X_14,join(X_16,X_15)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_14,join(X_16,X_15)))),bind(Y,$fot(join(X_14,join(X_15,X_16))))]]) ).
cnf(refute_0_497,plain,
join(X_14,join(X_15,X_16)) = join(X_14,join(X_16,X_15)),
inference(resolve,[$cnf( $equal(join(X_14,join(X_16,X_15)),join(X_14,join(X_15,X_16))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
join(complement(X_54),join(meet(X_53,X_54),complement(X_53))) = join(complement(X_54),join(complement(X_53),meet(X_53,X_54))),
inference(subst,[],[refute_0_497:[bind(X_14,$fot(complement(X_54))),bind(X_15,$fot(meet(X_53,X_54))),bind(X_16,$fot(complement(X_53)))]]) ).
cnf(refute_0_499,plain,
join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = join(complement(X_54),join(meet(X_53,X_54),complement(X_53))),
inference(subst,[],[refute_0_86:[bind(A,$fot(complement(X_54))),bind(B,$fot(meet(X_53,X_54))),bind(C,$fot(complement(X_53)))]]) ).
cnf(refute_0_500,plain,
( join(complement(X_54),join(meet(X_53,X_54),complement(X_53))) != join(complement(X_54),join(complement(X_53),meet(X_53,X_54)))
| join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) != join(complement(X_54),join(meet(X_53,X_54),complement(X_53)))
| join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = join(complement(X_54),join(complement(X_53),meet(X_53,X_54))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)))),bind(Y,$fot(join(complement(X_54),join(meet(X_53,X_54),complement(X_53))))),bind(Z,$fot(join(complement(X_54),join(complement(X_53),meet(X_53,X_54)))))]]) ).
cnf(refute_0_501,plain,
( join(complement(X_54),join(meet(X_53,X_54),complement(X_53))) != join(complement(X_54),join(complement(X_53),meet(X_53,X_54)))
| join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = join(complement(X_54),join(complement(X_53),meet(X_53,X_54))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)),join(complement(X_54),join(meet(X_53,X_54),complement(X_53)))) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) = join(complement(X_54),join(complement(X_53),meet(X_53,X_54))),
inference(resolve,[$cnf( $equal(join(complement(X_54),join(meet(X_53,X_54),complement(X_53))),join(complement(X_54),join(complement(X_53),meet(X_53,X_54)))) )],[refute_0_498,refute_0_501]) ).
cnf(refute_0_503,plain,
( join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) != join(complement(X_54),join(complement(X_53),meet(X_53,X_54)))
| join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) != top
| join(complement(X_54),join(complement(X_53),meet(X_53,X_54))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)),top) ),[0],$fot(join(complement(X_54),join(complement(X_53),meet(X_53,X_54))))]]) ).
cnf(refute_0_504,plain,
( join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)) != top
| join(complement(X_54),join(complement(X_53),meet(X_53,X_54))) = top ),
inference(resolve,[$cnf( $equal(join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)),join(complement(X_54),join(complement(X_53),meet(X_53,X_54)))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
join(complement(X_54),join(complement(X_53),meet(X_53,X_54))) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_54),meet(X_53,X_54)),complement(X_53)),top) )],[refute_0_485,refute_0_504]) ).
cnf(refute_0_506,plain,
join(complement(X_128),join(complement(X_128),meet(X_128,X_128))) = top,
inference(subst,[],[refute_0_505:[bind(X_53,$fot(X_128)),bind(X_54,$fot(X_128))]]) ).
cnf(refute_0_507,plain,
( complement(complement(B)) != B
| meet(B,B) != complement(complement(B))
| meet(B,B) = B ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(complement(B))) ),[1],$fot(B)]]) ).
cnf(refute_0_508,plain,
( meet(B,B) != complement(complement(B))
| meet(B,B) = B ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_398,refute_0_507]) ).
cnf(refute_0_509,plain,
meet(B,B) = B,
inference(resolve,[$cnf( $equal(meet(B,B),complement(complement(B))) )],[refute_0_349,refute_0_508]) ).
cnf(refute_0_510,plain,
meet(X_128,X_128) = X_128,
inference(subst,[],[refute_0_509:[bind(B,$fot(X_128))]]) ).
cnf(refute_0_511,plain,
( join(complement(X_128),join(complement(X_128),meet(X_128,X_128))) != top
| meet(X_128,X_128) != X_128
| join(complement(X_128),join(complement(X_128),X_128)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_128),join(complement(X_128),meet(X_128,X_128))),top) ),[0,1,1],$fot(X_128)]]) ).
cnf(refute_0_512,plain,
( join(complement(X_128),join(complement(X_128),meet(X_128,X_128))) != top
| join(complement(X_128),join(complement(X_128),X_128)) = top ),
inference(resolve,[$cnf( $equal(meet(X_128,X_128),X_128) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
join(complement(X_128),join(complement(X_128),X_128)) = top,
inference(resolve,[$cnf( $equal(join(complement(X_128),join(complement(X_128),meet(X_128,X_128))),top) )],[refute_0_506,refute_0_512]) ).
cnf(refute_0_514,plain,
join(top,complement(X_79)) = join(zero,meet(join(top,complement(X_79)),complement(complement(join(top,complement(X_79)))))),
inference(subst,[],[refute_0_265:[bind(X_10,$fot(join(top,complement(X_79))))]]) ).
cnf(refute_0_515,plain,
meet(zero,B) = complement(join(complement(zero),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(zero))]]) ).
cnf(refute_0_516,plain,
complement(zero) = join(meet(top,complement(zero)),meet(complement(zero),zero)),
inference(subst,[],[refute_0_148:[bind(X_35,$fot(complement(zero)))]]) ).
cnf(refute_0_517,plain,
top = join(meet(top,meet(X_13,complement(complement(X_13)))),complement(join(complement(top),meet(X_13,complement(complement(X_13)))))),
inference(subst,[],[refute_0_38:[bind(A,$fot(top)),bind(B,$fot(meet(X_13,complement(complement(X_13)))))]]) ).
cnf(refute_0_518,plain,
X_13 = join(complement(top),meet(X_13,complement(complement(X_13)))),
inference(subst,[],[refute_0_258:[bind(X_10,$fot(X_13))]]) ).
cnf(refute_0_519,plain,
( X_13 != join(complement(top),meet(X_13,complement(complement(X_13))))
| join(complement(top),meet(X_13,complement(complement(X_13)))) = X_13 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_13)),bind(Y,$fot(join(complement(top),meet(X_13,complement(complement(X_13))))))]]) ).
cnf(refute_0_520,plain,
join(complement(top),meet(X_13,complement(complement(X_13)))) = X_13,
inference(resolve,[$cnf( $equal(X_13,join(complement(top),meet(X_13,complement(complement(X_13))))) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
( join(complement(top),meet(X_13,complement(complement(X_13)))) != X_13
| top != join(meet(top,meet(X_13,complement(complement(X_13)))),complement(join(complement(top),meet(X_13,complement(complement(X_13))))))
| top = join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,meet(X_13,complement(complement(X_13)))),complement(join(complement(top),meet(X_13,complement(complement(X_13))))))) ),[1,1,0],$fot(X_13)]]) ).
cnf(refute_0_522,plain,
( top != join(meet(top,meet(X_13,complement(complement(X_13)))),complement(join(complement(top),meet(X_13,complement(complement(X_13))))))
| top = join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_13,complement(complement(X_13)))),X_13) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
top = join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13)),
inference(resolve,[$cnf( $equal(top,join(meet(top,meet(X_13,complement(complement(X_13)))),complement(join(complement(top),meet(X_13,complement(complement(X_13))))))) )],[refute_0_517,refute_0_522]) ).
cnf(refute_0_524,plain,
join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13)) = join(complement(X_13),meet(top,meet(X_13,complement(complement(X_13))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_13))),bind(B,$fot(meet(top,meet(X_13,complement(complement(X_13))))))]]) ).
cnf(refute_0_525,plain,
( join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13)) != join(complement(X_13),meet(top,meet(X_13,complement(complement(X_13)))))
| top != join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13))
| top = join(complement(X_13),meet(top,meet(X_13,complement(complement(X_13))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13))) ),[1],$fot(join(complement(X_13),meet(top,meet(X_13,complement(complement(X_13))))))]]) ).
cnf(refute_0_526,plain,
( top != join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13))
| top = join(complement(X_13),meet(top,meet(X_13,complement(complement(X_13))))) ),
inference(resolve,[$cnf( $equal(join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13)),join(complement(X_13),meet(top,meet(X_13,complement(complement(X_13)))))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
top = join(complement(X_13),meet(top,meet(X_13,complement(complement(X_13))))),
inference(resolve,[$cnf( $equal(top,join(meet(top,meet(X_13,complement(complement(X_13)))),complement(X_13))) )],[refute_0_523,refute_0_526]) ).
cnf(refute_0_528,plain,
top = join(complement(top),meet(top,meet(top,complement(complement(top))))),
inference(subst,[],[refute_0_527:[bind(X_13,$fot(top))]]) ).
cnf(refute_0_529,plain,
( complement(top) != zero
| top != join(complement(top),meet(top,meet(top,complement(complement(top)))))
| top = join(complement(top),meet(top,meet(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(top),meet(top,meet(top,complement(complement(top)))))) ),[1,1,1,1,0],$fot(zero)]]) ).
cnf(refute_0_530,plain,
( top != join(complement(top),meet(top,meet(top,complement(complement(top)))))
| top = join(complement(top),meet(top,meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_529]) ).
cnf(refute_0_531,plain,
top = join(complement(top),meet(top,meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(top,join(complement(top),meet(top,meet(top,complement(complement(top)))))) )],[refute_0_528,refute_0_530]) ).
cnf(refute_0_532,plain,
meet(top,complement(zero)) = join(meet(meet(top,complement(zero)),top),complement(join(top,complement(meet(top,complement(zero)))))),
inference(subst,[],[refute_0_155:[bind(X_10,$fot(meet(top,complement(zero)))),bind(X_11,$fot(top))]]) ).
cnf(refute_0_533,plain,
join(zero,join(meet(top,complement(zero)),C)) = join(join(zero,meet(top,complement(zero))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_534,plain,
top = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_265:[bind(X_10,$fot(top))]]) ).
cnf(refute_0_535,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_536,plain,
( top != join(zero,meet(top,complement(complement(top))))
| top = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_535]) ).
cnf(refute_0_537,plain,
top = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_534,refute_0_536]) ).
cnf(refute_0_538,plain,
( top != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(zero)))))]]) ).
cnf(refute_0_539,plain,
join(zero,meet(top,complement(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(zero)))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
( join(zero,join(meet(top,complement(zero)),C)) != join(join(zero,meet(top,complement(zero))),C)
| join(zero,meet(top,complement(zero))) != top
| join(zero,join(meet(top,complement(zero)),C)) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,complement(zero)),C)),join(join(zero,meet(top,complement(zero))),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_541,plain,
( join(zero,join(meet(top,complement(zero)),C)) != join(join(zero,meet(top,complement(zero))),C)
| join(zero,join(meet(top,complement(zero)),C)) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(zero))),top) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
join(zero,join(meet(top,complement(zero)),C)) = join(top,C),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,complement(zero)),C)),join(join(zero,meet(top,complement(zero))),C)) )],[refute_0_533,refute_0_541]) ).
cnf(refute_0_543,plain,
join(zero,join(meet(top,complement(zero)),complement(meet(top,complement(zero))))) = join(top,complement(meet(top,complement(zero)))),
inference(subst,[],[refute_0_542:[bind(C,$fot(complement(meet(top,complement(zero)))))]]) ).
cnf(refute_0_544,plain,
top = join(meet(top,complement(zero)),complement(meet(top,complement(zero)))),
inference(subst,[],[def_top_12:[bind(A,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_545,plain,
( top != join(meet(top,complement(zero)),complement(meet(top,complement(zero))))
| join(meet(top,complement(zero)),complement(meet(top,complement(zero)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(meet(top,complement(zero)),complement(meet(top,complement(zero))))))]]) ).
cnf(refute_0_546,plain,
join(meet(top,complement(zero)),complement(meet(top,complement(zero)))) = top,
inference(resolve,[$cnf( $equal(top,join(meet(top,complement(zero)),complement(meet(top,complement(zero))))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
( join(meet(top,complement(zero)),complement(meet(top,complement(zero)))) != top
| join(zero,join(meet(top,complement(zero)),complement(meet(top,complement(zero))))) != join(top,complement(meet(top,complement(zero))))
| join(zero,top) = join(top,complement(meet(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,complement(zero)),complement(meet(top,complement(zero))))),join(top,complement(meet(top,complement(zero))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_548,plain,
( join(zero,join(meet(top,complement(zero)),complement(meet(top,complement(zero))))) != join(top,complement(meet(top,complement(zero))))
| join(zero,top) = join(top,complement(meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(zero)),complement(meet(top,complement(zero)))),top) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
join(zero,top) = join(top,complement(meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,complement(zero)),complement(meet(top,complement(zero))))),join(top,complement(meet(top,complement(zero))))) )],[refute_0_543,refute_0_548]) ).
cnf(refute_0_550,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_551,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_552,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_551]) ).
cnf(refute_0_553,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_550,refute_0_552]) ).
cnf(refute_0_554,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_555,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
join(zero,top) = join(top,zero),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(zero))]]) ).
cnf(refute_0_557,plain,
( join(top,zero) != top
| join(zero,top) != join(top,zero)
| join(zero,top) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,top))),bind(Y,$fot(join(top,zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_558,plain,
( join(top,zero) != top
| join(zero,top) = top ),
inference(resolve,[$cnf( $equal(join(zero,top),join(top,zero)) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
join(zero,top) = top,
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_555,refute_0_558]) ).
cnf(refute_0_560,plain,
( join(zero,top) != join(top,complement(meet(top,complement(zero))))
| join(zero,top) != top
| top = join(top,complement(meet(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,top),join(top,complement(meet(top,complement(zero))))) ),[0],$fot(top)]]) ).
cnf(refute_0_561,plain,
( join(zero,top) != join(top,complement(meet(top,complement(zero))))
| top = join(top,complement(meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,top),top) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
top = join(top,complement(meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(join(zero,top),join(top,complement(meet(top,complement(zero))))) )],[refute_0_549,refute_0_561]) ).
cnf(refute_0_563,plain,
( top != join(top,complement(meet(top,complement(zero))))
| join(top,complement(meet(top,complement(zero)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(meet(top,complement(zero))))))]]) ).
cnf(refute_0_564,plain,
join(top,complement(meet(top,complement(zero)))) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(meet(top,complement(zero))))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
( join(top,complement(meet(top,complement(zero)))) != top
| meet(top,complement(zero)) != join(meet(meet(top,complement(zero)),top),complement(join(top,complement(meet(top,complement(zero))))))
| meet(top,complement(zero)) = join(meet(meet(top,complement(zero)),top),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(zero)),join(meet(meet(top,complement(zero)),top),complement(join(top,complement(meet(top,complement(zero))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_566,plain,
( meet(top,complement(zero)) != join(meet(meet(top,complement(zero)),top),complement(join(top,complement(meet(top,complement(zero))))))
| meet(top,complement(zero)) = join(meet(meet(top,complement(zero)),top),complement(top)) ),
inference(resolve,[$cnf( $equal(join(top,complement(meet(top,complement(zero)))),top) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
meet(top,complement(zero)) = join(meet(meet(top,complement(zero)),top),complement(top)),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),join(meet(meet(top,complement(zero)),top),complement(join(top,complement(meet(top,complement(zero))))))) )],[refute_0_532,refute_0_566]) ).
cnf(refute_0_568,plain,
meet(meet(top,complement(zero)),top) = meet(top,meet(top,complement(zero))),
inference(subst,[],[refute_0_144:[bind(A,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_569,plain,
join(zero,meet(meet(top,complement(zero)),top)) = join(zero,meet(meet(top,complement(zero)),top)),
introduced(tautology,[refl,[$fot(join(zero,meet(meet(top,complement(zero)),top)))]]) ).
cnf(refute_0_570,plain,
( join(zero,meet(meet(top,complement(zero)),top)) != join(zero,meet(meet(top,complement(zero)),top))
| meet(meet(top,complement(zero)),top) != meet(top,meet(top,complement(zero)))
| join(zero,meet(meet(top,complement(zero)),top)) = join(zero,meet(top,meet(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(meet(top,complement(zero)),top)),join(zero,meet(meet(top,complement(zero)),top))) ),[1,1],$fot(meet(top,meet(top,complement(zero))))]]) ).
cnf(refute_0_571,plain,
( meet(meet(top,complement(zero)),top) != meet(top,meet(top,complement(zero)))
| join(zero,meet(meet(top,complement(zero)),top)) = join(zero,meet(top,meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(top,complement(zero)),top)),join(zero,meet(meet(top,complement(zero)),top))) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
join(zero,meet(meet(top,complement(zero)),top)) = join(zero,meet(top,meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(meet(meet(top,complement(zero)),top),meet(top,meet(top,complement(zero)))) )],[refute_0_568,refute_0_571]) ).
cnf(refute_0_573,plain,
join(complement(top),meet(meet(top,complement(zero)),top)) = join(complement(top),meet(meet(top,complement(zero)),top)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(meet(top,complement(zero)),top)))]]) ).
cnf(refute_0_574,plain,
( complement(top) != zero
| join(complement(top),meet(meet(top,complement(zero)),top)) != join(complement(top),meet(meet(top,complement(zero)),top))
| join(complement(top),meet(meet(top,complement(zero)),top)) = join(zero,meet(meet(top,complement(zero)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(meet(top,complement(zero)),top)),join(complement(top),meet(meet(top,complement(zero)),top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_575,plain,
( complement(top) != zero
| join(complement(top),meet(meet(top,complement(zero)),top)) = join(zero,meet(meet(top,complement(zero)),top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(meet(top,complement(zero)),top)),join(complement(top),meet(meet(top,complement(zero)),top))) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
join(complement(top),meet(meet(top,complement(zero)),top)) = join(zero,meet(meet(top,complement(zero)),top)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_575]) ).
cnf(refute_0_577,plain,
( join(complement(top),meet(meet(top,complement(zero)),top)) != join(zero,meet(meet(top,complement(zero)),top))
| join(zero,meet(meet(top,complement(zero)),top)) != join(zero,meet(top,meet(top,complement(zero))))
| join(complement(top),meet(meet(top,complement(zero)),top)) = join(zero,meet(top,meet(top,complement(zero)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(top),meet(meet(top,complement(zero)),top)))),bind(Y,$fot(join(zero,meet(meet(top,complement(zero)),top)))),bind(Z,$fot(join(zero,meet(top,meet(top,complement(zero))))))]]) ).
cnf(refute_0_578,plain,
( join(zero,meet(meet(top,complement(zero)),top)) != join(zero,meet(top,meet(top,complement(zero))))
| join(complement(top),meet(meet(top,complement(zero)),top)) = join(zero,meet(top,meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(meet(top,complement(zero)),top)),join(zero,meet(meet(top,complement(zero)),top))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
join(complement(top),meet(meet(top,complement(zero)),top)) = join(zero,meet(top,meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(top,complement(zero)),top)),join(zero,meet(top,meet(top,complement(zero))))) )],[refute_0_572,refute_0_578]) ).
cnf(refute_0_580,plain,
join(meet(meet(top,complement(zero)),top),complement(top)) = join(complement(top),meet(meet(top,complement(zero)),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(meet(top,complement(zero)),top)))]]) ).
cnf(refute_0_581,plain,
( join(complement(top),meet(meet(top,complement(zero)),top)) != join(zero,meet(top,meet(top,complement(zero))))
| join(meet(meet(top,complement(zero)),top),complement(top)) != join(complement(top),meet(meet(top,complement(zero)),top))
| join(meet(meet(top,complement(zero)),top),complement(top)) = join(zero,meet(top,meet(top,complement(zero)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(meet(top,complement(zero)),top),complement(top)))),bind(Y,$fot(join(complement(top),meet(meet(top,complement(zero)),top)))),bind(Z,$fot(join(zero,meet(top,meet(top,complement(zero))))))]]) ).
cnf(refute_0_582,plain,
( join(complement(top),meet(meet(top,complement(zero)),top)) != join(zero,meet(top,meet(top,complement(zero))))
| join(meet(meet(top,complement(zero)),top),complement(top)) = join(zero,meet(top,meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(meet(top,complement(zero)),top),complement(top)),join(complement(top),meet(meet(top,complement(zero)),top))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
join(meet(meet(top,complement(zero)),top),complement(top)) = join(zero,meet(top,meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(meet(top,complement(zero)),top)),join(zero,meet(top,meet(top,complement(zero))))) )],[refute_0_579,refute_0_582]) ).
cnf(refute_0_584,plain,
( join(meet(meet(top,complement(zero)),top),complement(top)) != join(zero,meet(top,meet(top,complement(zero))))
| meet(top,complement(zero)) != join(meet(meet(top,complement(zero)),top),complement(top))
| meet(top,complement(zero)) = join(zero,meet(top,meet(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(zero)),join(meet(meet(top,complement(zero)),top),complement(top))) ),[1],$fot(join(zero,meet(top,meet(top,complement(zero)))))]]) ).
cnf(refute_0_585,plain,
( meet(top,complement(zero)) != join(meet(meet(top,complement(zero)),top),complement(top))
| meet(top,complement(zero)) = join(zero,meet(top,meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(meet(top,complement(zero)),top),complement(top)),join(zero,meet(top,meet(top,complement(zero))))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
meet(top,complement(zero)) = join(zero,meet(top,meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),join(meet(meet(top,complement(zero)),top),complement(top))) )],[refute_0_567,refute_0_585]) ).
cnf(refute_0_587,plain,
( meet(top,complement(zero)) != join(zero,meet(top,meet(top,complement(zero))))
| join(zero,meet(top,meet(top,complement(zero)))) = meet(top,complement(zero)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,complement(zero)))),bind(Y,$fot(join(zero,meet(top,meet(top,complement(zero))))))]]) ).
cnf(refute_0_588,plain,
join(zero,meet(top,meet(top,complement(zero)))) = meet(top,complement(zero)),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),join(zero,meet(top,meet(top,complement(zero))))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
join(complement(top),meet(top,meet(top,complement(zero)))) = join(complement(top),meet(top,meet(top,complement(zero)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(top,meet(top,complement(zero)))))]]) ).
cnf(refute_0_590,plain,
( complement(top) != zero
| join(complement(top),meet(top,meet(top,complement(zero)))) != join(complement(top),meet(top,meet(top,complement(zero))))
| join(complement(top),meet(top,meet(top,complement(zero)))) = join(zero,meet(top,meet(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(top,meet(top,complement(zero)))),join(complement(top),meet(top,meet(top,complement(zero))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_591,plain,
( complement(top) != zero
| join(complement(top),meet(top,meet(top,complement(zero)))) = join(zero,meet(top,meet(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,meet(top,complement(zero)))),join(complement(top),meet(top,meet(top,complement(zero))))) )],[refute_0_589,refute_0_590]) ).
cnf(refute_0_592,plain,
join(complement(top),meet(top,meet(top,complement(zero)))) = join(zero,meet(top,meet(top,complement(zero)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_591]) ).
cnf(refute_0_593,plain,
( join(complement(top),meet(top,meet(top,complement(zero)))) != join(zero,meet(top,meet(top,complement(zero))))
| join(zero,meet(top,meet(top,complement(zero)))) != meet(top,complement(zero))
| join(complement(top),meet(top,meet(top,complement(zero)))) = meet(top,complement(zero)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(top),meet(top,meet(top,complement(zero)))))),bind(Y,$fot(join(zero,meet(top,meet(top,complement(zero)))))),bind(Z,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_594,plain,
( join(zero,meet(top,meet(top,complement(zero)))) != meet(top,complement(zero))
| join(complement(top),meet(top,meet(top,complement(zero)))) = meet(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,meet(top,complement(zero)))),join(zero,meet(top,meet(top,complement(zero))))) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
join(complement(top),meet(top,meet(top,complement(zero)))) = meet(top,complement(zero)),
inference(resolve,[$cnf( $equal(join(zero,meet(top,meet(top,complement(zero)))),meet(top,complement(zero))) )],[refute_0_588,refute_0_594]) ).
cnf(refute_0_596,plain,
( join(complement(top),meet(top,meet(top,complement(zero)))) != meet(top,complement(zero))
| top != join(complement(top),meet(top,meet(top,complement(zero))))
| top = meet(top,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(top),meet(top,meet(top,complement(zero))))) ),[1],$fot(meet(top,complement(zero)))]]) ).
cnf(refute_0_597,plain,
( top != join(complement(top),meet(top,meet(top,complement(zero))))
| top = meet(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,meet(top,complement(zero)))),meet(top,complement(zero))) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
top = meet(top,complement(zero)),
inference(resolve,[$cnf( $equal(top,join(complement(top),meet(top,meet(top,complement(zero))))) )],[refute_0_531,refute_0_597]) ).
cnf(refute_0_599,plain,
( top != meet(top,complement(zero))
| meet(top,complement(zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_600,plain,
meet(top,complement(zero)) = top,
inference(resolve,[$cnf( $equal(top,meet(top,complement(zero))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
( complement(zero) != join(meet(top,complement(zero)),meet(complement(zero),zero))
| meet(top,complement(zero)) != top
| complement(zero) = join(top,meet(complement(zero),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(zero),join(meet(top,complement(zero)),meet(complement(zero),zero))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_602,plain,
( complement(zero) != join(meet(top,complement(zero)),meet(complement(zero),zero))
| complement(zero) = join(top,meet(complement(zero),zero)) ),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),top) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
complement(zero) = join(top,meet(complement(zero),zero)),
inference(resolve,[$cnf( $equal(complement(zero),join(meet(top,complement(zero)),meet(complement(zero),zero))) )],[refute_0_516,refute_0_602]) ).
cnf(refute_0_604,plain,
meet(zero,complement(zero)) = zero,
inference(subst,[],[refute_0_220:[bind(A,$fot(zero))]]) ).
cnf(refute_0_605,plain,
meet(complement(zero),zero) = meet(zero,complement(zero)),
inference(subst,[],[refute_0_274:[bind(X_17,$fot(zero)),bind(X_18,$fot(complement(zero)))]]) ).
cnf(refute_0_606,plain,
( meet(complement(zero),zero) != meet(zero,complement(zero))
| meet(zero,complement(zero)) != zero
| meet(complement(zero),zero) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(complement(zero),zero))),bind(Y,$fot(meet(zero,complement(zero)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_607,plain,
( meet(zero,complement(zero)) != zero
| meet(complement(zero),zero) = zero ),
inference(resolve,[$cnf( $equal(meet(complement(zero),zero),meet(zero,complement(zero))) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
meet(complement(zero),zero) = zero,
inference(resolve,[$cnf( $equal(meet(zero,complement(zero)),zero) )],[refute_0_604,refute_0_607]) ).
cnf(refute_0_609,plain,
join(top,meet(complement(zero),zero)) = join(top,meet(complement(zero),zero)),
introduced(tautology,[refl,[$fot(join(top,meet(complement(zero),zero)))]]) ).
cnf(refute_0_610,plain,
( join(top,meet(complement(zero),zero)) != join(top,meet(complement(zero),zero))
| meet(complement(zero),zero) != zero
| join(top,meet(complement(zero),zero)) = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,meet(complement(zero),zero)),join(top,meet(complement(zero),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_611,plain,
( meet(complement(zero),zero) != zero
| join(top,meet(complement(zero),zero)) = join(top,zero) ),
inference(resolve,[$cnf( $equal(join(top,meet(complement(zero),zero)),join(top,meet(complement(zero),zero))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
join(top,meet(complement(zero),zero)) = join(top,zero),
inference(resolve,[$cnf( $equal(meet(complement(zero),zero),zero) )],[refute_0_608,refute_0_611]) ).
cnf(refute_0_613,plain,
( join(top,meet(complement(zero),zero)) != join(top,zero)
| join(top,zero) != top
| join(top,meet(complement(zero),zero)) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(top,meet(complement(zero),zero)))),bind(Y,$fot(join(top,zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_614,plain,
( join(top,zero) != top
| join(top,meet(complement(zero),zero)) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(complement(zero),zero)),join(top,zero)) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
join(top,meet(complement(zero),zero)) = top,
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_555,refute_0_614]) ).
cnf(refute_0_616,plain,
( complement(zero) != join(top,meet(complement(zero),zero))
| join(top,meet(complement(zero),zero)) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(top,meet(complement(zero),zero)))]]) ).
cnf(refute_0_617,plain,
( complement(zero) != join(top,meet(complement(zero),zero))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(complement(zero),zero)),top) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(zero),join(top,meet(complement(zero),zero))) )],[refute_0_603,refute_0_617]) ).
cnf(refute_0_619,plain,
( complement(zero) != top
| meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) ),[1,0,0],$fot(top)]]) ).
cnf(refute_0_620,plain,
( meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
meet(zero,B) = complement(join(top,complement(B))),
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) )],[refute_0_515,refute_0_620]) ).
cnf(refute_0_622,plain,
meet(zero,X_79) = complement(join(top,complement(X_79))),
inference(subst,[],[refute_0_621:[bind(B,$fot(X_79))]]) ).
cnf(refute_0_623,plain,
( meet(zero,X_79) != complement(join(top,complement(X_79)))
| complement(join(top,complement(X_79))) = meet(zero,X_79) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(zero,X_79))),bind(Y,$fot(complement(join(top,complement(X_79)))))]]) ).
cnf(refute_0_624,plain,
complement(join(top,complement(X_79))) = meet(zero,X_79),
inference(resolve,[$cnf( $equal(meet(zero,X_79),complement(join(top,complement(X_79)))) )],[refute_0_622,refute_0_623]) ).
cnf(refute_0_625,plain,
( complement(join(top,complement(X_79))) != meet(zero,X_79)
| join(top,complement(X_79)) != join(zero,meet(join(top,complement(X_79)),complement(complement(join(top,complement(X_79))))))
| join(top,complement(X_79)) = join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(X_79)),join(zero,meet(join(top,complement(X_79)),complement(complement(join(top,complement(X_79))))))) ),[1,1,1,0],$fot(meet(zero,X_79))]]) ).
cnf(refute_0_626,plain,
( join(top,complement(X_79)) != join(zero,meet(join(top,complement(X_79)),complement(complement(join(top,complement(X_79))))))
| join(top,complement(X_79)) = join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(X_79))),meet(zero,X_79)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
join(top,complement(X_79)) = join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))),
inference(resolve,[$cnf( $equal(join(top,complement(X_79)),join(zero,meet(join(top,complement(X_79)),complement(complement(join(top,complement(X_79))))))) )],[refute_0_514,refute_0_626]) ).
cnf(refute_0_628,plain,
meet(join(top,complement(X_79)),complement(meet(zero,X_79))) = meet(complement(meet(zero,X_79)),join(top,complement(X_79))),
inference(subst,[],[refute_0_274:[bind(X_17,$fot(complement(meet(zero,X_79)))),bind(X_18,$fot(join(top,complement(X_79))))]]) ).
cnf(refute_0_629,plain,
join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) = join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))))]]) ).
cnf(refute_0_630,plain,
( join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) != join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79))))
| meet(join(top,complement(X_79)),complement(meet(zero,X_79))) != meet(complement(meet(zero,X_79)),join(top,complement(X_79)))
| join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) = join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))),join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79))))) ),[1,1],$fot(meet(complement(meet(zero,X_79)),join(top,complement(X_79))))]]) ).
cnf(refute_0_631,plain,
( meet(join(top,complement(X_79)),complement(meet(zero,X_79))) != meet(complement(meet(zero,X_79)),join(top,complement(X_79)))
| join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) = join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))),join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79))))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) = join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))),
inference(resolve,[$cnf( $equal(meet(join(top,complement(X_79)),complement(meet(zero,X_79))),meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) )],[refute_0_628,refute_0_631]) ).
cnf(refute_0_633,plain,
( join(top,complement(X_79)) != join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79))))
| join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))) != join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79))))
| join(top,complement(X_79)) = join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(top,complement(X_79)),join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79))))) ),[0],$fot(join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))))]]) ).
cnf(refute_0_634,plain,
( join(top,complement(X_79)) != join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79))))
| join(top,complement(X_79)) = join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79)))),join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79))))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
join(top,complement(X_79)) = join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))),
inference(resolve,[$cnf( $equal(join(top,complement(X_79)),join(zero,meet(join(top,complement(X_79)),complement(meet(zero,X_79))))) )],[refute_0_627,refute_0_634]) ).
cnf(refute_0_636,plain,
join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) = meet(complement(meet(zero,X_79)),join(top,complement(X_79))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(meet(complement(meet(zero,X_79)),join(top,complement(X_79)))))]]) ).
cnf(refute_0_637,plain,
( join(top,complement(X_79)) != join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79))))
| join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) != meet(complement(meet(zero,X_79)),join(top,complement(X_79)))
| join(top,complement(X_79)) = meet(complement(meet(zero,X_79)),join(top,complement(X_79))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(top,complement(X_79)),meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) ),[0],$fot(join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))))]]) ).
cnf(refute_0_638,plain,
( join(top,complement(X_79)) != join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79))))
| join(top,complement(X_79)) = meet(complement(meet(zero,X_79)),join(top,complement(X_79))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79)))),meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
join(top,complement(X_79)) = meet(complement(meet(zero,X_79)),join(top,complement(X_79))),
inference(resolve,[$cnf( $equal(join(top,complement(X_79)),join(zero,meet(complement(meet(zero,X_79)),join(top,complement(X_79))))) )],[refute_0_635,refute_0_638]) ).
cnf(refute_0_640,plain,
meet(complement(meet(zero,X_79)),complement(meet(zero,X_79))) = complement(meet(zero,X_79)),
inference(subst,[],[refute_0_509:[bind(B,$fot(complement(meet(zero,X_79))))]]) ).
cnf(refute_0_641,plain,
meet(A,join(top,complement(X_79))) = complement(join(complement(A),complement(join(top,complement(X_79))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(top,complement(X_79))))]]) ).
cnf(refute_0_642,plain,
( complement(join(top,complement(X_79))) != meet(zero,X_79)
| meet(A,join(top,complement(X_79))) != complement(join(complement(A),complement(join(top,complement(X_79)))))
| meet(A,join(top,complement(X_79))) = complement(join(complement(A),meet(zero,X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(top,complement(X_79))),complement(join(complement(A),complement(join(top,complement(X_79)))))) ),[1,0,1],$fot(meet(zero,X_79))]]) ).
cnf(refute_0_643,plain,
( meet(A,join(top,complement(X_79))) != complement(join(complement(A),complement(join(top,complement(X_79)))))
| meet(A,join(top,complement(X_79))) = complement(join(complement(A),meet(zero,X_79))) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(X_79))),meet(zero,X_79)) )],[refute_0_624,refute_0_642]) ).
cnf(refute_0_644,plain,
meet(A,join(top,complement(X_79))) = complement(join(complement(A),meet(zero,X_79))),
inference(resolve,[$cnf( $equal(meet(A,join(top,complement(X_79))),complement(join(complement(A),complement(join(top,complement(X_79)))))) )],[refute_0_641,refute_0_643]) ).
cnf(refute_0_645,plain,
complement(join(complement(A),meet(zero,X_79))) = meet(A,complement(meet(zero,X_79))),
inference(subst,[],[refute_0_367:[bind(X_17,$fot(zero)),bind(X_18,$fot(X_79))]]) ).
cnf(refute_0_646,plain,
( complement(join(complement(A),meet(zero,X_79))) != meet(A,complement(meet(zero,X_79)))
| meet(A,join(top,complement(X_79))) != complement(join(complement(A),meet(zero,X_79)))
| meet(A,join(top,complement(X_79))) = meet(A,complement(meet(zero,X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(top,complement(X_79))),complement(join(complement(A),meet(zero,X_79)))) ),[1],$fot(meet(A,complement(meet(zero,X_79))))]]) ).
cnf(refute_0_647,plain,
( meet(A,join(top,complement(X_79))) != complement(join(complement(A),meet(zero,X_79)))
| meet(A,join(top,complement(X_79))) = meet(A,complement(meet(zero,X_79))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(zero,X_79))),meet(A,complement(meet(zero,X_79)))) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
meet(A,join(top,complement(X_79))) = meet(A,complement(meet(zero,X_79))),
inference(resolve,[$cnf( $equal(meet(A,join(top,complement(X_79))),complement(join(complement(A),meet(zero,X_79)))) )],[refute_0_644,refute_0_647]) ).
cnf(refute_0_649,plain,
meet(complement(meet(zero,X_79)),join(top,complement(X_79))) = meet(complement(meet(zero,X_79)),complement(meet(zero,X_79))),
inference(subst,[],[refute_0_648:[bind(A,$fot(complement(meet(zero,X_79))))]]) ).
cnf(refute_0_650,plain,
( meet(complement(meet(zero,X_79)),complement(meet(zero,X_79))) != complement(meet(zero,X_79))
| meet(complement(meet(zero,X_79)),join(top,complement(X_79))) != meet(complement(meet(zero,X_79)),complement(meet(zero,X_79)))
| meet(complement(meet(zero,X_79)),join(top,complement(X_79))) = complement(meet(zero,X_79)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(complement(meet(zero,X_79)),join(top,complement(X_79))))),bind(Y,$fot(meet(complement(meet(zero,X_79)),complement(meet(zero,X_79))))),bind(Z,$fot(complement(meet(zero,X_79))))]]) ).
cnf(refute_0_651,plain,
( meet(complement(meet(zero,X_79)),complement(meet(zero,X_79))) != complement(meet(zero,X_79))
| meet(complement(meet(zero,X_79)),join(top,complement(X_79))) = complement(meet(zero,X_79)) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(zero,X_79)),join(top,complement(X_79))),meet(complement(meet(zero,X_79)),complement(meet(zero,X_79)))) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
meet(complement(meet(zero,X_79)),join(top,complement(X_79))) = complement(meet(zero,X_79)),
inference(resolve,[$cnf( $equal(meet(complement(meet(zero,X_79)),complement(meet(zero,X_79))),complement(meet(zero,X_79))) )],[refute_0_640,refute_0_651]) ).
cnf(refute_0_653,plain,
( join(top,complement(X_79)) != meet(complement(meet(zero,X_79)),join(top,complement(X_79)))
| meet(complement(meet(zero,X_79)),join(top,complement(X_79))) != complement(meet(zero,X_79))
| join(top,complement(X_79)) = complement(meet(zero,X_79)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(top,complement(X_79)),complement(meet(zero,X_79))) ),[0],$fot(meet(complement(meet(zero,X_79)),join(top,complement(X_79))))]]) ).
cnf(refute_0_654,plain,
( join(top,complement(X_79)) != meet(complement(meet(zero,X_79)),join(top,complement(X_79)))
| join(top,complement(X_79)) = complement(meet(zero,X_79)) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(zero,X_79)),join(top,complement(X_79))),complement(meet(zero,X_79))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
join(top,complement(X_79)) = complement(meet(zero,X_79)),
inference(resolve,[$cnf( $equal(join(top,complement(X_79)),meet(complement(meet(zero,X_79)),join(top,complement(X_79)))) )],[refute_0_639,refute_0_654]) ).
cnf(refute_0_656,plain,
join(top,complement(X_128)) = complement(meet(zero,X_128)),
inference(subst,[],[refute_0_655:[bind(X_79,$fot(X_128))]]) ).
cnf(refute_0_657,plain,
join(X_118,join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) = join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),
inference(subst,[],[refute_0_90:[bind(X_14,$fot(X_118)),bind(X_15,$fot(top)),bind(X_16,$fot(composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))]]) ).
cnf(refute_0_658,plain,
join(complement(zero),composition(converse(X_45),complement(composition(X_45,zero)))) = complement(zero),
inference(subst,[],[refute_0_160:[bind(A,$fot(X_45)),bind(B,$fot(zero))]]) ).
cnf(refute_0_659,plain,
( complement(zero) != top
| join(complement(zero),composition(converse(X_45),complement(composition(X_45,zero)))) != complement(zero)
| join(top,composition(converse(X_45),complement(composition(X_45,zero)))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),composition(converse(X_45),complement(composition(X_45,zero)))),complement(zero)) ),[0,0],$fot(top)]]) ).
cnf(refute_0_660,plain,
( join(complement(zero),composition(converse(X_45),complement(composition(X_45,zero)))) != complement(zero)
| join(top,composition(converse(X_45),complement(composition(X_45,zero)))) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_659]) ).
cnf(refute_0_661,plain,
join(top,composition(converse(X_45),complement(composition(X_45,zero)))) = complement(zero),
inference(resolve,[$cnf( $equal(join(complement(zero),composition(converse(X_45),complement(composition(X_45,zero)))),complement(zero)) )],[refute_0_658,refute_0_660]) ).
cnf(refute_0_662,plain,
( complement(zero) != top
| join(top,composition(converse(X_45),complement(composition(X_45,zero)))) != complement(zero)
| join(top,composition(converse(X_45),complement(composition(X_45,zero)))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),complement(zero)) ),[1],$fot(top)]]) ).
cnf(refute_0_663,plain,
( join(top,composition(converse(X_45),complement(composition(X_45,zero)))) != complement(zero)
| join(top,composition(converse(X_45),complement(composition(X_45,zero)))) = top ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_662]) ).
cnf(refute_0_664,plain,
join(top,composition(converse(X_45),complement(composition(X_45,zero)))) = top,
inference(resolve,[$cnf( $equal(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),complement(zero)) )],[refute_0_661,refute_0_663]) ).
cnf(refute_0_665,plain,
join(top,composition(converse(composition(zero,complement(one))),complement(composition(composition(zero,complement(one)),zero)))) = top,
inference(subst,[],[refute_0_664:[bind(X_45,$fot(composition(zero,complement(one))))]]) ).
cnf(refute_0_666,plain,
composition(join(X_104,one),X_106) = join(composition(X_104,X_106),composition(one,X_106)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_104)),bind(B,$fot(one)),bind(C,$fot(X_106))]]) ).
cnf(refute_0_667,plain,
X_106 = composition(one,X_106),
inference(subst,[],[refute_0_190:[bind(X_24,$fot(X_106))]]) ).
cnf(refute_0_668,plain,
( X_106 != composition(one,X_106)
| composition(one,X_106) = X_106 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_106)),bind(Y,$fot(composition(one,X_106)))]]) ).
cnf(refute_0_669,plain,
composition(one,X_106) = X_106,
inference(resolve,[$cnf( $equal(X_106,composition(one,X_106)) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
( composition(join(X_104,one),X_106) != join(composition(X_104,X_106),composition(one,X_106))
| composition(one,X_106) != X_106
| composition(join(X_104,one),X_106) = join(composition(X_104,X_106),X_106) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_104,one),X_106),join(composition(X_104,X_106),composition(one,X_106))) ),[1,1],$fot(X_106)]]) ).
cnf(refute_0_671,plain,
( composition(join(X_104,one),X_106) != join(composition(X_104,X_106),composition(one,X_106))
| composition(join(X_104,one),X_106) = join(composition(X_104,X_106),X_106) ),
inference(resolve,[$cnf( $equal(composition(one,X_106),X_106) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
composition(join(X_104,one),X_106) = join(composition(X_104,X_106),X_106),
inference(resolve,[$cnf( $equal(composition(join(X_104,one),X_106),join(composition(X_104,X_106),composition(one,X_106))) )],[refute_0_666,refute_0_671]) ).
cnf(refute_0_673,plain,
join(composition(X_104,X_106),X_106) = join(X_106,composition(X_104,X_106)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_106)),bind(B,$fot(composition(X_104,X_106)))]]) ).
cnf(refute_0_674,plain,
( composition(join(X_104,one),X_106) != join(composition(X_104,X_106),X_106)
| join(composition(X_104,X_106),X_106) != join(X_106,composition(X_104,X_106))
| composition(join(X_104,one),X_106) = join(X_106,composition(X_104,X_106)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_104,one),X_106),join(X_106,composition(X_104,X_106))) ),[0],$fot(join(composition(X_104,X_106),X_106))]]) ).
cnf(refute_0_675,plain,
( composition(join(X_104,one),X_106) != join(composition(X_104,X_106),X_106)
| composition(join(X_104,one),X_106) = join(X_106,composition(X_104,X_106)) ),
inference(resolve,[$cnf( $equal(join(composition(X_104,X_106),X_106),join(X_106,composition(X_104,X_106))) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
composition(join(X_104,one),X_106) = join(X_106,composition(X_104,X_106)),
inference(resolve,[$cnf( $equal(composition(join(X_104,one),X_106),join(composition(X_104,X_106),X_106)) )],[refute_0_672,refute_0_675]) ).
cnf(refute_0_677,plain,
composition(join(join(one,join(X_107,one)),one),zero) = join(zero,composition(join(one,join(X_107,one)),zero)),
inference(subst,[],[refute_0_676:[bind(X_104,$fot(join(one,join(X_107,one)))),bind(X_106,$fot(zero))]]) ).
cnf(refute_0_678,plain,
composition(join(X_104,join(one,one)),zero) = join(composition(X_104,zero),composition(join(one,one),zero)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_104)),bind(B,$fot(join(one,one))),bind(C,$fot(zero))]]) ).
cnf(refute_0_679,plain,
join(complement(top),composition(converse(X_45),complement(composition(X_45,top)))) = complement(top),
inference(subst,[],[refute_0_160:[bind(A,$fot(X_45)),bind(B,$fot(top))]]) ).
cnf(refute_0_680,plain,
( complement(top) != zero
| join(complement(top),composition(converse(X_45),complement(composition(X_45,top)))) != complement(top)
| join(zero,composition(converse(X_45),complement(composition(X_45,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(X_45),complement(composition(X_45,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_681,plain,
( join(complement(top),composition(converse(X_45),complement(composition(X_45,top)))) != complement(top)
| join(zero,composition(converse(X_45),complement(composition(X_45,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_680]) ).
cnf(refute_0_682,plain,
join(zero,composition(converse(X_45),complement(composition(X_45,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(X_45),complement(composition(X_45,top)))),complement(top)) )],[refute_0_679,refute_0_681]) ).
cnf(refute_0_683,plain,
( complement(top) != zero
| join(zero,composition(converse(X_45),complement(composition(X_45,top)))) != complement(top)
| join(zero,composition(converse(X_45),complement(composition(X_45,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_45),complement(composition(X_45,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_684,plain,
( join(zero,composition(converse(X_45),complement(composition(X_45,top)))) != complement(top)
| join(zero,composition(converse(X_45),complement(composition(X_45,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_683]) ).
cnf(refute_0_685,plain,
join(zero,composition(converse(X_45),complement(composition(X_45,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_45),complement(composition(X_45,top)))),complement(top)) )],[refute_0_682,refute_0_684]) ).
cnf(refute_0_686,plain,
join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))) = zero,
inference(subst,[],[refute_0_685:[bind(X_45,$fot(join(one,one)))]]) ).
cnf(refute_0_687,plain,
converse(join(one,B)) = join(converse(one),converse(B)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(one))]]) ).
cnf(refute_0_688,plain,
( converse(join(one,B)) != join(converse(one),converse(B))
| converse(one) != one
| converse(join(one,B)) = join(one,converse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,B)),join(converse(one),converse(B))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_689,plain,
( converse(join(one,B)) != join(converse(one),converse(B))
| converse(join(one,B)) = join(one,converse(B)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_688]) ).
cnf(refute_0_690,plain,
converse(join(one,B)) = join(one,converse(B)),
inference(resolve,[$cnf( $equal(converse(join(one,B)),join(converse(one),converse(B))) )],[refute_0_687,refute_0_689]) ).
cnf(refute_0_691,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_690:[bind(B,$fot(one))]]) ).
cnf(refute_0_692,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(one) != one
| converse(join(one,one)) = join(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_693,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_692]) ).
cnf(refute_0_694,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_691,refute_0_693]) ).
cnf(refute_0_695,plain,
( converse(join(one,one)) != join(one,one)
| join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))) != zero
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))),zero) ),[0,1,0],$fot(join(one,one))]]) ).
cnf(refute_0_696,plain,
( join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))) != zero
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_695]) ).
cnf(refute_0_697,plain,
join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))),zero) )],[refute_0_686,refute_0_696]) ).
cnf(refute_0_698,plain,
join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = composition(join(one,one),complement(composition(join(one,one),top))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(composition(join(one,one),complement(composition(join(one,one),top)))))]]) ).
cnf(refute_0_699,plain,
( join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) != composition(join(one,one),complement(composition(join(one,one),top)))
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) != zero
| composition(join(one,one),complement(composition(join(one,one),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),zero) ),[0],$fot(composition(join(one,one),complement(composition(join(one,one),top))))]]) ).
cnf(refute_0_700,plain,
( join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) != zero
| composition(join(one,one),complement(composition(join(one,one),top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),composition(join(one,one),complement(composition(join(one,one),top)))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
composition(join(one,one),complement(composition(join(one,one),top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),zero) )],[refute_0_697,refute_0_700]) ).
cnf(refute_0_702,plain,
composition(one,top) = top,
inference(subst,[],[refute_0_198:[bind(X_24,$fot(top))]]) ).
cnf(refute_0_703,plain,
join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(composition(converse(X_95),complement(composition(X_95,top)))))) = complement(complement(composition(X_95,top))),
inference(subst,[],[refute_0_160:[bind(A,$fot(converse(X_95))),bind(B,$fot(complement(composition(X_95,top))))]]) ).
cnf(refute_0_704,plain,
join(zero,composition(converse(X_45),complement(composition(X_45,top)))) = composition(converse(X_45),complement(composition(X_45,top))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(composition(converse(X_45),complement(composition(X_45,top)))))]]) ).
cnf(refute_0_705,plain,
( join(zero,composition(converse(X_45),complement(composition(X_45,top)))) != composition(converse(X_45),complement(composition(X_45,top)))
| join(zero,composition(converse(X_45),complement(composition(X_45,top)))) != zero
| composition(converse(X_45),complement(composition(X_45,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_45),complement(composition(X_45,top)))),zero) ),[0],$fot(composition(converse(X_45),complement(composition(X_45,top))))]]) ).
cnf(refute_0_706,plain,
( join(zero,composition(converse(X_45),complement(composition(X_45,top)))) != zero
| composition(converse(X_45),complement(composition(X_45,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_45),complement(composition(X_45,top)))),composition(converse(X_45),complement(composition(X_45,top)))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
composition(converse(X_45),complement(composition(X_45,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_45),complement(composition(X_45,top)))),zero) )],[refute_0_685,refute_0_706]) ).
cnf(refute_0_708,plain,
composition(converse(X_95),complement(composition(X_95,top))) = zero,
inference(subst,[],[refute_0_707:[bind(X_45,$fot(X_95))]]) ).
cnf(refute_0_709,plain,
( composition(converse(X_95),complement(composition(X_95,top))) != zero
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(composition(converse(X_95),complement(composition(X_95,top)))))) != complement(complement(composition(X_95,top)))
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = complement(complement(composition(X_95,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(composition(converse(X_95),complement(composition(X_95,top)))))),complement(complement(composition(X_95,top)))) ),[0,1,1,0],$fot(zero)]]) ).
cnf(refute_0_710,plain,
( join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(composition(converse(X_95),complement(composition(X_95,top)))))) != complement(complement(composition(X_95,top)))
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = complement(complement(composition(X_95,top))) ),
inference(resolve,[$cnf( $equal(composition(converse(X_95),complement(composition(X_95,top))),zero) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = complement(complement(composition(X_95,top))),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(composition(converse(X_95),complement(composition(X_95,top)))))),complement(complement(composition(X_95,top)))) )],[refute_0_703,refute_0_710]) ).
cnf(refute_0_712,plain,
join(composition(X_95,top),composition(X_95,top)) = composition(join(X_95,X_95),top),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_95)),bind(B,$fot(X_95)),bind(C,$fot(top))]]) ).
cnf(refute_0_713,plain,
composition(X_95,complement(zero)) = composition(X_95,complement(zero)),
introduced(tautology,[refl,[$fot(composition(X_95,complement(zero)))]]) ).
cnf(refute_0_714,plain,
( complement(zero) != top
| composition(X_95,complement(zero)) != composition(X_95,complement(zero))
| composition(X_95,complement(zero)) = composition(X_95,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_95,complement(zero)),composition(X_95,complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_715,plain,
( complement(zero) != top
| composition(X_95,complement(zero)) = composition(X_95,top) ),
inference(resolve,[$cnf( $equal(composition(X_95,complement(zero)),composition(X_95,complement(zero))) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
composition(X_95,complement(zero)) = composition(X_95,top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_715]) ).
cnf(refute_0_717,plain,
converse(converse(X_95)) = X_95,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_95))]]) ).
cnf(refute_0_718,plain,
composition(converse(converse(X_95)),complement(zero)) = composition(converse(converse(X_95)),complement(zero)),
introduced(tautology,[refl,[$fot(composition(converse(converse(X_95)),complement(zero)))]]) ).
cnf(refute_0_719,plain,
( composition(converse(converse(X_95)),complement(zero)) != composition(converse(converse(X_95)),complement(zero))
| converse(converse(X_95)) != X_95
| composition(converse(converse(X_95)),complement(zero)) = composition(X_95,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(X_95)),complement(zero)),composition(converse(converse(X_95)),complement(zero))) ),[1,0],$fot(X_95)]]) ).
cnf(refute_0_720,plain,
( converse(converse(X_95)) != X_95
| composition(converse(converse(X_95)),complement(zero)) = composition(X_95,complement(zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(X_95)),complement(zero)),composition(converse(converse(X_95)),complement(zero))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
composition(converse(converse(X_95)),complement(zero)) = composition(X_95,complement(zero)),
inference(resolve,[$cnf( $equal(converse(converse(X_95)),X_95) )],[refute_0_717,refute_0_720]) ).
cnf(refute_0_722,plain,
( composition(X_95,complement(zero)) != composition(X_95,top)
| composition(converse(converse(X_95)),complement(zero)) != composition(X_95,complement(zero))
| composition(converse(converse(X_95)),complement(zero)) = composition(X_95,top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(converse(converse(X_95)),complement(zero)))),bind(Y,$fot(composition(X_95,complement(zero)))),bind(Z,$fot(composition(X_95,top)))]]) ).
cnf(refute_0_723,plain,
( composition(X_95,complement(zero)) != composition(X_95,top)
| composition(converse(converse(X_95)),complement(zero)) = composition(X_95,top) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(X_95)),complement(zero)),composition(X_95,complement(zero))) )],[refute_0_721,refute_0_722]) ).
cnf(refute_0_724,plain,
composition(converse(converse(X_95)),complement(zero)) = composition(X_95,top),
inference(resolve,[$cnf( $equal(composition(X_95,complement(zero)),composition(X_95,top)) )],[refute_0_716,refute_0_723]) ).
cnf(refute_0_725,plain,
join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))),
introduced(tautology,[refl,[$fot(join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))))]]) ).
cnf(refute_0_726,plain,
( composition(converse(converse(X_95)),complement(zero)) != composition(X_95,top)
| join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) != join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero)))
| join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(X_95,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))),join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero)))) ),[1,1],$fot(composition(X_95,top))]]) ).
cnf(refute_0_727,plain,
( composition(converse(converse(X_95)),complement(zero)) != composition(X_95,top)
| join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(X_95,top)) ),
inference(resolve,[$cnf( $equal(join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))),join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero)))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(X_95,top)),
inference(resolve,[$cnf( $equal(composition(converse(converse(X_95)),complement(zero)),composition(X_95,top)) )],[refute_0_724,refute_0_727]) ).
cnf(refute_0_729,plain,
complement(complement(composition(X_95,top))) = composition(X_95,top),
inference(subst,[],[refute_0_397:[bind(X_10,$fot(composition(X_95,top)))]]) ).
cnf(refute_0_730,plain,
join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),
introduced(tautology,[refl,[$fot(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))))]]) ).
cnf(refute_0_731,plain,
( complement(complement(composition(X_95,top))) != composition(X_95,top)
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) != join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero)))
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero)))) ),[1,0],$fot(composition(X_95,top))]]) ).
cnf(refute_0_732,plain,
( complement(complement(composition(X_95,top))) != composition(X_95,top)
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero)))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))),
inference(resolve,[$cnf( $equal(complement(complement(composition(X_95,top))),composition(X_95,top)) )],[refute_0_729,refute_0_732]) ).
cnf(refute_0_734,plain,
( join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) != join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero)))
| join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) != join(composition(X_95,top),composition(X_95,top))
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(X_95,top)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))))),bind(Y,$fot(join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))))),bind(Z,$fot(join(composition(X_95,top),composition(X_95,top))))]]) ).
cnf(refute_0_735,plain,
( join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))) != join(composition(X_95,top),composition(X_95,top))
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(X_95,top)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero)))) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = join(composition(X_95,top),composition(X_95,top)),
inference(resolve,[$cnf( $equal(join(composition(X_95,top),composition(converse(converse(X_95)),complement(zero))),join(composition(X_95,top),composition(X_95,top))) )],[refute_0_728,refute_0_735]) ).
cnf(refute_0_737,plain,
( join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) != join(composition(X_95,top),composition(X_95,top))
| join(composition(X_95,top),composition(X_95,top)) != composition(join(X_95,X_95),top)
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = composition(join(X_95,X_95),top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))))),bind(Y,$fot(join(composition(X_95,top),composition(X_95,top)))),bind(Z,$fot(composition(join(X_95,X_95),top)))]]) ).
cnf(refute_0_738,plain,
( join(composition(X_95,top),composition(X_95,top)) != composition(join(X_95,X_95),top)
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = composition(join(X_95,X_95),top) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),join(composition(X_95,top),composition(X_95,top))) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) = composition(join(X_95,X_95),top),
inference(resolve,[$cnf( $equal(join(composition(X_95,top),composition(X_95,top)),composition(join(X_95,X_95),top)) )],[refute_0_712,refute_0_738]) ).
cnf(refute_0_740,plain,
( join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) != complement(complement(composition(X_95,top)))
| join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) != composition(join(X_95,X_95),top)
| composition(join(X_95,X_95),top) = complement(complement(composition(X_95,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),complement(complement(composition(X_95,top)))) ),[0],$fot(composition(join(X_95,X_95),top))]]) ).
cnf(refute_0_741,plain,
( join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) != complement(complement(composition(X_95,top)))
| composition(join(X_95,X_95),top) = complement(complement(composition(X_95,top))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),composition(join(X_95,X_95),top)) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
( complement(complement(composition(X_95,top))) != composition(X_95,top)
| composition(join(X_95,X_95),top) != complement(complement(composition(X_95,top)))
| composition(join(X_95,X_95),top) = composition(X_95,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_95,X_95),top),complement(complement(composition(X_95,top)))) ),[1],$fot(composition(X_95,top))]]) ).
cnf(refute_0_743,plain,
( composition(join(X_95,X_95),top) != complement(complement(composition(X_95,top)))
| composition(join(X_95,X_95),top) = composition(X_95,top) ),
inference(resolve,[$cnf( $equal(complement(complement(composition(X_95,top))),composition(X_95,top)) )],[refute_0_729,refute_0_742]) ).
cnf(refute_0_744,plain,
( join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))) != complement(complement(composition(X_95,top)))
| composition(join(X_95,X_95),top) = composition(X_95,top) ),
inference(resolve,[$cnf( $equal(composition(join(X_95,X_95),top),complement(complement(composition(X_95,top)))) )],[refute_0_741,refute_0_743]) ).
cnf(refute_0_745,plain,
composition(join(X_95,X_95),top) = composition(X_95,top),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(X_95,top))),composition(converse(converse(X_95)),complement(zero))),complement(complement(composition(X_95,top)))) )],[refute_0_711,refute_0_744]) ).
cnf(refute_0_746,plain,
composition(join(one,one),top) = composition(one,top),
inference(subst,[],[refute_0_745:[bind(X_95,$fot(one))]]) ).
cnf(refute_0_747,plain,
( composition(join(one,one),top) != composition(one,top)
| composition(one,top) != top
| composition(join(one,one),top) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(one,one),top))),bind(Y,$fot(composition(one,top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_748,plain,
( composition(one,top) != top
| composition(join(one,one),top) = top ),
inference(resolve,[$cnf( $equal(composition(join(one,one),top),composition(one,top)) )],[refute_0_746,refute_0_747]) ).
cnf(refute_0_749,plain,
composition(join(one,one),top) = top,
inference(resolve,[$cnf( $equal(composition(one,top),top) )],[refute_0_702,refute_0_748]) ).
cnf(refute_0_750,plain,
complement(composition(join(one,one),top)) = complement(composition(join(one,one),top)),
introduced(tautology,[refl,[$fot(complement(composition(join(one,one),top)))]]) ).
cnf(refute_0_751,plain,
( complement(composition(join(one,one),top)) != complement(composition(join(one,one),top))
| composition(join(one,one),top) != top
| complement(composition(join(one,one),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(join(one,one),top)),complement(composition(join(one,one),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_752,plain,
( composition(join(one,one),top) != top
| complement(composition(join(one,one),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),top)),complement(composition(join(one,one),top))) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
complement(composition(join(one,one),top)) = complement(top),
inference(resolve,[$cnf( $equal(composition(join(one,one),top),top) )],[refute_0_749,refute_0_752]) ).
cnf(refute_0_754,plain,
( complement(composition(join(one,one),top)) != complement(top)
| complement(top) != zero
| complement(composition(join(one,one),top)) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(composition(join(one,one),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_755,plain,
( complement(top) != zero
| complement(composition(join(one,one),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),top)),complement(top)) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
complement(composition(join(one,one),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_755]) ).
cnf(refute_0_757,plain,
composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),complement(composition(join(one,one),top))),
introduced(tautology,[refl,[$fot(composition(join(one,one),complement(composition(join(one,one),top))))]]) ).
cnf(refute_0_758,plain,
( complement(composition(join(one,one),top)) != zero
| composition(join(one,one),complement(composition(join(one,one),top))) != composition(join(one,one),complement(composition(join(one,one),top)))
| composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),composition(join(one,one),complement(composition(join(one,one),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_759,plain,
( complement(composition(join(one,one),top)) != zero
| composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),zero) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),composition(join(one,one),complement(composition(join(one,one),top)))) )],[refute_0_757,refute_0_758]) ).
cnf(refute_0_760,plain,
composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),zero),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),top)),zero) )],[refute_0_756,refute_0_759]) ).
cnf(refute_0_761,plain,
( composition(join(one,one),complement(composition(join(one,one),top))) != composition(join(one,one),zero)
| composition(join(one,one),complement(composition(join(one,one),top))) != zero
| composition(join(one,one),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),zero) ),[0],$fot(composition(join(one,one),zero))]]) ).
cnf(refute_0_762,plain,
( composition(join(one,one),complement(composition(join(one,one),top))) != zero
| composition(join(one,one),zero) = zero ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),composition(join(one,one),zero)) )],[refute_0_760,refute_0_761]) ).
cnf(refute_0_763,plain,
composition(join(one,one),zero) = zero,
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),zero) )],[refute_0_701,refute_0_762]) ).
cnf(refute_0_764,plain,
( composition(join(X_104,join(one,one)),zero) != join(composition(X_104,zero),composition(join(one,one),zero))
| composition(join(one,one),zero) != zero
| composition(join(X_104,join(one,one)),zero) = join(composition(X_104,zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_104,join(one,one)),zero),join(composition(X_104,zero),composition(join(one,one),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_765,plain,
( composition(join(X_104,join(one,one)),zero) != join(composition(X_104,zero),composition(join(one,one),zero))
| composition(join(X_104,join(one,one)),zero) = join(composition(X_104,zero),zero) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),zero),zero) )],[refute_0_763,refute_0_764]) ).
cnf(refute_0_766,plain,
composition(join(X_104,join(one,one)),zero) = join(composition(X_104,zero),zero),
inference(resolve,[$cnf( $equal(composition(join(X_104,join(one,one)),zero),join(composition(X_104,zero),composition(join(one,one),zero))) )],[refute_0_678,refute_0_765]) ).
cnf(refute_0_767,plain,
join(composition(X_104,zero),zero) = composition(X_104,zero),
inference(subst,[],[refute_0_464:[bind(X_10,$fot(composition(X_104,zero)))]]) ).
cnf(refute_0_768,plain,
( composition(join(X_104,join(one,one)),zero) != join(composition(X_104,zero),zero)
| join(composition(X_104,zero),zero) != composition(X_104,zero)
| composition(join(X_104,join(one,one)),zero) = composition(X_104,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_104,join(one,one)),zero),composition(X_104,zero)) ),[0],$fot(join(composition(X_104,zero),zero))]]) ).
cnf(refute_0_769,plain,
( composition(join(X_104,join(one,one)),zero) != join(composition(X_104,zero),zero)
| composition(join(X_104,join(one,one)),zero) = composition(X_104,zero) ),
inference(resolve,[$cnf( $equal(join(composition(X_104,zero),zero),composition(X_104,zero)) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
composition(join(X_104,join(one,one)),zero) = composition(X_104,zero),
inference(resolve,[$cnf( $equal(composition(join(X_104,join(one,one)),zero),join(composition(X_104,zero),zero)) )],[refute_0_766,refute_0_769]) ).
cnf(refute_0_771,plain,
composition(join(X_107,join(one,one)),zero) = composition(X_107,zero),
inference(subst,[],[refute_0_770:[bind(X_104,$fot(X_107))]]) ).
cnf(refute_0_772,plain,
converse(join(converse(A),X_5)) = join(converse(converse(A)),converse(X_5)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_5))]]) ).
cnf(refute_0_773,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_5)) != join(converse(converse(A)),converse(X_5))
| converse(join(converse(A),X_5)) = join(A,converse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_5)),join(converse(converse(A)),converse(X_5))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_774,plain,
( converse(join(converse(A),X_5)) != join(converse(converse(A)),converse(X_5))
| converse(join(converse(A),X_5)) = join(A,converse(X_5)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_773]) ).
cnf(refute_0_775,plain,
converse(join(converse(A),X_5)) = join(A,converse(X_5)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_5)),join(converse(converse(A)),converse(X_5))) )],[refute_0_772,refute_0_774]) ).
cnf(refute_0_776,plain,
converse(join(converse(X_82),join(one,one))) = join(X_82,converse(join(one,one))),
inference(subst,[],[refute_0_775:[bind(A,$fot(X_82)),bind(X_5,$fot(join(one,one)))]]) ).
cnf(refute_0_777,plain,
( converse(join(converse(X_82),join(one,one))) != join(X_82,converse(join(one,one)))
| converse(join(one,one)) != join(one,one)
| converse(join(converse(X_82),join(one,one))) = join(X_82,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),join(X_82,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_0_778,plain,
( converse(join(converse(X_82),join(one,one))) != join(X_82,converse(join(one,one)))
| converse(join(converse(X_82),join(one,one))) = join(X_82,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_777]) ).
cnf(refute_0_779,plain,
converse(join(converse(X_82),join(one,one))) = join(X_82,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),join(X_82,converse(join(one,one)))) )],[refute_0_776,refute_0_778]) ).
cnf(refute_0_780,plain,
join(X_82,converse(one)) = join(X_82,converse(one)),
introduced(tautology,[refl,[$fot(join(X_82,converse(one)))]]) ).
cnf(refute_0_781,plain,
( converse(one) != one
| join(X_82,converse(one)) != join(X_82,converse(one))
| join(X_82,converse(one)) = join(X_82,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_82,converse(one)),join(X_82,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_782,plain,
( converse(one) != one
| join(X_82,converse(one)) = join(X_82,one) ),
inference(resolve,[$cnf( $equal(join(X_82,converse(one)),join(X_82,converse(one))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
join(X_82,converse(one)) = join(X_82,one),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_782]) ).
cnf(refute_0_784,plain,
join(one,join(X_82,converse(one))) = join(one,join(X_82,converse(one))),
introduced(tautology,[refl,[$fot(join(one,join(X_82,converse(one))))]]) ).
cnf(refute_0_785,plain,
( join(X_82,converse(one)) != join(X_82,one)
| join(one,join(X_82,converse(one))) != join(one,join(X_82,converse(one)))
| join(one,join(X_82,converse(one))) = join(one,join(X_82,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(X_82,converse(one))),join(one,join(X_82,converse(one)))) ),[1,1],$fot(join(X_82,one))]]) ).
cnf(refute_0_786,plain,
( join(X_82,converse(one)) != join(X_82,one)
| join(one,join(X_82,converse(one))) = join(one,join(X_82,one)) ),
inference(resolve,[$cnf( $equal(join(one,join(X_82,converse(one))),join(one,join(X_82,converse(one)))) )],[refute_0_784,refute_0_785]) ).
cnf(refute_0_787,plain,
join(one,join(X_82,converse(one))) = join(one,join(X_82,one)),
inference(resolve,[$cnf( $equal(join(X_82,converse(one)),join(X_82,one)) )],[refute_0_783,refute_0_786]) ).
cnf(refute_0_788,plain,
converse(join(one,join(converse(X_82),X_83))) = join(one,converse(join(converse(X_82),X_83))),
inference(subst,[],[refute_0_690:[bind(B,$fot(join(converse(X_82),X_83)))]]) ).
cnf(refute_0_789,plain,
converse(join(converse(X_82),X_83)) = join(X_82,converse(X_83)),
inference(subst,[],[refute_0_775:[bind(A,$fot(X_82)),bind(X_5,$fot(X_83))]]) ).
cnf(refute_0_790,plain,
( converse(join(converse(X_82),X_83)) != join(X_82,converse(X_83))
| converse(join(one,join(converse(X_82),X_83))) != join(one,converse(join(converse(X_82),X_83)))
| converse(join(one,join(converse(X_82),X_83))) = join(one,join(X_82,converse(X_83))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(converse(X_82),X_83))),join(one,converse(join(converse(X_82),X_83)))) ),[1,1],$fot(join(X_82,converse(X_83)))]]) ).
cnf(refute_0_791,plain,
( converse(join(one,join(converse(X_82),X_83))) != join(one,converse(join(converse(X_82),X_83)))
| converse(join(one,join(converse(X_82),X_83))) = join(one,join(X_82,converse(X_83))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),X_83)),join(X_82,converse(X_83))) )],[refute_0_789,refute_0_790]) ).
cnf(refute_0_792,plain,
converse(join(one,join(converse(X_82),X_83))) = join(one,join(X_82,converse(X_83))),
inference(resolve,[$cnf( $equal(converse(join(one,join(converse(X_82),X_83))),join(one,converse(join(converse(X_82),X_83)))) )],[refute_0_788,refute_0_791]) ).
cnf(refute_0_793,plain,
converse(join(one,join(converse(X_82),one))) = join(one,join(X_82,converse(one))),
inference(subst,[],[refute_0_792:[bind(X_83,$fot(one))]]) ).
cnf(refute_0_794,plain,
converse(join(X_4,converse(A))) = join(converse(X_4),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_4)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_795,plain,
( converse(converse(A)) != A
| converse(join(X_4,converse(A))) != join(converse(X_4),converse(converse(A)))
| converse(join(X_4,converse(A))) = join(converse(X_4),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_796,plain,
( converse(join(X_4,converse(A))) != join(converse(X_4),converse(converse(A)))
| converse(join(X_4,converse(A))) = join(converse(X_4),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_795]) ).
cnf(refute_0_797,plain,
converse(join(X_4,converse(A))) = join(converse(X_4),A),
inference(resolve,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),converse(converse(A)))) )],[refute_0_794,refute_0_796]) ).
cnf(refute_0_798,plain,
converse(join(X_42,converse(join(one,one)))) = join(converse(X_42),join(one,one)),
inference(subst,[],[refute_0_797:[bind(A,$fot(join(one,one))),bind(X_4,$fot(X_42))]]) ).
cnf(refute_0_799,plain,
( converse(join(X_42,converse(join(one,one)))) != join(converse(X_42),join(one,one))
| converse(join(one,one)) != join(one,one)
| converse(join(X_42,join(one,one))) = join(converse(X_42),join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_42,converse(join(one,one)))),join(converse(X_42),join(one,one))) ),[0,0,1],$fot(join(one,one))]]) ).
cnf(refute_0_800,plain,
( converse(join(X_42,converse(join(one,one)))) != join(converse(X_42),join(one,one))
| converse(join(X_42,join(one,one))) = join(converse(X_42),join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_799]) ).
cnf(refute_0_801,plain,
converse(join(X_42,join(one,one))) = join(converse(X_42),join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(X_42,converse(join(one,one)))),join(converse(X_42),join(one,one))) )],[refute_0_798,refute_0_800]) ).
cnf(refute_0_802,plain,
( converse(join(one,B)) != join(one,converse(B))
| join(one,converse(B)) = converse(join(one,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(one,B)))),bind(Y,$fot(join(one,converse(B))))]]) ).
cnf(refute_0_803,plain,
join(one,converse(B)) = converse(join(one,B)),
inference(resolve,[$cnf( $equal(converse(join(one,B)),join(one,converse(B))) )],[refute_0_690,refute_0_802]) ).
cnf(refute_0_804,plain,
join(one,converse(join(one,X_42))) = converse(join(one,join(one,X_42))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(one,X_42)))]]) ).
cnf(refute_0_805,plain,
join(one,converse(X_42)) = converse(join(one,X_42)),
inference(subst,[],[refute_0_803:[bind(B,$fot(X_42))]]) ).
cnf(refute_0_806,plain,
join(one,join(one,converse(X_42))) = join(one,join(one,converse(X_42))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(X_42))))]]) ).
cnf(refute_0_807,plain,
( join(one,converse(X_42)) != converse(join(one,X_42))
| join(one,join(one,converse(X_42))) != join(one,join(one,converse(X_42)))
| join(one,join(one,converse(X_42))) = join(one,converse(join(one,X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(X_42))),join(one,join(one,converse(X_42)))) ),[1,1],$fot(converse(join(one,X_42)))]]) ).
cnf(refute_0_808,plain,
( join(one,converse(X_42)) != converse(join(one,X_42))
| join(one,join(one,converse(X_42))) = join(one,converse(join(one,X_42))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(X_42))),join(one,join(one,converse(X_42)))) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
join(one,join(one,converse(X_42))) = join(one,converse(join(one,X_42))),
inference(resolve,[$cnf( $equal(join(one,converse(X_42)),converse(join(one,X_42))) )],[refute_0_805,refute_0_808]) ).
cnf(refute_0_810,plain,
( join(one,converse(join(one,X_42))) != converse(join(one,join(one,X_42)))
| join(one,join(one,converse(X_42))) != join(one,converse(join(one,X_42)))
| join(one,join(one,converse(X_42))) = converse(join(one,join(one,X_42))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,converse(X_42))))),bind(Y,$fot(join(one,converse(join(one,X_42))))),bind(Z,$fot(converse(join(one,join(one,X_42)))))]]) ).
cnf(refute_0_811,plain,
( join(one,converse(join(one,X_42))) != converse(join(one,join(one,X_42)))
| join(one,join(one,converse(X_42))) = converse(join(one,join(one,X_42))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(X_42))),join(one,converse(join(one,X_42)))) )],[refute_0_809,refute_0_810]) ).
cnf(refute_0_812,plain,
join(one,join(one,converse(X_42))) = converse(join(one,join(one,X_42))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,X_42))),converse(join(one,join(one,X_42)))) )],[refute_0_804,refute_0_811]) ).
cnf(refute_0_813,plain,
join(one,join(converse(X_42),one)) = join(one,join(one,converse(X_42))),
inference(subst,[],[refute_0_497:[bind(X_14,$fot(one)),bind(X_15,$fot(converse(X_42))),bind(X_16,$fot(one))]]) ).
cnf(refute_0_814,plain,
( join(X_14,join(X_15,X_16)) != join(X_15,join(X_14,X_16))
| join(X_15,join(X_14,X_16)) = join(X_14,join(X_15,X_16)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_14,join(X_15,X_16)))),bind(Y,$fot(join(X_15,join(X_14,X_16))))]]) ).
cnf(refute_0_815,plain,
join(X_15,join(X_14,X_16)) = join(X_14,join(X_15,X_16)),
inference(resolve,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(X_15,join(X_14,X_16))) )],[refute_0_90,refute_0_814]) ).
cnf(refute_0_816,plain,
join(converse(X_42),join(one,one)) = join(one,join(converse(X_42),one)),
inference(subst,[],[refute_0_815:[bind(X_14,$fot(one)),bind(X_15,$fot(converse(X_42))),bind(X_16,$fot(one))]]) ).
cnf(refute_0_817,plain,
( join(converse(X_42),join(one,one)) != join(one,join(converse(X_42),one))
| join(one,join(converse(X_42),one)) != join(one,join(one,converse(X_42)))
| join(converse(X_42),join(one,one)) = join(one,join(one,converse(X_42))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(converse(X_42),join(one,one)))),bind(Y,$fot(join(one,join(converse(X_42),one)))),bind(Z,$fot(join(one,join(one,converse(X_42)))))]]) ).
cnf(refute_0_818,plain,
( join(one,join(converse(X_42),one)) != join(one,join(one,converse(X_42)))
| join(converse(X_42),join(one,one)) = join(one,join(one,converse(X_42))) ),
inference(resolve,[$cnf( $equal(join(converse(X_42),join(one,one)),join(one,join(converse(X_42),one))) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
join(converse(X_42),join(one,one)) = join(one,join(one,converse(X_42))),
inference(resolve,[$cnf( $equal(join(one,join(converse(X_42),one)),join(one,join(one,converse(X_42)))) )],[refute_0_813,refute_0_818]) ).
cnf(refute_0_820,plain,
( join(converse(X_42),join(one,one)) != join(one,join(one,converse(X_42)))
| join(one,join(one,converse(X_42))) != converse(join(one,join(one,X_42)))
| join(converse(X_42),join(one,one)) = converse(join(one,join(one,X_42))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(converse(X_42),join(one,one)))),bind(Y,$fot(join(one,join(one,converse(X_42))))),bind(Z,$fot(converse(join(one,join(one,X_42)))))]]) ).
cnf(refute_0_821,plain,
( join(one,join(one,converse(X_42))) != converse(join(one,join(one,X_42)))
| join(converse(X_42),join(one,one)) = converse(join(one,join(one,X_42))) ),
inference(resolve,[$cnf( $equal(join(converse(X_42),join(one,one)),join(one,join(one,converse(X_42)))) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
join(converse(X_42),join(one,one)) = converse(join(one,join(one,X_42))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(X_42))),converse(join(one,join(one,X_42)))) )],[refute_0_812,refute_0_821]) ).
cnf(refute_0_823,plain,
( converse(join(X_42,join(one,one))) != join(converse(X_42),join(one,one))
| join(converse(X_42),join(one,one)) != converse(join(one,join(one,X_42)))
| converse(join(X_42,join(one,one))) = converse(join(one,join(one,X_42))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_42,join(one,one))),converse(join(one,join(one,X_42)))) ),[0],$fot(join(converse(X_42),join(one,one)))]]) ).
cnf(refute_0_824,plain,
( converse(join(X_42,join(one,one))) != join(converse(X_42),join(one,one))
| converse(join(X_42,join(one,one))) = converse(join(one,join(one,X_42))) ),
inference(resolve,[$cnf( $equal(join(converse(X_42),join(one,one)),converse(join(one,join(one,X_42)))) )],[refute_0_822,refute_0_823]) ).
cnf(refute_0_825,plain,
converse(join(X_42,join(one,one))) = converse(join(one,join(one,X_42))),
inference(resolve,[$cnf( $equal(converse(join(X_42,join(one,one))),join(converse(X_42),join(one,one))) )],[refute_0_801,refute_0_824]) ).
cnf(refute_0_826,plain,
converse(join(X_80,join(one,one))) = converse(join(one,join(one,X_80))),
inference(subst,[],[refute_0_825:[bind(X_42,$fot(X_80))]]) ).
cnf(refute_0_827,plain,
join(X_80,one) = join(one,X_80),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_80)),bind(B,$fot(one))]]) ).
cnf(refute_0_828,plain,
( join(X_80,one) != join(one,X_80)
| join(one,X_80) = join(X_80,one) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_80,one))),bind(Y,$fot(join(one,X_80)))]]) ).
cnf(refute_0_829,plain,
join(one,X_80) = join(X_80,one),
inference(resolve,[$cnf( $equal(join(X_80,one),join(one,X_80)) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
( converse(join(X_80,join(one,one))) != converse(join(one,join(one,X_80)))
| join(one,X_80) != join(X_80,one)
| converse(join(X_80,join(one,one))) = converse(join(one,join(X_80,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_80,join(one,one))),converse(join(one,join(one,X_80)))) ),[1,0,1],$fot(join(X_80,one))]]) ).
cnf(refute_0_831,plain,
( converse(join(X_80,join(one,one))) != converse(join(one,join(one,X_80)))
| converse(join(X_80,join(one,one))) = converse(join(one,join(X_80,one))) ),
inference(resolve,[$cnf( $equal(join(one,X_80),join(X_80,one)) )],[refute_0_829,refute_0_830]) ).
cnf(refute_0_832,plain,
converse(join(X_80,join(one,one))) = converse(join(one,join(X_80,one))),
inference(resolve,[$cnf( $equal(converse(join(X_80,join(one,one))),converse(join(one,join(one,X_80)))) )],[refute_0_826,refute_0_831]) ).
cnf(refute_0_833,plain,
converse(join(converse(X_82),join(one,one))) = converse(join(one,join(converse(X_82),one))),
inference(subst,[],[refute_0_832:[bind(X_80,$fot(converse(X_82)))]]) ).
cnf(refute_0_834,plain,
( converse(join(converse(X_82),join(one,one))) != converse(join(one,join(converse(X_82),one)))
| converse(join(one,join(converse(X_82),one))) != join(one,join(X_82,converse(one)))
| converse(join(converse(X_82),join(one,one))) = join(one,join(X_82,converse(one))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(converse(X_82),join(one,one))))),bind(Y,$fot(converse(join(one,join(converse(X_82),one))))),bind(Z,$fot(join(one,join(X_82,converse(one)))))]]) ).
cnf(refute_0_835,plain,
( converse(join(one,join(converse(X_82),one))) != join(one,join(X_82,converse(one)))
| converse(join(converse(X_82),join(one,one))) = join(one,join(X_82,converse(one))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),converse(join(one,join(converse(X_82),one)))) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
converse(join(converse(X_82),join(one,one))) = join(one,join(X_82,converse(one))),
inference(resolve,[$cnf( $equal(converse(join(one,join(converse(X_82),one))),join(one,join(X_82,converse(one)))) )],[refute_0_793,refute_0_835]) ).
cnf(refute_0_837,plain,
( converse(join(converse(X_82),join(one,one))) != join(one,join(X_82,converse(one)))
| join(one,join(X_82,converse(one))) != join(one,join(X_82,one))
| converse(join(converse(X_82),join(one,one))) = join(one,join(X_82,one)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(converse(X_82),join(one,one))))),bind(Y,$fot(join(one,join(X_82,converse(one))))),bind(Z,$fot(join(one,join(X_82,one))))]]) ).
cnf(refute_0_838,plain,
( join(one,join(X_82,converse(one))) != join(one,join(X_82,one))
| converse(join(converse(X_82),join(one,one))) = join(one,join(X_82,one)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),join(one,join(X_82,converse(one)))) )],[refute_0_836,refute_0_837]) ).
cnf(refute_0_839,plain,
converse(join(converse(X_82),join(one,one))) = join(one,join(X_82,one)),
inference(resolve,[$cnf( $equal(join(one,join(X_82,converse(one))),join(one,join(X_82,one))) )],[refute_0_787,refute_0_838]) ).
cnf(refute_0_840,plain,
( converse(join(converse(X_82),join(one,one))) != join(X_82,join(one,one))
| converse(join(converse(X_82),join(one,one))) != join(one,join(X_82,one))
| join(one,join(X_82,one)) = join(X_82,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),join(X_82,join(one,one))) ),[0],$fot(join(one,join(X_82,one)))]]) ).
cnf(refute_0_841,plain,
( converse(join(converse(X_82),join(one,one))) != join(X_82,join(one,one))
| join(one,join(X_82,one)) = join(X_82,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),join(one,join(X_82,one))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
join(one,join(X_82,one)) = join(X_82,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),join(X_82,join(one,one))) )],[refute_0_779,refute_0_841]) ).
cnf(refute_0_843,plain,
join(one,join(X_107,one)) = join(X_107,join(one,one)),
inference(subst,[],[refute_0_842:[bind(X_82,$fot(X_107))]]) ).
cnf(refute_0_844,plain,
( join(one,join(X_107,one)) != join(X_107,join(one,one))
| join(X_107,join(one,one)) = join(one,join(X_107,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(X_107,one)))),bind(Y,$fot(join(X_107,join(one,one))))]]) ).
cnf(refute_0_845,plain,
join(X_107,join(one,one)) = join(one,join(X_107,one)),
inference(resolve,[$cnf( $equal(join(one,join(X_107,one)),join(X_107,join(one,one))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
( composition(join(X_107,join(one,one)),zero) != composition(X_107,zero)
| join(X_107,join(one,one)) != join(one,join(X_107,one))
| composition(join(one,join(X_107,one)),zero) = composition(X_107,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_107,join(one,one)),zero),composition(X_107,zero)) ),[0,0],$fot(join(one,join(X_107,one)))]]) ).
cnf(refute_0_847,plain,
( composition(join(X_107,join(one,one)),zero) != composition(X_107,zero)
| composition(join(one,join(X_107,one)),zero) = composition(X_107,zero) ),
inference(resolve,[$cnf( $equal(join(X_107,join(one,one)),join(one,join(X_107,one))) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
composition(join(one,join(X_107,one)),zero) = composition(X_107,zero),
inference(resolve,[$cnf( $equal(composition(join(X_107,join(one,one)),zero),composition(X_107,zero)) )],[refute_0_771,refute_0_847]) ).
cnf(refute_0_849,plain,
( composition(join(join(one,join(X_107,one)),one),zero) != join(zero,composition(join(one,join(X_107,one)),zero))
| composition(join(one,join(X_107,one)),zero) != composition(X_107,zero)
| composition(join(join(one,join(X_107,one)),one),zero) = join(zero,composition(X_107,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,join(X_107,one)),one),zero),join(zero,composition(join(one,join(X_107,one)),zero))) ),[1,1],$fot(composition(X_107,zero))]]) ).
cnf(refute_0_850,plain,
( composition(join(join(one,join(X_107,one)),one),zero) != join(zero,composition(join(one,join(X_107,one)),zero))
| composition(join(join(one,join(X_107,one)),one),zero) = join(zero,composition(X_107,zero)) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(X_107,one)),zero),composition(X_107,zero)) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
composition(join(join(one,join(X_107,one)),one),zero) = join(zero,composition(X_107,zero)),
inference(resolve,[$cnf( $equal(composition(join(join(one,join(X_107,one)),one),zero),join(zero,composition(join(one,join(X_107,one)),zero))) )],[refute_0_677,refute_0_850]) ).
cnf(refute_0_852,plain,
composition(join(one,join(join(A,B),one)),zero) = composition(join(A,B),zero),
inference(subst,[],[refute_0_848:[bind(X_107,$fot(join(A,B)))]]) ).
cnf(refute_0_853,plain,
join(A,join(B,one)) = join(join(A,B),one),
inference(subst,[],[maddux2_join_associativity_2:[bind(C,$fot(one))]]) ).
cnf(refute_0_854,plain,
( join(A,join(B,one)) != join(join(A,B),one)
| join(join(A,B),one) = join(A,join(B,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,one)))),bind(Y,$fot(join(join(A,B),one)))]]) ).
cnf(refute_0_855,plain,
join(join(A,B),one) = join(A,join(B,one)),
inference(resolve,[$cnf( $equal(join(A,join(B,one)),join(join(A,B),one)) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
( composition(join(one,join(join(A,B),one)),zero) != composition(join(A,B),zero)
| join(join(A,B),one) != join(A,join(B,one))
| composition(join(one,join(A,join(B,one))),zero) = composition(join(A,B),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(join(A,B),one)),zero),composition(join(A,B),zero)) ),[0,0,1],$fot(join(A,join(B,one)))]]) ).
cnf(refute_0_857,plain,
( composition(join(one,join(join(A,B),one)),zero) != composition(join(A,B),zero)
| composition(join(one,join(A,join(B,one))),zero) = composition(join(A,B),zero) ),
inference(resolve,[$cnf( $equal(join(join(A,B),one),join(A,join(B,one))) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
composition(join(one,join(A,join(B,one))),zero) = composition(join(A,B),zero),
inference(resolve,[$cnf( $equal(composition(join(one,join(join(A,B),one)),zero),composition(join(A,B),zero)) )],[refute_0_852,refute_0_857]) ).
cnf(refute_0_859,plain,
composition(join(one,join(one,join(X_107,one))),zero) = composition(join(one,X_107),zero),
inference(subst,[],[refute_0_858:[bind(A,$fot(one)),bind(B,$fot(X_107))]]) ).
cnf(refute_0_860,plain,
composition(join(X_110,one),X_111) = join(X_111,composition(X_110,X_111)),
inference(subst,[],[refute_0_676:[bind(X_104,$fot(X_110)),bind(X_106,$fot(X_111))]]) ).
cnf(refute_0_861,plain,
join(one,X_110) = join(X_110,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_110))]]) ).
cnf(refute_0_862,plain,
( join(one,X_110) != join(X_110,one)
| join(X_110,one) = join(one,X_110) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_110))),bind(Y,$fot(join(X_110,one)))]]) ).
cnf(refute_0_863,plain,
join(X_110,one) = join(one,X_110),
inference(resolve,[$cnf( $equal(join(one,X_110),join(X_110,one)) )],[refute_0_861,refute_0_862]) ).
cnf(refute_0_864,plain,
( composition(join(X_110,one),X_111) != join(X_111,composition(X_110,X_111))
| join(X_110,one) != join(one,X_110)
| composition(join(one,X_110),X_111) = join(X_111,composition(X_110,X_111)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_110,one),X_111),join(X_111,composition(X_110,X_111))) ),[0,0],$fot(join(one,X_110))]]) ).
cnf(refute_0_865,plain,
( composition(join(X_110,one),X_111) != join(X_111,composition(X_110,X_111))
| composition(join(one,X_110),X_111) = join(X_111,composition(X_110,X_111)) ),
inference(resolve,[$cnf( $equal(join(X_110,one),join(one,X_110)) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
composition(join(one,X_110),X_111) = join(X_111,composition(X_110,X_111)),
inference(resolve,[$cnf( $equal(composition(join(X_110,one),X_111),join(X_111,composition(X_110,X_111))) )],[refute_0_860,refute_0_865]) ).
cnf(refute_0_867,plain,
( composition(join(X_104,one),X_106) != join(X_106,composition(X_104,X_106))
| join(X_106,composition(X_104,X_106)) = composition(join(X_104,one),X_106) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_104,one),X_106))),bind(Y,$fot(join(X_106,composition(X_104,X_106))))]]) ).
cnf(refute_0_868,plain,
join(X_106,composition(X_104,X_106)) = composition(join(X_104,one),X_106),
inference(resolve,[$cnf( $equal(composition(join(X_104,one),X_106),join(X_106,composition(X_104,X_106))) )],[refute_0_676,refute_0_867]) ).
cnf(refute_0_869,plain,
join(X_111,composition(X_110,X_111)) = composition(join(X_110,one),X_111),
inference(subst,[],[refute_0_868:[bind(X_104,$fot(X_110)),bind(X_106,$fot(X_111))]]) ).
cnf(refute_0_870,plain,
( composition(join(one,X_110),X_111) != join(X_111,composition(X_110,X_111))
| join(X_111,composition(X_110,X_111)) != composition(join(X_110,one),X_111)
| composition(join(one,X_110),X_111) = composition(join(X_110,one),X_111) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_110),X_111),composition(join(X_110,one),X_111)) ),[0],$fot(join(X_111,composition(X_110,X_111)))]]) ).
cnf(refute_0_871,plain,
( composition(join(one,X_110),X_111) != join(X_111,composition(X_110,X_111))
| composition(join(one,X_110),X_111) = composition(join(X_110,one),X_111) ),
inference(resolve,[$cnf( $equal(join(X_111,composition(X_110,X_111)),composition(join(X_110,one),X_111)) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
composition(join(one,X_110),X_111) = composition(join(X_110,one),X_111),
inference(resolve,[$cnf( $equal(composition(join(one,X_110),X_111),join(X_111,composition(X_110,X_111))) )],[refute_0_866,refute_0_871]) ).
cnf(refute_0_873,plain,
( composition(join(one,X_110),X_111) != composition(join(X_110,one),X_111)
| composition(join(X_110,one),X_111) = composition(join(one,X_110),X_111) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,X_110),X_111))),bind(Y,$fot(composition(join(X_110,one),X_111)))]]) ).
cnf(refute_0_874,plain,
composition(join(X_110,one),X_111) = composition(join(one,X_110),X_111),
inference(resolve,[$cnf( $equal(composition(join(one,X_110),X_111),composition(join(X_110,one),X_111)) )],[refute_0_872,refute_0_873]) ).
cnf(refute_0_875,plain,
composition(join(join(one,join(X_107,one)),one),zero) = composition(join(one,join(one,join(X_107,one))),zero),
inference(subst,[],[refute_0_874:[bind(X_110,$fot(join(one,join(X_107,one)))),bind(X_111,$fot(zero))]]) ).
cnf(refute_0_876,plain,
( composition(join(join(one,join(X_107,one)),one),zero) != composition(join(one,join(one,join(X_107,one))),zero)
| composition(join(one,join(one,join(X_107,one))),zero) != composition(join(one,X_107),zero)
| composition(join(join(one,join(X_107,one)),one),zero) = composition(join(one,X_107),zero) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(join(one,join(X_107,one)),one),zero))),bind(Y,$fot(composition(join(one,join(one,join(X_107,one))),zero))),bind(Z,$fot(composition(join(one,X_107),zero)))]]) ).
cnf(refute_0_877,plain,
( composition(join(one,join(one,join(X_107,one))),zero) != composition(join(one,X_107),zero)
| composition(join(join(one,join(X_107,one)),one),zero) = composition(join(one,X_107),zero) ),
inference(resolve,[$cnf( $equal(composition(join(join(one,join(X_107,one)),one),zero),composition(join(one,join(one,join(X_107,one))),zero)) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
composition(join(join(one,join(X_107,one)),one),zero) = composition(join(one,X_107),zero),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(X_107,one))),zero),composition(join(one,X_107),zero)) )],[refute_0_859,refute_0_877]) ).
cnf(refute_0_879,plain,
( composition(join(join(one,join(X_107,one)),one),zero) != composition(join(one,X_107),zero)
| composition(join(join(one,join(X_107,one)),one),zero) != join(zero,composition(X_107,zero))
| composition(join(one,X_107),zero) = join(zero,composition(X_107,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,join(X_107,one)),one),zero),join(zero,composition(X_107,zero))) ),[0],$fot(composition(join(one,X_107),zero))]]) ).
cnf(refute_0_880,plain,
( composition(join(join(one,join(X_107,one)),one),zero) != join(zero,composition(X_107,zero))
| composition(join(one,X_107),zero) = join(zero,composition(X_107,zero)) ),
inference(resolve,[$cnf( $equal(composition(join(join(one,join(X_107,one)),one),zero),composition(join(one,X_107),zero)) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
composition(join(X_104,join(one,join(one,join(one,one)))),zero) = join(composition(X_104,zero),composition(join(one,join(one,join(one,one))),zero)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_104)),bind(B,$fot(join(one,join(one,join(one,one))))),bind(C,$fot(zero))]]) ).
cnf(refute_0_882,plain,
composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,join(one,join(one,one))),top))) = zero,
inference(subst,[],[refute_0_707:[bind(X_45,$fot(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_883,plain,
join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(composition(join(one,one),complement(composition(join(one,one),top)))))) = complement(complement(composition(join(one,one),top))),
inference(subst,[],[refute_0_160:[bind(A,$fot(join(one,one))),bind(B,$fot(complement(composition(join(one,one),top))))]]) ).
cnf(refute_0_884,plain,
( composition(join(one,one),complement(composition(join(one,one),top))) != zero
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(composition(join(one,one),complement(composition(join(one,one),top)))))) != complement(complement(composition(join(one,one),top)))
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = complement(complement(composition(join(one,one),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(composition(join(one,one),complement(composition(join(one,one),top)))))),complement(complement(composition(join(one,one),top)))) ),[0,1,1,0],$fot(zero)]]) ).
cnf(refute_0_885,plain,
( join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(composition(join(one,one),complement(composition(join(one,one),top)))))) != complement(complement(composition(join(one,one),top)))
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = complement(complement(composition(join(one,one),top))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),zero) )],[refute_0_701,refute_0_884]) ).
cnf(refute_0_886,plain,
join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = complement(complement(composition(join(one,one),top))),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(composition(join(one,one),complement(composition(join(one,one),top)))))),complement(complement(composition(join(one,one),top)))) )],[refute_0_883,refute_0_885]) ).
cnf(refute_0_887,plain,
join(one,join(X_85,one)) = join(X_85,join(one,one)),
inference(subst,[],[refute_0_842:[bind(X_82,$fot(X_85))]]) ).
cnf(refute_0_888,plain,
join(one,X_85) = join(X_85,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_85))]]) ).
cnf(refute_0_889,plain,
( join(one,X_85) != join(X_85,one)
| join(X_85,one) = join(one,X_85) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_85))),bind(Y,$fot(join(X_85,one)))]]) ).
cnf(refute_0_890,plain,
join(X_85,one) = join(one,X_85),
inference(resolve,[$cnf( $equal(join(one,X_85),join(X_85,one)) )],[refute_0_888,refute_0_889]) ).
cnf(refute_0_891,plain,
( join(X_85,one) != join(one,X_85)
| join(one,join(X_85,one)) != join(X_85,join(one,one))
| join(one,join(one,X_85)) = join(X_85,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(X_85,one)),join(X_85,join(one,one))) ),[0,1],$fot(join(one,X_85))]]) ).
cnf(refute_0_892,plain,
( join(one,join(X_85,one)) != join(X_85,join(one,one))
| join(one,join(one,X_85)) = join(X_85,join(one,one)) ),
inference(resolve,[$cnf( $equal(join(X_85,one),join(one,X_85)) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
join(one,join(one,X_85)) = join(X_85,join(one,one)),
inference(resolve,[$cnf( $equal(join(one,join(X_85,one)),join(X_85,join(one,one))) )],[refute_0_887,refute_0_892]) ).
cnf(refute_0_894,plain,
( join(one,join(one,X_85)) != join(X_85,join(one,one))
| join(X_85,join(one,one)) = join(one,join(one,X_85)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(one,X_85)))),bind(Y,$fot(join(X_85,join(one,one))))]]) ).
cnf(refute_0_895,plain,
join(X_85,join(one,one)) = join(one,join(one,X_85)),
inference(resolve,[$cnf( $equal(join(one,join(one,X_85)),join(X_85,join(one,one))) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
join(join(one,one),join(one,one)) = join(one,join(one,join(one,one))),
inference(subst,[],[refute_0_895:[bind(X_85,$fot(join(one,one)))]]) ).
cnf(refute_0_897,plain,
composition(join(join(one,one),join(one,one)),top) = composition(join(join(one,one),join(one,one)),top),
introduced(tautology,[refl,[$fot(composition(join(join(one,one),join(one,one)),top))]]) ).
cnf(refute_0_898,plain,
( composition(join(join(one,one),join(one,one)),top) != composition(join(join(one,one),join(one,one)),top)
| join(join(one,one),join(one,one)) != join(one,join(one,join(one,one)))
| composition(join(join(one,one),join(one,one)),top) = composition(join(one,join(one,join(one,one))),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,one),join(one,one)),top),composition(join(join(one,one),join(one,one)),top)) ),[1,0],$fot(join(one,join(one,join(one,one))))]]) ).
cnf(refute_0_899,plain,
( join(join(one,one),join(one,one)) != join(one,join(one,join(one,one)))
| composition(join(join(one,one),join(one,one)),top) = composition(join(one,join(one,join(one,one))),top) ),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),join(one,one)),top),composition(join(join(one,one),join(one,one)),top)) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
composition(join(join(one,one),join(one,one)),top) = composition(join(one,join(one,join(one,one))),top),
inference(resolve,[$cnf( $equal(join(join(one,one),join(one,one)),join(one,join(one,join(one,one)))) )],[refute_0_896,refute_0_899]) ).
cnf(refute_0_901,plain,
join(composition(join(one,one),top),composition(join(one,one),top)) = composition(join(join(one,one),join(one,one)),top),
inference(subst,[],[refute_0_11:[bind(A,$fot(join(one,one))),bind(B,$fot(join(one,one))),bind(C,$fot(top))]]) ).
cnf(refute_0_902,plain,
( composition(join(join(one,one),join(one,one)),top) != composition(join(one,join(one,join(one,one))),top)
| join(composition(join(one,one),top),composition(join(one,one),top)) != composition(join(join(one,one),join(one,one)),top)
| join(composition(join(one,one),top),composition(join(one,one),top)) = composition(join(one,join(one,join(one,one))),top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(composition(join(one,one),top),composition(join(one,one),top)))),bind(Y,$fot(composition(join(join(one,one),join(one,one)),top))),bind(Z,$fot(composition(join(one,join(one,join(one,one))),top)))]]) ).
cnf(refute_0_903,plain,
( composition(join(join(one,one),join(one,one)),top) != composition(join(one,join(one,join(one,one))),top)
| join(composition(join(one,one),top),composition(join(one,one),top)) = composition(join(one,join(one,join(one,one))),top) ),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),top),composition(join(one,one),top)),composition(join(join(one,one),join(one,one)),top)) )],[refute_0_901,refute_0_902]) ).
cnf(refute_0_904,plain,
join(composition(join(one,one),top),composition(join(one,one),top)) = composition(join(one,join(one,join(one,one))),top),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),join(one,one)),top),composition(join(one,join(one,join(one,one))),top)) )],[refute_0_900,refute_0_903]) ).
cnf(refute_0_905,plain,
composition(join(one,one),complement(zero)) = composition(join(one,one),complement(zero)),
introduced(tautology,[refl,[$fot(composition(join(one,one),complement(zero)))]]) ).
cnf(refute_0_906,plain,
( complement(zero) != top
| composition(join(one,one),complement(zero)) != composition(join(one,one),complement(zero))
| composition(join(one,one),complement(zero)) = composition(join(one,one),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(zero)),composition(join(one,one),complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_907,plain,
( complement(zero) != top
| composition(join(one,one),complement(zero)) = composition(join(one,one),top) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(zero)),composition(join(one,one),complement(zero))) )],[refute_0_905,refute_0_906]) ).
cnf(refute_0_908,plain,
composition(join(one,one),complement(zero)) = composition(join(one,one),top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_907]) ).
cnf(refute_0_909,plain,
composition(converse(join(one,one)),complement(zero)) = composition(converse(join(one,one)),complement(zero)),
introduced(tautology,[refl,[$fot(composition(converse(join(one,one)),complement(zero)))]]) ).
cnf(refute_0_910,plain,
( composition(converse(join(one,one)),complement(zero)) != composition(converse(join(one,one)),complement(zero))
| converse(join(one,one)) != join(one,one)
| composition(converse(join(one,one)),complement(zero)) = composition(join(one,one),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,one)),complement(zero)),composition(converse(join(one,one)),complement(zero))) ),[1,0],$fot(join(one,one))]]) ).
cnf(refute_0_911,plain,
( converse(join(one,one)) != join(one,one)
| composition(converse(join(one,one)),complement(zero)) = composition(join(one,one),complement(zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),complement(zero)),composition(converse(join(one,one)),complement(zero))) )],[refute_0_909,refute_0_910]) ).
cnf(refute_0_912,plain,
composition(converse(join(one,one)),complement(zero)) = composition(join(one,one),complement(zero)),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_911]) ).
cnf(refute_0_913,plain,
( composition(converse(join(one,one)),complement(zero)) != composition(join(one,one),complement(zero))
| composition(join(one,one),complement(zero)) != composition(join(one,one),top)
| composition(converse(join(one,one)),complement(zero)) = composition(join(one,one),top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(converse(join(one,one)),complement(zero)))),bind(Y,$fot(composition(join(one,one),complement(zero)))),bind(Z,$fot(composition(join(one,one),top)))]]) ).
cnf(refute_0_914,plain,
( composition(join(one,one),complement(zero)) != composition(join(one,one),top)
| composition(converse(join(one,one)),complement(zero)) = composition(join(one,one),top) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),complement(zero)),composition(join(one,one),complement(zero))) )],[refute_0_912,refute_0_913]) ).
cnf(refute_0_915,plain,
composition(converse(join(one,one)),complement(zero)) = composition(join(one,one),top),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(zero)),composition(join(one,one),top)) )],[refute_0_908,refute_0_914]) ).
cnf(refute_0_916,plain,
join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))),
introduced(tautology,[refl,[$fot(join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))))]]) ).
cnf(refute_0_917,plain,
( composition(converse(join(one,one)),complement(zero)) != composition(join(one,one),top)
| join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) != join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero)))
| join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(join(one,one),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))),join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero)))) ),[1,1],$fot(composition(join(one,one),top))]]) ).
cnf(refute_0_918,plain,
( composition(converse(join(one,one)),complement(zero)) != composition(join(one,one),top)
| join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(join(one,one),top)) ),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))),join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero)))) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(join(one,one),top)),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),complement(zero)),composition(join(one,one),top)) )],[refute_0_915,refute_0_918]) ).
cnf(refute_0_920,plain,
complement(complement(composition(join(one,one),top))) = composition(join(one,one),top),
inference(subst,[],[refute_0_397:[bind(X_10,$fot(composition(join(one,one),top)))]]) ).
cnf(refute_0_921,plain,
join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),
introduced(tautology,[refl,[$fot(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))))]]) ).
cnf(refute_0_922,plain,
( complement(complement(composition(join(one,one),top))) != composition(join(one,one),top)
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) != join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero)))
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero)))) ),[1,0],$fot(composition(join(one,one),top))]]) ).
cnf(refute_0_923,plain,
( complement(complement(composition(join(one,one),top))) != composition(join(one,one),top)
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero)))) )],[refute_0_921,refute_0_922]) ).
cnf(refute_0_924,plain,
join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))),
inference(resolve,[$cnf( $equal(complement(complement(composition(join(one,one),top))),composition(join(one,one),top)) )],[refute_0_920,refute_0_923]) ).
cnf(refute_0_925,plain,
( join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) != join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero)))
| join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) != join(composition(join(one,one),top),composition(join(one,one),top))
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(join(one,one),top)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))))),bind(Y,$fot(join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))))),bind(Z,$fot(join(composition(join(one,one),top),composition(join(one,one),top))))]]) ).
cnf(refute_0_926,plain,
( join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))) != join(composition(join(one,one),top),composition(join(one,one),top))
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(join(one,one),top)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero)))) )],[refute_0_924,refute_0_925]) ).
cnf(refute_0_927,plain,
join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = join(composition(join(one,one),top),composition(join(one,one),top)),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),top),composition(converse(join(one,one)),complement(zero))),join(composition(join(one,one),top),composition(join(one,one),top))) )],[refute_0_919,refute_0_926]) ).
cnf(refute_0_928,plain,
( join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) != join(composition(join(one,one),top),composition(join(one,one),top))
| join(composition(join(one,one),top),composition(join(one,one),top)) != composition(join(one,join(one,join(one,one))),top)
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = composition(join(one,join(one,join(one,one))),top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))))),bind(Y,$fot(join(composition(join(one,one),top),composition(join(one,one),top)))),bind(Z,$fot(composition(join(one,join(one,join(one,one))),top)))]]) ).
cnf(refute_0_929,plain,
( join(composition(join(one,one),top),composition(join(one,one),top)) != composition(join(one,join(one,join(one,one))),top)
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = composition(join(one,join(one,join(one,one))),top) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),join(composition(join(one,one),top),composition(join(one,one),top))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) = composition(join(one,join(one,join(one,one))),top),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),top),composition(join(one,one),top)),composition(join(one,join(one,join(one,one))),top)) )],[refute_0_904,refute_0_929]) ).
cnf(refute_0_931,plain,
( join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) != complement(complement(composition(join(one,one),top)))
| join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) != composition(join(one,join(one,join(one,one))),top)
| composition(join(one,join(one,join(one,one))),top) = complement(complement(composition(join(one,one),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),complement(complement(composition(join(one,one),top)))) ),[0],$fot(composition(join(one,join(one,join(one,one))),top))]]) ).
cnf(refute_0_932,plain,
( join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) != complement(complement(composition(join(one,one),top)))
| composition(join(one,join(one,join(one,one))),top) = complement(complement(composition(join(one,one),top))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),composition(join(one,join(one,join(one,one))),top)) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
( complement(complement(composition(join(one,one),top))) != composition(join(one,one),top)
| composition(join(one,join(one,join(one,one))),top) != complement(complement(composition(join(one,one),top)))
| composition(join(one,join(one,join(one,one))),top) = composition(join(one,one),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,join(one,one))),top),complement(complement(composition(join(one,one),top)))) ),[1],$fot(composition(join(one,one),top))]]) ).
cnf(refute_0_934,plain,
( composition(join(one,join(one,join(one,one))),top) != complement(complement(composition(join(one,one),top)))
| composition(join(one,join(one,join(one,one))),top) = composition(join(one,one),top) ),
inference(resolve,[$cnf( $equal(complement(complement(composition(join(one,one),top))),composition(join(one,one),top)) )],[refute_0_920,refute_0_933]) ).
cnf(refute_0_935,plain,
( join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))) != complement(complement(composition(join(one,one),top)))
| composition(join(one,join(one,join(one,one))),top) = composition(join(one,one),top) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),top),complement(complement(composition(join(one,one),top)))) )],[refute_0_932,refute_0_934]) ).
cnf(refute_0_936,plain,
composition(join(one,join(one,join(one,one))),top) = composition(join(one,one),top),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(join(one,one),top))),composition(converse(join(one,one)),complement(zero))),complement(complement(composition(join(one,one),top)))) )],[refute_0_886,refute_0_935]) ).
cnf(refute_0_937,plain,
( composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,join(one,join(one,one))),top))) != zero
| composition(join(one,join(one,join(one,one))),top) != composition(join(one,one),top)
| composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,join(one,join(one,one))),top))),zero) ),[0,1,0],$fot(composition(join(one,one),top))]]) ).
cnf(refute_0_938,plain,
( composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,join(one,join(one,one))),top))) != zero
| composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = zero ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),top),composition(join(one,one),top)) )],[refute_0_936,refute_0_937]) ).
cnf(refute_0_939,plain,
composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = zero,
inference(resolve,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,join(one,join(one,one))),top))),zero) )],[refute_0_882,refute_0_938]) ).
cnf(refute_0_940,plain,
composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))),
introduced(tautology,[refl,[$fot(composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))))]]) ).
cnf(refute_0_941,plain,
( complement(composition(join(one,one),top)) != zero
| composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) != composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top)))
| composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))),composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_942,plain,
( complement(composition(join(one,one),top)) != zero
| composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),zero) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))),composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top)))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),zero),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),top)),zero) )],[refute_0_756,refute_0_942]) ).
cnf(refute_0_944,plain,
converse(join(one,join(one,join(one,one)))) = join(one,converse(join(one,join(one,one)))),
inference(subst,[],[refute_0_690:[bind(B,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_945,plain,
converse(join(one,join(one,one))) = join(one,converse(join(one,one))),
inference(subst,[],[refute_0_690:[bind(B,$fot(join(one,one)))]]) ).
cnf(refute_0_946,plain,
( converse(join(one,join(one,one))) != join(one,converse(join(one,one)))
| converse(join(one,one)) != join(one,one)
| converse(join(one,join(one,one))) = join(one,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,one))),join(one,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_0_947,plain,
( converse(join(one,join(one,one))) != join(one,converse(join(one,one)))
| converse(join(one,join(one,one))) = join(one,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_946]) ).
cnf(refute_0_948,plain,
converse(join(one,join(one,one))) = join(one,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,converse(join(one,one)))) )],[refute_0_945,refute_0_947]) ).
cnf(refute_0_949,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,converse(join(one,join(one,one))))
| converse(join(one,join(one,one))) != join(one,join(one,one))
| converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,converse(join(one,join(one,one))))) ),[1,1],$fot(join(one,join(one,one)))]]) ).
cnf(refute_0_950,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,converse(join(one,join(one,one))))
| converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_948,refute_0_949]) ).
cnf(refute_0_951,plain,
converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,converse(join(one,join(one,one))))) )],[refute_0_944,refute_0_950]) ).
cnf(refute_0_952,plain,
composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))),
introduced(tautology,[refl,[$fot(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))))]]) ).
cnf(refute_0_953,plain,
( composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) != composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top)))
| converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))),composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top)))) ),[1,0],$fot(join(one,join(one,join(one,one))))]]) ).
cnf(refute_0_954,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))),composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top)))) )],[refute_0_952,refute_0_953]) ).
cnf(refute_0_955,plain,
composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,join(one,join(one,one)))) )],[refute_0_951,refute_0_954]) ).
cnf(refute_0_956,plain,
( composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) != composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top)))
| composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) != composition(join(one,join(one,join(one,one))),zero)
| composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),zero) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))))),bind(Y,$fot(composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))))),bind(Z,$fot(composition(join(one,join(one,join(one,one))),zero)))]]) ).
cnf(refute_0_957,plain,
( composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))) != composition(join(one,join(one,join(one,one))),zero)
| composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),zero) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))),composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top)))) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) = composition(join(one,join(one,join(one,one))),zero),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),complement(composition(join(one,one),top))),composition(join(one,join(one,join(one,one))),zero)) )],[refute_0_943,refute_0_957]) ).
cnf(refute_0_959,plain,
( composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) != composition(join(one,join(one,join(one,one))),zero)
| composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) != zero
| composition(join(one,join(one,join(one,one))),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))),zero) ),[0],$fot(composition(join(one,join(one,join(one,one))),zero))]]) ).
cnf(refute_0_960,plain,
( composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))) != zero
| composition(join(one,join(one,join(one,one))),zero) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))),composition(join(one,join(one,join(one,one))),zero)) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
composition(join(one,join(one,join(one,one))),zero) = zero,
inference(resolve,[$cnf( $equal(composition(converse(join(one,join(one,join(one,one)))),complement(composition(join(one,one),top))),zero) )],[refute_0_939,refute_0_960]) ).
cnf(refute_0_962,plain,
( composition(join(X_104,join(one,join(one,join(one,one)))),zero) != join(composition(X_104,zero),composition(join(one,join(one,join(one,one))),zero))
| composition(join(one,join(one,join(one,one))),zero) != zero
| composition(join(X_104,join(one,join(one,join(one,one)))),zero) = join(composition(X_104,zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),join(composition(X_104,zero),composition(join(one,join(one,join(one,one))),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_963,plain,
( composition(join(X_104,join(one,join(one,join(one,one)))),zero) != join(composition(X_104,zero),composition(join(one,join(one,join(one,one))),zero))
| composition(join(X_104,join(one,join(one,join(one,one)))),zero) = join(composition(X_104,zero),zero) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),zero),zero) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
composition(join(X_104,join(one,join(one,join(one,one)))),zero) = join(composition(X_104,zero),zero),
inference(resolve,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),join(composition(X_104,zero),composition(join(one,join(one,join(one,one))),zero))) )],[refute_0_881,refute_0_963]) ).
cnf(refute_0_965,plain,
( composition(join(X_104,join(one,join(one,join(one,one)))),zero) != join(composition(X_104,zero),zero)
| join(composition(X_104,zero),zero) != composition(X_104,zero)
| composition(join(X_104,join(one,join(one,join(one,one)))),zero) = composition(X_104,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),composition(X_104,zero)) ),[0],$fot(join(composition(X_104,zero),zero))]]) ).
cnf(refute_0_966,plain,
( composition(join(X_104,join(one,join(one,join(one,one)))),zero) != join(composition(X_104,zero),zero)
| composition(join(X_104,join(one,join(one,join(one,one)))),zero) = composition(X_104,zero) ),
inference(resolve,[$cnf( $equal(join(composition(X_104,zero),zero),composition(X_104,zero)) )],[refute_0_767,refute_0_965]) ).
cnf(refute_0_967,plain,
composition(join(X_104,join(one,join(one,join(one,one)))),zero) = composition(X_104,zero),
inference(resolve,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),join(composition(X_104,zero),zero)) )],[refute_0_964,refute_0_966]) ).
cnf(refute_0_968,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(composition(join(one,join(one,one)),complement(one))))) = complement(complement(one)),
inference(subst,[],[refute_0_160:[bind(A,$fot(join(one,join(one,one)))),bind(B,$fot(complement(one)))]]) ).
cnf(refute_0_969,plain,
join(complement(one),composition(converse(X_45),complement(composition(X_45,one)))) = complement(one),
inference(subst,[],[refute_0_160:[bind(A,$fot(X_45)),bind(B,$fot(one))]]) ).
cnf(refute_0_970,plain,
composition(X_45,one) = X_45,
inference(subst,[],[composition_identity_6:[bind(A,$fot(X_45))]]) ).
cnf(refute_0_971,plain,
( composition(X_45,one) != X_45
| join(complement(one),composition(converse(X_45),complement(composition(X_45,one)))) != complement(one)
| join(complement(one),composition(converse(X_45),complement(X_45))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(X_45),complement(composition(X_45,one)))),complement(one)) ),[0,1,1,0],$fot(X_45)]]) ).
cnf(refute_0_972,plain,
( join(complement(one),composition(converse(X_45),complement(composition(X_45,one)))) != complement(one)
| join(complement(one),composition(converse(X_45),complement(X_45))) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(X_45,one),X_45) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
join(complement(one),composition(converse(X_45),complement(X_45))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(X_45),complement(composition(X_45,one)))),complement(one)) )],[refute_0_969,refute_0_972]) ).
cnf(refute_0_974,plain,
join(complement(one),composition(converse(join(one,one)),complement(join(one,one)))) = complement(one),
inference(subst,[],[refute_0_973:[bind(X_45,$fot(join(one,one)))]]) ).
cnf(refute_0_975,plain,
( converse(join(one,one)) != join(one,one)
| join(complement(one),composition(converse(join(one,one)),complement(join(one,one)))) != complement(one)
| join(complement(one),composition(join(one,one),complement(join(one,one)))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(join(one,one)),complement(join(one,one)))),complement(one)) ),[0,1,0],$fot(join(one,one))]]) ).
cnf(refute_0_976,plain,
( join(complement(one),composition(converse(join(one,one)),complement(join(one,one)))) != complement(one)
| join(complement(one),composition(join(one,one),complement(join(one,one)))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_975]) ).
cnf(refute_0_977,plain,
join(complement(one),composition(join(one,one),complement(join(one,one)))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(one,one)),complement(join(one,one)))),complement(one)) )],[refute_0_974,refute_0_976]) ).
cnf(refute_0_978,plain,
complement(complement(X_89)) = X_89,
inference(subst,[],[refute_0_397:[bind(X_10,$fot(X_89))]]) ).
cnf(refute_0_979,plain,
join(X_89,complement(complement(X_89))) = join(X_89,complement(complement(X_89))),
introduced(tautology,[refl,[$fot(join(X_89,complement(complement(X_89))))]]) ).
cnf(refute_0_980,plain,
( complement(complement(X_89)) != X_89
| join(X_89,complement(complement(X_89))) != join(X_89,complement(complement(X_89)))
| join(X_89,complement(complement(X_89))) = join(X_89,X_89) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_89,complement(complement(X_89))),join(X_89,complement(complement(X_89)))) ),[1,1],$fot(X_89)]]) ).
cnf(refute_0_981,plain,
( complement(complement(X_89)) != X_89
| join(X_89,complement(complement(X_89))) = join(X_89,X_89) ),
inference(resolve,[$cnf( $equal(join(X_89,complement(complement(X_89))),join(X_89,complement(complement(X_89)))) )],[refute_0_979,refute_0_980]) ).
cnf(refute_0_982,plain,
join(X_89,complement(complement(X_89))) = join(X_89,X_89),
inference(resolve,[$cnf( $equal(complement(complement(X_89)),X_89) )],[refute_0_978,refute_0_981]) ).
cnf(refute_0_983,plain,
complement(join(X_89,complement(complement(X_89)))) = complement(join(X_89,complement(complement(X_89)))),
introduced(tautology,[refl,[$fot(complement(join(X_89,complement(complement(X_89)))))]]) ).
cnf(refute_0_984,plain,
( complement(join(X_89,complement(complement(X_89)))) != complement(join(X_89,complement(complement(X_89))))
| join(X_89,complement(complement(X_89))) != join(X_89,X_89)
| complement(join(X_89,complement(complement(X_89)))) = complement(join(X_89,X_89)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(X_89,complement(complement(X_89)))),complement(join(X_89,complement(complement(X_89))))) ),[1,0],$fot(join(X_89,X_89))]]) ).
cnf(refute_0_985,plain,
( join(X_89,complement(complement(X_89))) != join(X_89,X_89)
| complement(join(X_89,complement(complement(X_89)))) = complement(join(X_89,X_89)) ),
inference(resolve,[$cnf( $equal(complement(join(X_89,complement(complement(X_89)))),complement(join(X_89,complement(complement(X_89))))) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
complement(join(X_89,complement(complement(X_89)))) = complement(join(X_89,X_89)),
inference(resolve,[$cnf( $equal(join(X_89,complement(complement(X_89))),join(X_89,X_89)) )],[refute_0_982,refute_0_985]) ).
cnf(refute_0_987,plain,
join(zero,complement(join(X_89,complement(complement(X_89))))) = complement(join(X_89,complement(complement(X_89)))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(complement(join(X_89,complement(complement(X_89))))))]]) ).
cnf(refute_0_988,plain,
( complement(join(X_89,complement(complement(X_89)))) != complement(join(X_89,X_89))
| join(zero,complement(join(X_89,complement(complement(X_89))))) != complement(join(X_89,complement(complement(X_89))))
| join(zero,complement(join(X_89,complement(complement(X_89))))) = complement(join(X_89,X_89)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,complement(join(X_89,complement(complement(X_89))))))),bind(Y,$fot(complement(join(X_89,complement(complement(X_89)))))),bind(Z,$fot(complement(join(X_89,X_89))))]]) ).
cnf(refute_0_989,plain,
( complement(join(X_89,complement(complement(X_89)))) != complement(join(X_89,X_89))
| join(zero,complement(join(X_89,complement(complement(X_89))))) = complement(join(X_89,X_89)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(X_89,complement(complement(X_89))))),complement(join(X_89,complement(complement(X_89))))) )],[refute_0_987,refute_0_988]) ).
cnf(refute_0_990,plain,
join(zero,complement(join(X_89,complement(complement(X_89))))) = complement(join(X_89,X_89)),
inference(resolve,[$cnf( $equal(complement(join(X_89,complement(complement(X_89)))),complement(join(X_89,X_89))) )],[refute_0_986,refute_0_989]) ).
cnf(refute_0_991,plain,
( complement(X_89) != join(zero,complement(join(X_89,complement(complement(X_89)))))
| join(zero,complement(join(X_89,complement(complement(X_89))))) != complement(join(X_89,X_89))
| complement(X_89) = complement(join(X_89,X_89)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_89),complement(join(X_89,X_89))) ),[0],$fot(join(zero,complement(join(X_89,complement(complement(X_89))))))]]) ).
cnf(refute_0_992,plain,
( complement(X_89) != join(zero,complement(join(X_89,complement(complement(X_89)))))
| complement(X_89) = complement(join(X_89,X_89)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(X_89,complement(complement(X_89))))),complement(join(X_89,X_89))) )],[refute_0_990,refute_0_991]) ).
cnf(refute_0_993,plain,
complement(X_89) = complement(join(X_89,X_89)),
inference(resolve,[$cnf( $equal(complement(X_89),join(zero,complement(join(X_89,complement(complement(X_89)))))) )],[refute_0_312,refute_0_992]) ).
cnf(refute_0_994,plain,
( complement(X_89) != complement(join(X_89,X_89))
| complement(join(X_89,X_89)) = complement(X_89) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_89))),bind(Y,$fot(complement(join(X_89,X_89))))]]) ).
cnf(refute_0_995,plain,
complement(join(X_89,X_89)) = complement(X_89),
inference(resolve,[$cnf( $equal(complement(X_89),complement(join(X_89,X_89))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
complement(join(one,one)) = complement(one),
inference(subst,[],[refute_0_995:[bind(X_89,$fot(one))]]) ).
cnf(refute_0_997,plain,
composition(join(one,one),complement(join(one,one))) = composition(join(one,one),complement(join(one,one))),
introduced(tautology,[refl,[$fot(composition(join(one,one),complement(join(one,one))))]]) ).
cnf(refute_0_998,plain,
( complement(join(one,one)) != complement(one)
| composition(join(one,one),complement(join(one,one))) != composition(join(one,one),complement(join(one,one)))
| composition(join(one,one),complement(join(one,one))) = composition(join(one,one),complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(join(one,one))),composition(join(one,one),complement(join(one,one)))) ),[1,1],$fot(complement(one))]]) ).
cnf(refute_0_999,plain,
( complement(join(one,one)) != complement(one)
| composition(join(one,one),complement(join(one,one))) = composition(join(one,one),complement(one)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(one,one))),composition(join(one,one),complement(join(one,one)))) )],[refute_0_997,refute_0_998]) ).
cnf(refute_0_1000,plain,
composition(join(one,one),complement(join(one,one))) = composition(join(one,one),complement(one)),
inference(resolve,[$cnf( $equal(complement(join(one,one)),complement(one)) )],[refute_0_996,refute_0_999]) ).
cnf(refute_0_1001,plain,
join(complement(one),composition(join(one,one),complement(join(one,one)))) = join(complement(one),composition(join(one,one),complement(join(one,one)))),
introduced(tautology,[refl,[$fot(join(complement(one),composition(join(one,one),complement(join(one,one)))))]]) ).
cnf(refute_0_1002,plain,
( composition(join(one,one),complement(join(one,one))) != composition(join(one,one),complement(one))
| join(complement(one),composition(join(one,one),complement(join(one,one)))) != join(complement(one),composition(join(one,one),complement(join(one,one))))
| join(complement(one),composition(join(one,one),complement(join(one,one)))) = join(complement(one),composition(join(one,one),complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),join(complement(one),composition(join(one,one),complement(join(one,one))))) ),[1,1],$fot(composition(join(one,one),complement(one)))]]) ).
cnf(refute_0_1003,plain,
( composition(join(one,one),complement(join(one,one))) != composition(join(one,one),complement(one))
| join(complement(one),composition(join(one,one),complement(join(one,one)))) = join(complement(one),composition(join(one,one),complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),join(complement(one),composition(join(one,one),complement(join(one,one))))) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
join(complement(one),composition(join(one,one),complement(join(one,one)))) = join(complement(one),composition(join(one,one),complement(one))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(one,one))),composition(join(one,one),complement(one))) )],[refute_0_1000,refute_0_1003]) ).
cnf(refute_0_1005,plain,
( join(complement(one),composition(join(one,one),complement(join(one,one)))) != complement(one)
| join(complement(one),composition(join(one,one),complement(join(one,one)))) != join(complement(one),composition(join(one,one),complement(one)))
| join(complement(one),composition(join(one,one),complement(one))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),complement(one)) ),[0],$fot(join(complement(one),composition(join(one,one),complement(one))))]]) ).
cnf(refute_0_1006,plain,
( join(complement(one),composition(join(one,one),complement(join(one,one)))) != complement(one)
| join(complement(one),composition(join(one,one),complement(one))) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),join(complement(one),composition(join(one,one),complement(one)))) )],[refute_0_1004,refute_0_1005]) ).
cnf(refute_0_1007,plain,
join(complement(one),composition(join(one,one),complement(one))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),complement(one)) )],[refute_0_977,refute_0_1006]) ).
cnf(refute_0_1008,plain,
join(composition(X_105,X_106),composition(X_104,X_106)) = join(composition(X_104,X_106),composition(X_105,X_106)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(composition(X_105,X_106))),bind(B,$fot(composition(X_104,X_106)))]]) ).
cnf(refute_0_1009,plain,
composition(join(X_104,X_105),X_106) = join(composition(X_104,X_106),composition(X_105,X_106)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_104)),bind(B,$fot(X_105)),bind(C,$fot(X_106))]]) ).
cnf(refute_0_1010,plain,
( composition(join(X_104,X_105),X_106) != join(composition(X_104,X_106),composition(X_105,X_106))
| join(composition(X_104,X_106),composition(X_105,X_106)) = composition(join(X_104,X_105),X_106) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_104,X_105),X_106))),bind(Y,$fot(join(composition(X_104,X_106),composition(X_105,X_106))))]]) ).
cnf(refute_0_1011,plain,
join(composition(X_104,X_106),composition(X_105,X_106)) = composition(join(X_104,X_105),X_106),
inference(resolve,[$cnf( $equal(composition(join(X_104,X_105),X_106),join(composition(X_104,X_106),composition(X_105,X_106))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
( join(composition(X_104,X_106),composition(X_105,X_106)) != composition(join(X_104,X_105),X_106)
| join(composition(X_105,X_106),composition(X_104,X_106)) != join(composition(X_104,X_106),composition(X_105,X_106))
| join(composition(X_105,X_106),composition(X_104,X_106)) = composition(join(X_104,X_105),X_106) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_105,X_106),composition(X_104,X_106)),join(composition(X_104,X_106),composition(X_105,X_106))) ),[1],$fot(composition(join(X_104,X_105),X_106))]]) ).
cnf(refute_0_1013,plain,
( join(composition(X_105,X_106),composition(X_104,X_106)) != join(composition(X_104,X_106),composition(X_105,X_106))
| join(composition(X_105,X_106),composition(X_104,X_106)) = composition(join(X_104,X_105),X_106) ),
inference(resolve,[$cnf( $equal(join(composition(X_104,X_106),composition(X_105,X_106)),composition(join(X_104,X_105),X_106)) )],[refute_0_1011,refute_0_1012]) ).
cnf(refute_0_1014,plain,
join(composition(X_105,X_106),composition(X_104,X_106)) = composition(join(X_104,X_105),X_106),
inference(resolve,[$cnf( $equal(join(composition(X_105,X_106),composition(X_104,X_106)),join(composition(X_104,X_106),composition(X_105,X_106))) )],[refute_0_1008,refute_0_1013]) ).
cnf(refute_0_1015,plain,
join(composition(X_105,X_106),composition(X_104,X_106)) = composition(join(X_105,X_104),X_106),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_105)),bind(B,$fot(X_104)),bind(C,$fot(X_106))]]) ).
cnf(refute_0_1016,plain,
( join(composition(X_105,X_106),composition(X_104,X_106)) != composition(join(X_104,X_105),X_106)
| join(composition(X_105,X_106),composition(X_104,X_106)) != composition(join(X_105,X_104),X_106)
| composition(join(X_105,X_104),X_106) = composition(join(X_104,X_105),X_106) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_105,X_106),composition(X_104,X_106)),composition(join(X_104,X_105),X_106)) ),[0],$fot(composition(join(X_105,X_104),X_106))]]) ).
cnf(refute_0_1017,plain,
( join(composition(X_105,X_106),composition(X_104,X_106)) != composition(join(X_104,X_105),X_106)
| composition(join(X_105,X_104),X_106) = composition(join(X_104,X_105),X_106) ),
inference(resolve,[$cnf( $equal(join(composition(X_105,X_106),composition(X_104,X_106)),composition(join(X_105,X_104),X_106)) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
composition(join(X_105,X_104),X_106) = composition(join(X_104,X_105),X_106),
inference(resolve,[$cnf( $equal(join(composition(X_105,X_106),composition(X_104,X_106)),composition(join(X_104,X_105),X_106)) )],[refute_0_1014,refute_0_1017]) ).
cnf(refute_0_1019,plain,
( composition(join(X_105,X_104),X_106) != composition(join(X_104,X_105),X_106)
| composition(join(X_104,X_105),X_106) = composition(join(X_105,X_104),X_106) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_105,X_104),X_106))),bind(Y,$fot(composition(join(X_104,X_105),X_106)))]]) ).
cnf(refute_0_1020,plain,
composition(join(X_104,X_105),X_106) = composition(join(X_105,X_104),X_106),
inference(resolve,[$cnf( $equal(composition(join(X_105,X_104),X_106),composition(join(X_104,X_105),X_106)) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
composition(join(join(one,one),one),complement(one)) = composition(join(one,join(one,one)),complement(one)),
inference(subst,[],[refute_0_1020:[bind(X_104,$fot(join(one,one))),bind(X_105,$fot(one)),bind(X_106,$fot(complement(one)))]]) ).
cnf(refute_0_1022,plain,
join(complement(one),composition(join(one,one),complement(one))) = composition(join(join(one,one),one),complement(one)),
inference(subst,[],[refute_0_868:[bind(X_104,$fot(join(one,one))),bind(X_106,$fot(complement(one)))]]) ).
cnf(refute_0_1023,plain,
( composition(join(join(one,one),one),complement(one)) != composition(join(one,join(one,one)),complement(one))
| join(complement(one),composition(join(one,one),complement(one))) != composition(join(join(one,one),one),complement(one))
| join(complement(one),composition(join(one,one),complement(one))) = composition(join(one,join(one,one)),complement(one)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(one),composition(join(one,one),complement(one))))),bind(Y,$fot(composition(join(join(one,one),one),complement(one)))),bind(Z,$fot(composition(join(one,join(one,one)),complement(one))))]]) ).
cnf(refute_0_1024,plain,
( composition(join(join(one,one),one),complement(one)) != composition(join(one,join(one,one)),complement(one))
| join(complement(one),composition(join(one,one),complement(one))) = composition(join(one,join(one,one)),complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(one))),composition(join(join(one,one),one),complement(one))) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
join(complement(one),composition(join(one,one),complement(one))) = composition(join(one,join(one,one)),complement(one)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),complement(one)),composition(join(one,join(one,one)),complement(one))) )],[refute_0_1021,refute_0_1024]) ).
cnf(refute_0_1026,plain,
( join(complement(one),composition(join(one,one),complement(one))) != complement(one)
| join(complement(one),composition(join(one,one),complement(one))) != composition(join(one,join(one,one)),complement(one))
| composition(join(one,join(one,one)),complement(one)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(one))),complement(one)) ),[0],$fot(composition(join(one,join(one,one)),complement(one)))]]) ).
cnf(refute_0_1027,plain,
( join(complement(one),composition(join(one,one),complement(one))) != complement(one)
| composition(join(one,join(one,one)),complement(one)) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(one))),composition(join(one,join(one,one)),complement(one))) )],[refute_0_1025,refute_0_1026]) ).
cnf(refute_0_1028,plain,
composition(join(one,join(one,one)),complement(one)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(one))),complement(one)) )],[refute_0_1007,refute_0_1027]) ).
cnf(refute_0_1029,plain,
( composition(join(one,join(one,one)),complement(one)) != complement(one)
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(composition(join(one,join(one,one)),complement(one))))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(composition(join(one,join(one,one)),complement(one))))),complement(complement(one))) ),[0,1,1,0],$fot(complement(one))]]) ).
cnf(refute_0_1030,plain,
( join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(composition(join(one,join(one,one)),complement(one))))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),complement(one)),complement(one)) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(composition(join(one,join(one,one)),complement(one))))),complement(complement(one))) )],[refute_0_968,refute_0_1030]) ).
cnf(refute_0_1032,plain,
composition(join(one,join(one,join(one,one))),one) = join(one,join(one,join(one,one))),
inference(subst,[],[composition_identity_6:[bind(A,$fot(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1033,plain,
complement(complement(one)) = one,
inference(subst,[],[refute_0_397:[bind(X_10,$fot(one))]]) ).
cnf(refute_0_1034,plain,
composition(join(one,join(one,join(one,one))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(join(one,join(one,join(one,one))),complement(complement(one))))]]) ).
cnf(refute_0_1035,plain,
( complement(complement(one)) != one
| composition(join(one,join(one,join(one,one))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),complement(complement(one)))
| composition(join(one,join(one,join(one,one))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,join(one,one))),complement(complement(one))),composition(join(one,join(one,join(one,one))),complement(complement(one)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1036,plain,
( complement(complement(one)) != one
| composition(join(one,join(one,join(one,one))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),complement(complement(one))),composition(join(one,join(one,join(one,one))),complement(complement(one)))) )],[refute_0_1034,refute_0_1035]) ).
cnf(refute_0_1037,plain,
composition(join(one,join(one,join(one,one))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1033,refute_0_1036]) ).
cnf(refute_0_1038,plain,
join(one,converse(join(one,join(one,one)))) = converse(join(one,join(one,join(one,one)))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1039,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| join(one,converse(join(one,join(one,one)))) != converse(join(one,join(one,join(one,one))))
| join(one,converse(join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,converse(join(one,join(one,one)))))),bind(Y,$fot(converse(join(one,join(one,join(one,one)))))),bind(Z,$fot(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1040,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| join(one,converse(join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,one)))),converse(join(one,join(one,join(one,one))))) )],[refute_0_1038,refute_0_1039]) ).
cnf(refute_0_1041,plain,
join(one,converse(join(one,join(one,one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,join(one,join(one,one)))) )],[refute_0_951,refute_0_1040]) ).
cnf(refute_0_1042,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))))]]) ).
cnf(refute_0_1043,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))
| join(one,converse(join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),complement(complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))) ),[1,0],$fot(join(one,join(one,join(one,one))))]]) ).
cnf(refute_0_1044,plain,
( join(one,converse(join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))) )],[refute_0_1042,refute_0_1043]) ).
cnf(refute_0_1045,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),complement(complement(one))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,one)))),join(one,join(one,join(one,one)))) )],[refute_0_1041,refute_0_1044]) ).
cnf(refute_0_1046,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),complement(complement(one)))
| composition(join(one,join(one,join(one,one))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),one)
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))))),bind(Y,$fot(composition(join(one,join(one,join(one,one))),complement(complement(one))))),bind(Z,$fot(composition(join(one,join(one,join(one,one))),one)))]]) ).
cnf(refute_0_1047,plain,
( composition(join(one,join(one,join(one,one))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),one)
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),composition(join(one,join(one,join(one,one))),complement(complement(one)))) )],[refute_0_1045,refute_0_1046]) ).
cnf(refute_0_1048,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),complement(complement(one))),composition(join(one,join(one,join(one,one))),one)) )],[refute_0_1037,refute_0_1047]) ).
cnf(refute_0_1049,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),one)
| composition(join(one,join(one,join(one,one))),one) != join(one,join(one,join(one,one)))
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = join(one,join(one,join(one,one))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))))),bind(Y,$fot(composition(join(one,join(one,join(one,one))),one))),bind(Z,$fot(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1050,plain,
( composition(join(one,join(one,join(one,one))),one) != join(one,join(one,join(one,one)))
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),composition(join(one,join(one,join(one,one))),one)) )],[refute_0_1048,refute_0_1049]) ).
cnf(refute_0_1051,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),one),join(one,join(one,join(one,one)))) )],[refute_0_1032,refute_0_1050]) ).
cnf(refute_0_1052,plain,
composition(join(converse(join(one,join(one,one))),one),complement(complement(one))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),
inference(subst,[],[refute_0_1020:[bind(X_104,$fot(converse(join(one,join(one,one))))),bind(X_105,$fot(one)),bind(X_106,$fot(complement(complement(one))))]]) ).
cnf(refute_0_1053,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = composition(join(converse(join(one,join(one,one))),one),complement(complement(one))),
inference(subst,[],[refute_0_868:[bind(X_104,$fot(converse(join(one,join(one,one))))),bind(X_106,$fot(complement(complement(one))))]]) ).
cnf(refute_0_1054,plain,
( composition(join(converse(join(one,join(one,one))),one),complement(complement(one))) != composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != composition(join(converse(join(one,join(one,one))),one),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))))),bind(Y,$fot(composition(join(converse(join(one,join(one,one))),one),complement(complement(one))))),bind(Z,$fot(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))))]]) ).
cnf(refute_0_1055,plain,
( composition(join(converse(join(one,join(one,one))),one),complement(complement(one))) != composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),composition(join(converse(join(one,join(one,one))),one),complement(complement(one)))) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),
inference(resolve,[$cnf( $equal(composition(join(converse(join(one,join(one,one))),one),complement(complement(one))),composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))) )],[refute_0_1052,refute_0_1055]) ).
cnf(refute_0_1057,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != join(one,join(one,join(one,one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = join(one,join(one,join(one,one))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))))),bind(Y,$fot(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))))),bind(Z,$fot(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1058,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != join(one,join(one,join(one,one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))) )],[refute_0_1056,refute_0_1057]) ).
cnf(refute_0_1059,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),join(one,join(one,join(one,one)))) )],[refute_0_1051,refute_0_1058]) ).
cnf(refute_0_1060,plain,
( join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != join(one,join(one,join(one,one)))
| join(one,join(one,join(one,one))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),complement(complement(one))) ),[0],$fot(join(one,join(one,join(one,one))))]]) ).
cnf(refute_0_1061,plain,
( join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != complement(complement(one))
| join(one,join(one,join(one,one))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),join(one,join(one,join(one,one)))) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
( complement(complement(one)) != one
| join(one,join(one,join(one,one))) != complement(complement(one))
| join(one,join(one,join(one,one))) = one ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(one,one))),complement(complement(one))) ),[1],$fot(one)]]) ).
cnf(refute_0_1063,plain,
( join(one,join(one,join(one,one))) != complement(complement(one))
| join(one,join(one,join(one,one))) = one ),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1033,refute_0_1062]) ).
cnf(refute_0_1064,plain,
( join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != complement(complement(one))
| join(one,join(one,join(one,one))) = one ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),complement(complement(one))) )],[refute_0_1061,refute_0_1063]) ).
cnf(refute_0_1065,plain,
join(one,join(one,join(one,one))) = one,
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),complement(complement(one))) )],[refute_0_1031,refute_0_1064]) ).
cnf(refute_0_1066,plain,
join(X_104,join(one,join(one,join(one,one)))) = join(X_104,join(one,join(one,join(one,one)))),
introduced(tautology,[refl,[$fot(join(X_104,join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1067,plain,
( join(X_104,join(one,join(one,join(one,one)))) != join(X_104,join(one,join(one,join(one,one))))
| join(one,join(one,join(one,one))) != one
| join(X_104,join(one,join(one,join(one,one)))) = join(X_104,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_104,join(one,join(one,join(one,one)))),join(X_104,join(one,join(one,join(one,one))))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1068,plain,
( join(one,join(one,join(one,one))) != one
| join(X_104,join(one,join(one,join(one,one)))) = join(X_104,one) ),
inference(resolve,[$cnf( $equal(join(X_104,join(one,join(one,join(one,one)))),join(X_104,join(one,join(one,join(one,one))))) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
join(X_104,join(one,join(one,join(one,one)))) = join(X_104,one),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),one) )],[refute_0_1065,refute_0_1068]) ).
cnf(refute_0_1070,plain,
composition(join(X_104,join(one,join(one,join(one,one)))),zero) = composition(join(X_104,join(one,join(one,join(one,one)))),zero),
introduced(tautology,[refl,[$fot(composition(join(X_104,join(one,join(one,join(one,one)))),zero))]]) ).
cnf(refute_0_1071,plain,
( composition(join(X_104,join(one,join(one,join(one,one)))),zero) != composition(join(X_104,join(one,join(one,join(one,one)))),zero)
| join(X_104,join(one,join(one,join(one,one)))) != join(X_104,one)
| composition(join(X_104,join(one,join(one,join(one,one)))),zero) = composition(join(X_104,one),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),composition(join(X_104,join(one,join(one,join(one,one)))),zero)) ),[1,0],$fot(join(X_104,one))]]) ).
cnf(refute_0_1072,plain,
( join(X_104,join(one,join(one,join(one,one)))) != join(X_104,one)
| composition(join(X_104,join(one,join(one,join(one,one)))),zero) = composition(join(X_104,one),zero) ),
inference(resolve,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),composition(join(X_104,join(one,join(one,join(one,one)))),zero)) )],[refute_0_1070,refute_0_1071]) ).
cnf(refute_0_1073,plain,
composition(join(X_104,join(one,join(one,join(one,one)))),zero) = composition(join(X_104,one),zero),
inference(resolve,[$cnf( $equal(join(X_104,join(one,join(one,join(one,one)))),join(X_104,one)) )],[refute_0_1069,refute_0_1072]) ).
cnf(refute_0_1074,plain,
( composition(join(X_104,join(one,join(one,join(one,one)))),zero) != composition(X_104,zero)
| composition(join(X_104,join(one,join(one,join(one,one)))),zero) != composition(join(X_104,one),zero)
| composition(join(X_104,one),zero) = composition(X_104,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),composition(X_104,zero)) ),[0],$fot(composition(join(X_104,one),zero))]]) ).
cnf(refute_0_1075,plain,
( composition(join(X_104,join(one,join(one,join(one,one)))),zero) != composition(X_104,zero)
| composition(join(X_104,one),zero) = composition(X_104,zero) ),
inference(resolve,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),composition(join(X_104,one),zero)) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
composition(join(X_104,one),zero) = composition(X_104,zero),
inference(resolve,[$cnf( $equal(composition(join(X_104,join(one,join(one,join(one,one)))),zero),composition(X_104,zero)) )],[refute_0_967,refute_0_1075]) ).
cnf(refute_0_1077,plain,
composition(join(X_107,one),zero) = composition(X_107,zero),
inference(subst,[],[refute_0_1076:[bind(X_104,$fot(X_107))]]) ).
cnf(refute_0_1078,plain,
join(zero,composition(X_107,zero)) = composition(join(X_107,one),zero),
inference(subst,[],[refute_0_868:[bind(X_104,$fot(X_107)),bind(X_106,$fot(zero))]]) ).
cnf(refute_0_1079,plain,
( composition(join(X_107,one),zero) != composition(X_107,zero)
| join(zero,composition(X_107,zero)) != composition(join(X_107,one),zero)
| join(zero,composition(X_107,zero)) = composition(X_107,zero) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(zero,composition(X_107,zero)))),bind(Y,$fot(composition(join(X_107,one),zero))),bind(Z,$fot(composition(X_107,zero)))]]) ).
cnf(refute_0_1080,plain,
( composition(join(X_107,one),zero) != composition(X_107,zero)
| join(zero,composition(X_107,zero)) = composition(X_107,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X_107,zero)),composition(join(X_107,one),zero)) )],[refute_0_1078,refute_0_1079]) ).
cnf(refute_0_1081,plain,
join(zero,composition(X_107,zero)) = composition(X_107,zero),
inference(resolve,[$cnf( $equal(composition(join(X_107,one),zero),composition(X_107,zero)) )],[refute_0_1077,refute_0_1080]) ).
cnf(refute_0_1082,plain,
( composition(join(one,X_107),zero) != join(zero,composition(X_107,zero))
| join(zero,composition(X_107,zero)) != composition(X_107,zero)
| composition(join(one,X_107),zero) = composition(X_107,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_107),zero),composition(X_107,zero)) ),[0],$fot(join(zero,composition(X_107,zero)))]]) ).
cnf(refute_0_1083,plain,
( composition(join(one,X_107),zero) != join(zero,composition(X_107,zero))
| composition(join(one,X_107),zero) = composition(X_107,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X_107,zero)),composition(X_107,zero)) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
( composition(join(join(one,join(X_107,one)),one),zero) != join(zero,composition(X_107,zero))
| composition(join(one,X_107),zero) = composition(X_107,zero) ),
inference(resolve,[$cnf( $equal(composition(join(one,X_107),zero),join(zero,composition(X_107,zero))) )],[refute_0_880,refute_0_1083]) ).
cnf(refute_0_1085,plain,
composition(join(one,X_107),zero) = composition(X_107,zero),
inference(resolve,[$cnf( $equal(composition(join(join(one,join(X_107,one)),one),zero),join(zero,composition(X_107,zero))) )],[refute_0_851,refute_0_1084]) ).
cnf(refute_0_1086,plain,
composition(join(one,converse(complement(converse(one)))),zero) = composition(converse(complement(converse(one))),zero),
inference(subst,[],[refute_0_1085:[bind(X_107,$fot(converse(complement(converse(one)))))]]) ).
cnf(refute_0_1087,plain,
converse(join(converse(X_82),complement(converse(X_82)))) = join(X_82,converse(complement(converse(X_82)))),
inference(subst,[],[refute_0_775:[bind(A,$fot(X_82)),bind(X_5,$fot(complement(converse(X_82))))]]) ).
cnf(refute_0_1088,plain,
top = join(converse(X_82),complement(converse(X_82))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_82)))]]) ).
cnf(refute_0_1089,plain,
( top != join(converse(X_82),complement(converse(X_82)))
| join(converse(X_82),complement(converse(X_82))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_82),complement(converse(X_82)))))]]) ).
cnf(refute_0_1090,plain,
join(converse(X_82),complement(converse(X_82))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_82),complement(converse(X_82)))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
( converse(join(converse(X_82),complement(converse(X_82)))) != join(X_82,converse(complement(converse(X_82))))
| join(converse(X_82),complement(converse(X_82))) != top
| converse(top) = join(X_82,converse(complement(converse(X_82)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_82),complement(converse(X_82)))),join(X_82,converse(complement(converse(X_82))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1092,plain,
( converse(join(converse(X_82),complement(converse(X_82)))) != join(X_82,converse(complement(converse(X_82))))
| converse(top) = join(X_82,converse(complement(converse(X_82)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_82),complement(converse(X_82))),top) )],[refute_0_1090,refute_0_1091]) ).
cnf(refute_0_1093,plain,
converse(top) = join(X_82,converse(complement(converse(X_82)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),complement(converse(X_82)))),join(X_82,converse(complement(converse(X_82))))) )],[refute_0_1087,refute_0_1092]) ).
cnf(refute_0_1094,plain,
join(converse(A),converse(B)) = join(converse(B),converse(A)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(A))),bind(B,$fot(converse(B)))]]) ).
cnf(refute_0_1095,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) != join(converse(B),converse(A))
| converse(join(A,B)) = join(converse(B),converse(A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(A,B)),join(converse(B),converse(A))) ),[0],$fot(join(converse(A),converse(B)))]]) ).
cnf(refute_0_1096,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| converse(join(A,B)) = join(converse(B),converse(A)) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),join(converse(B),converse(A))) )],[refute_0_1094,refute_0_1095]) ).
cnf(refute_0_1097,plain,
converse(join(A,B)) = join(converse(B),converse(A)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_1096]) ).
cnf(refute_0_1098,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_1099,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_1098]) ).
cnf(refute_0_1100,plain,
join(converse(B),converse(A)) = converse(join(B,A)),
inference(subst,[],[refute_0_1099:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_1101,plain,
( converse(join(A,B)) != join(converse(B),converse(A))
| join(converse(B),converse(A)) != converse(join(B,A))
| converse(join(A,B)) = converse(join(B,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(A,B)),converse(join(B,A))) ),[0],$fot(join(converse(B),converse(A)))]]) ).
cnf(refute_0_1102,plain,
( converse(join(A,B)) != join(converse(B),converse(A))
| converse(join(A,B)) = converse(join(B,A)) ),
inference(resolve,[$cnf( $equal(join(converse(B),converse(A)),converse(join(B,A))) )],[refute_0_1100,refute_0_1101]) ).
cnf(refute_0_1103,plain,
converse(join(A,B)) = converse(join(B,A)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(B),converse(A))) )],[refute_0_1097,refute_0_1102]) ).
cnf(refute_0_1104,plain,
converse(join(converse(top),top)) = converse(join(top,converse(top))),
inference(subst,[],[refute_0_1103:[bind(A,$fot(converse(top))),bind(B,$fot(top))]]) ).
cnf(refute_0_1105,plain,
join(top,join(top,C)) = join(join(top,top),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(top))]]) ).
cnf(refute_0_1106,plain,
join(complement(zero),complement(zero)) = complement(zero),
inference(subst,[],[refute_0_213:[bind(X_46,$fot(zero))]]) ).
cnf(refute_0_1107,plain,
( complement(zero) != top
| join(complement(zero),complement(zero)) != complement(zero)
| join(complement(zero),top) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),complement(zero)),complement(zero)) ),[0,1],$fot(top)]]) ).
cnf(refute_0_1108,plain,
( join(complement(zero),complement(zero)) != complement(zero)
| join(complement(zero),top) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_1107]) ).
cnf(refute_0_1109,plain,
join(complement(zero),top) = complement(zero),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(zero)),complement(zero)) )],[refute_0_1106,refute_0_1108]) ).
cnf(refute_0_1110,plain,
join(top,complement(zero)) = join(top,complement(zero)),
introduced(tautology,[refl,[$fot(join(top,complement(zero)))]]) ).
cnf(refute_0_1111,plain,
( complement(zero) != top
| join(top,complement(zero)) != join(top,complement(zero))
| join(top,complement(zero)) = join(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(zero)),join(top,complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1112,plain,
( complement(zero) != top
| join(top,complement(zero)) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(top,complement(zero)),join(top,complement(zero))) )],[refute_0_1110,refute_0_1111]) ).
cnf(refute_0_1113,plain,
join(top,complement(zero)) = join(top,top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_1112]) ).
cnf(refute_0_1114,plain,
join(complement(zero),top) = join(top,complement(zero)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(zero)))]]) ).
cnf(refute_0_1115,plain,
( join(complement(zero),top) != join(top,complement(zero))
| join(top,complement(zero)) != join(top,top)
| join(complement(zero),top) = join(top,top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(zero),top))),bind(Y,$fot(join(top,complement(zero)))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_1116,plain,
( join(top,complement(zero)) != join(top,top)
| join(complement(zero),top) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(complement(zero),top),join(top,complement(zero))) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
join(complement(zero),top) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,complement(zero)),join(top,top)) )],[refute_0_1113,refute_0_1116]) ).
cnf(refute_0_1118,plain,
( join(complement(zero),top) != complement(zero)
| join(complement(zero),top) != join(top,top)
| join(top,top) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),top),complement(zero)) ),[0],$fot(join(top,top))]]) ).
cnf(refute_0_1119,plain,
( join(complement(zero),top) != complement(zero)
| join(top,top) = complement(zero) ),
inference(resolve,[$cnf( $equal(join(complement(zero),top),join(top,top)) )],[refute_0_1117,refute_0_1118]) ).
cnf(refute_0_1120,plain,
( complement(zero) != top
| join(top,top) != complement(zero)
| join(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,top),complement(zero)) ),[1],$fot(top)]]) ).
cnf(refute_0_1121,plain,
( join(top,top) != complement(zero)
| join(top,top) = top ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_1120]) ).
cnf(refute_0_1122,plain,
( join(complement(zero),top) != complement(zero)
| join(top,top) = top ),
inference(resolve,[$cnf( $equal(join(top,top),complement(zero)) )],[refute_0_1119,refute_0_1121]) ).
cnf(refute_0_1123,plain,
join(top,top) = top,
inference(resolve,[$cnf( $equal(join(complement(zero),top),complement(zero)) )],[refute_0_1109,refute_0_1122]) ).
cnf(refute_0_1124,plain,
( join(top,join(top,C)) != join(join(top,top),C)
| join(top,top) != top
| join(top,join(top,C)) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(top,C)),join(join(top,top),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1125,plain,
( join(top,join(top,C)) != join(join(top,top),C)
| join(top,join(top,C)) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(top,top),top) )],[refute_0_1123,refute_0_1124]) ).
cnf(refute_0_1126,plain,
join(top,join(top,C)) = join(top,C),
inference(resolve,[$cnf( $equal(join(top,join(top,C)),join(join(top,top),C)) )],[refute_0_1105,refute_0_1125]) ).
cnf(refute_0_1127,plain,
join(top,join(top,converse(complement(converse(top))))) = join(top,converse(complement(converse(top)))),
inference(subst,[],[refute_0_1126:[bind(C,$fot(converse(complement(converse(top)))))]]) ).
cnf(refute_0_1128,plain,
converse(top) = join(top,converse(complement(converse(top)))),
inference(subst,[],[refute_0_1093:[bind(X_82,$fot(top))]]) ).
cnf(refute_0_1129,plain,
( converse(top) != join(top,converse(complement(converse(top))))
| join(top,converse(complement(converse(top)))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(top,converse(complement(converse(top))))))]]) ).
cnf(refute_0_1130,plain,
join(top,converse(complement(converse(top)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(top,converse(complement(converse(top))))) )],[refute_0_1128,refute_0_1129]) ).
cnf(refute_0_1131,plain,
( join(top,converse(complement(converse(top)))) != converse(top)
| join(top,join(top,converse(complement(converse(top))))) != join(top,converse(complement(converse(top))))
| join(top,converse(top)) = join(top,converse(complement(converse(top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(top,converse(complement(converse(top))))),join(top,converse(complement(converse(top))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_1132,plain,
( join(top,join(top,converse(complement(converse(top))))) != join(top,converse(complement(converse(top))))
| join(top,converse(top)) = join(top,converse(complement(converse(top)))) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(top)))),converse(top)) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
join(top,converse(top)) = join(top,converse(complement(converse(top)))),
inference(resolve,[$cnf( $equal(join(top,join(top,converse(complement(converse(top))))),join(top,converse(complement(converse(top))))) )],[refute_0_1127,refute_0_1132]) ).
cnf(refute_0_1134,plain,
( join(top,converse(complement(converse(top)))) != converse(top)
| join(top,converse(top)) != join(top,converse(complement(converse(top))))
| join(top,converse(top)) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(top))))) ),[1],$fot(converse(top))]]) ).
cnf(refute_0_1135,plain,
( join(top,converse(top)) != join(top,converse(complement(converse(top))))
| join(top,converse(top)) = converse(top) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(top)))),converse(top)) )],[refute_0_1130,refute_0_1134]) ).
cnf(refute_0_1136,plain,
join(top,converse(top)) = converse(top),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(top))))) )],[refute_0_1133,refute_0_1135]) ).
cnf(refute_0_1137,plain,
( converse(join(converse(top),top)) != converse(join(top,converse(top)))
| join(top,converse(top)) != converse(top)
| converse(join(converse(top),top)) = converse(converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),top)),converse(join(top,converse(top)))) ),[1,0],$fot(converse(top))]]) ).
cnf(refute_0_1138,plain,
( converse(join(converse(top),top)) != converse(join(top,converse(top)))
| converse(join(converse(top),top)) = converse(converse(top)) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),converse(top)) )],[refute_0_1136,refute_0_1137]) ).
cnf(refute_0_1139,plain,
converse(join(converse(top),top)) = converse(converse(top)),
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(join(top,converse(top)))) )],[refute_0_1104,refute_0_1138]) ).
cnf(refute_0_1140,plain,
join(converse(top),top) = join(top,converse(top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(converse(top)))]]) ).
cnf(refute_0_1141,plain,
( join(converse(top),top) != join(top,converse(top))
| join(top,converse(top)) != converse(top)
| join(converse(top),top) = converse(top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(converse(top),top))),bind(Y,$fot(join(top,converse(top)))),bind(Z,$fot(converse(top)))]]) ).
cnf(refute_0_1142,plain,
( join(top,converse(top)) != converse(top)
| join(converse(top),top) = converse(top) ),
inference(resolve,[$cnf( $equal(join(converse(top),top),join(top,converse(top))) )],[refute_0_1140,refute_0_1141]) ).
cnf(refute_0_1143,plain,
join(converse(top),top) = converse(top),
inference(resolve,[$cnf( $equal(join(top,converse(top)),converse(top)) )],[refute_0_1136,refute_0_1142]) ).
cnf(refute_0_1144,plain,
converse(join(top,converse(top))) = join(converse(top),top),
inference(subst,[],[refute_0_797:[bind(A,$fot(top)),bind(X_4,$fot(top))]]) ).
cnf(refute_0_1145,plain,
( converse(join(top,converse(top))) != join(converse(top),top)
| join(converse(top),top) != converse(top)
| converse(join(top,converse(top))) = converse(top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(top,converse(top))))),bind(Y,$fot(join(converse(top),top))),bind(Z,$fot(converse(top)))]]) ).
cnf(refute_0_1146,plain,
( join(converse(top),top) != converse(top)
| converse(join(top,converse(top))) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),top)) )],[refute_0_1144,refute_0_1145]) ).
cnf(refute_0_1147,plain,
converse(join(top,converse(top))) = converse(top),
inference(resolve,[$cnf( $equal(join(converse(top),top),converse(top)) )],[refute_0_1143,refute_0_1146]) ).
cnf(refute_0_1148,plain,
( converse(join(converse(top),top)) != converse(join(top,converse(top)))
| converse(join(top,converse(top))) != converse(top)
| converse(join(converse(top),top)) = converse(top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(converse(top),top)))),bind(Y,$fot(converse(join(top,converse(top))))),bind(Z,$fot(converse(top)))]]) ).
cnf(refute_0_1149,plain,
( converse(join(top,converse(top))) != converse(top)
| converse(join(converse(top),top)) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(join(top,converse(top)))) )],[refute_0_1104,refute_0_1148]) ).
cnf(refute_0_1150,plain,
converse(join(converse(top),top)) = converse(top),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),converse(top)) )],[refute_0_1147,refute_0_1149]) ).
cnf(refute_0_1151,plain,
( converse(join(converse(top),top)) != converse(converse(top))
| converse(join(converse(top),top)) != converse(top)
| converse(top) = converse(converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),top)),converse(converse(top))) ),[0],$fot(converse(top))]]) ).
cnf(refute_0_1152,plain,
( converse(join(converse(top),top)) != converse(converse(top))
| converse(top) = converse(converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(top)) )],[refute_0_1150,refute_0_1151]) ).
cnf(refute_0_1153,plain,
converse(converse(top)) = top,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(top))]]) ).
cnf(refute_0_1154,plain,
( converse(converse(top)) != top
| converse(top) != converse(converse(top))
| converse(top) = top ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),converse(converse(top))) ),[1],$fot(top)]]) ).
cnf(refute_0_1155,plain,
( converse(top) != converse(converse(top))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_0_1153,refute_0_1154]) ).
cnf(refute_0_1156,plain,
( converse(join(converse(top),top)) != converse(converse(top))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(converse(top),converse(converse(top))) )],[refute_0_1152,refute_0_1155]) ).
cnf(refute_0_1157,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(converse(top))) )],[refute_0_1139,refute_0_1156]) ).
cnf(refute_0_1158,plain,
( converse(top) != join(X_82,converse(complement(converse(X_82))))
| converse(top) != top
| top = join(X_82,converse(complement(converse(X_82)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_82,converse(complement(converse(X_82))))) ),[0],$fot(top)]]) ).
cnf(refute_0_1159,plain,
( converse(top) != join(X_82,converse(complement(converse(X_82))))
| top = join(X_82,converse(complement(converse(X_82)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1158]) ).
cnf(refute_0_1160,plain,
top = join(X_82,converse(complement(converse(X_82)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_82,converse(complement(converse(X_82))))) )],[refute_0_1093,refute_0_1159]) ).
cnf(refute_0_1161,plain,
top = join(one,converse(complement(converse(one)))),
inference(subst,[],[refute_0_1160:[bind(X_82,$fot(one))]]) ).
cnf(refute_0_1162,plain,
( top != join(one,converse(complement(converse(one))))
| join(one,converse(complement(converse(one)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(one,converse(complement(converse(one))))))]]) ).
cnf(refute_0_1163,plain,
join(one,converse(complement(converse(one)))) = top,
inference(resolve,[$cnf( $equal(top,join(one,converse(complement(converse(one))))) )],[refute_0_1161,refute_0_1162]) ).
cnf(refute_0_1164,plain,
( composition(join(one,converse(complement(converse(one)))),zero) != composition(converse(complement(converse(one))),zero)
| join(one,converse(complement(converse(one)))) != top
| composition(top,zero) = composition(converse(complement(converse(one))),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(complement(converse(one)))),zero),composition(converse(complement(converse(one))),zero)) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1165,plain,
( composition(join(one,converse(complement(converse(one)))),zero) != composition(converse(complement(converse(one))),zero)
| composition(top,zero) = composition(converse(complement(converse(one))),zero) ),
inference(resolve,[$cnf( $equal(join(one,converse(complement(converse(one)))),top) )],[refute_0_1163,refute_0_1164]) ).
cnf(refute_0_1166,plain,
composition(top,zero) = composition(converse(complement(converse(one))),zero),
inference(resolve,[$cnf( $equal(composition(join(one,converse(complement(converse(one)))),zero),composition(converse(complement(converse(one))),zero)) )],[refute_0_1086,refute_0_1165]) ).
cnf(refute_0_1167,plain,
complement(converse(one)) = complement(converse(one)),
introduced(tautology,[refl,[$fot(complement(converse(one)))]]) ).
cnf(refute_0_1168,plain,
( complement(converse(one)) != complement(converse(one))
| converse(one) != one
| complement(converse(one)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(one)),complement(converse(one))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1169,plain,
( converse(one) != one
| complement(converse(one)) = complement(one) ),
inference(resolve,[$cnf( $equal(complement(converse(one)),complement(converse(one))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
complement(converse(one)) = complement(one),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_1169]) ).
cnf(refute_0_1171,plain,
composition(zero,complement(converse(one))) = composition(zero,complement(converse(one))),
introduced(tautology,[refl,[$fot(composition(zero,complement(converse(one))))]]) ).
cnf(refute_0_1172,plain,
( complement(converse(one)) != complement(one)
| composition(zero,complement(converse(one))) != composition(zero,complement(converse(one)))
| composition(zero,complement(converse(one))) = composition(zero,complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,complement(converse(one))),composition(zero,complement(converse(one)))) ),[1,1],$fot(complement(one))]]) ).
cnf(refute_0_1173,plain,
( complement(converse(one)) != complement(one)
| composition(zero,complement(converse(one))) = composition(zero,complement(one)) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(converse(one))),composition(zero,complement(converse(one)))) )],[refute_0_1171,refute_0_1172]) ).
cnf(refute_0_1174,plain,
composition(zero,complement(converse(one))) = composition(zero,complement(one)),
inference(resolve,[$cnf( $equal(complement(converse(one)),complement(one)) )],[refute_0_1170,refute_0_1173]) ).
cnf(refute_0_1175,plain,
converse(composition(zero,complement(converse(one)))) = converse(composition(zero,complement(converse(one)))),
introduced(tautology,[refl,[$fot(converse(composition(zero,complement(converse(one)))))]]) ).
cnf(refute_0_1176,plain,
( composition(zero,complement(converse(one))) != composition(zero,complement(one))
| converse(composition(zero,complement(converse(one)))) != converse(composition(zero,complement(converse(one))))
| converse(composition(zero,complement(converse(one)))) = converse(composition(zero,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(zero,complement(converse(one)))),converse(composition(zero,complement(converse(one))))) ),[1,0],$fot(composition(zero,complement(one)))]]) ).
cnf(refute_0_1177,plain,
( composition(zero,complement(converse(one))) != composition(zero,complement(one))
| converse(composition(zero,complement(converse(one)))) = converse(composition(zero,complement(one))) ),
inference(resolve,[$cnf( $equal(converse(composition(zero,complement(converse(one)))),converse(composition(zero,complement(converse(one))))) )],[refute_0_1175,refute_0_1176]) ).
cnf(refute_0_1178,plain,
converse(composition(zero,complement(converse(one)))) = converse(composition(zero,complement(one))),
inference(resolve,[$cnf( $equal(composition(zero,complement(converse(one))),composition(zero,complement(one))) )],[refute_0_1174,refute_0_1177]) ).
cnf(refute_0_1179,plain,
converse(composition(converse(zero),X_23)) = composition(converse(X_23),zero),
inference(subst,[],[refute_0_165:[bind(A,$fot(zero))]]) ).
cnf(refute_0_1180,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(subst,[],[def_zero_13:[bind(A,$fot(converse(zero)))]]) ).
cnf(refute_0_1181,plain,
converse(converse(complement(converse(zero)))) = complement(converse(zero)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_1182,plain,
top = join(meet(top,B),complement(join(complement(top),B))),
inference(subst,[],[refute_0_38:[bind(A,$fot(top))]]) ).
cnf(refute_0_1183,plain,
meet(B,top) = meet(top,B),
inference(subst,[],[refute_0_144:[bind(A,$fot(B))]]) ).
cnf(refute_0_1184,plain,
( meet(B,top) != meet(top,B)
| meet(top,B) = meet(B,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(B,top))),bind(Y,$fot(meet(top,B)))]]) ).
cnf(refute_0_1185,plain,
meet(top,B) = meet(B,top),
inference(resolve,[$cnf( $equal(meet(B,top),meet(top,B)) )],[refute_0_1183,refute_0_1184]) ).
cnf(refute_0_1186,plain,
( meet(top,B) != meet(B,top)
| top != join(meet(top,B),complement(join(complement(top),B)))
| top = join(meet(B,top),complement(join(complement(top),B))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,B),complement(join(complement(top),B)))) ),[1,0],$fot(meet(B,top))]]) ).
cnf(refute_0_1187,plain,
( top != join(meet(top,B),complement(join(complement(top),B)))
| top = join(meet(B,top),complement(join(complement(top),B))) ),
inference(resolve,[$cnf( $equal(meet(top,B),meet(B,top)) )],[refute_0_1185,refute_0_1186]) ).
cnf(refute_0_1188,plain,
top = join(meet(B,top),complement(join(complement(top),B))),
inference(resolve,[$cnf( $equal(top,join(meet(top,B),complement(join(complement(top),B)))) )],[refute_0_1182,refute_0_1187]) ).
cnf(refute_0_1189,plain,
join(complement(top),B) = join(complement(top),B),
introduced(tautology,[refl,[$fot(join(complement(top),B))]]) ).
cnf(refute_0_1190,plain,
( complement(top) != zero
| join(complement(top),B) != join(complement(top),B)
| join(complement(top),B) = join(zero,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),B),join(complement(top),B)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1191,plain,
( complement(top) != zero
| join(complement(top),B) = join(zero,B) ),
inference(resolve,[$cnf( $equal(join(complement(top),B),join(complement(top),B)) )],[refute_0_1189,refute_0_1190]) ).
cnf(refute_0_1192,plain,
join(complement(top),B) = join(zero,B),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_1191]) ).
cnf(refute_0_1193,plain,
complement(join(complement(top),B)) = complement(join(complement(top),B)),
introduced(tautology,[refl,[$fot(complement(join(complement(top),B)))]]) ).
cnf(refute_0_1194,plain,
( complement(join(complement(top),B)) != complement(join(complement(top),B))
| join(complement(top),B) != join(zero,B)
| complement(join(complement(top),B)) = complement(join(zero,B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(top),B)),complement(join(complement(top),B))) ),[1,0],$fot(join(zero,B))]]) ).
cnf(refute_0_1195,plain,
( join(complement(top),B) != join(zero,B)
| complement(join(complement(top),B)) = complement(join(zero,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(top),B)),complement(join(complement(top),B))) )],[refute_0_1193,refute_0_1194]) ).
cnf(refute_0_1196,plain,
complement(join(complement(top),B)) = complement(join(zero,B)),
inference(resolve,[$cnf( $equal(join(complement(top),B),join(zero,B)) )],[refute_0_1192,refute_0_1195]) ).
cnf(refute_0_1197,plain,
join(meet(B,top),complement(join(complement(top),B))) = join(meet(B,top),complement(join(complement(top),B))),
introduced(tautology,[refl,[$fot(join(meet(B,top),complement(join(complement(top),B))))]]) ).
cnf(refute_0_1198,plain,
( complement(join(complement(top),B)) != complement(join(zero,B))
| join(meet(B,top),complement(join(complement(top),B))) != join(meet(B,top),complement(join(complement(top),B)))
| join(meet(B,top),complement(join(complement(top),B))) = join(meet(B,top),complement(join(zero,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(B,top),complement(join(complement(top),B))),join(meet(B,top),complement(join(complement(top),B)))) ),[1,1],$fot(complement(join(zero,B)))]]) ).
cnf(refute_0_1199,plain,
( complement(join(complement(top),B)) != complement(join(zero,B))
| join(meet(B,top),complement(join(complement(top),B))) = join(meet(B,top),complement(join(zero,B))) ),
inference(resolve,[$cnf( $equal(join(meet(B,top),complement(join(complement(top),B))),join(meet(B,top),complement(join(complement(top),B)))) )],[refute_0_1197,refute_0_1198]) ).
cnf(refute_0_1200,plain,
join(meet(B,top),complement(join(complement(top),B))) = join(meet(B,top),complement(join(zero,B))),
inference(resolve,[$cnf( $equal(complement(join(complement(top),B)),complement(join(zero,B))) )],[refute_0_1196,refute_0_1199]) ).
cnf(refute_0_1201,plain,
( join(meet(B,top),complement(join(complement(top),B))) != join(meet(B,top),complement(join(zero,B)))
| top != join(meet(B,top),complement(join(complement(top),B)))
| top = join(meet(B,top),complement(join(zero,B))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(B,top),complement(join(complement(top),B)))) ),[1],$fot(join(meet(B,top),complement(join(zero,B))))]]) ).
cnf(refute_0_1202,plain,
( top != join(meet(B,top),complement(join(complement(top),B)))
| top = join(meet(B,top),complement(join(zero,B))) ),
inference(resolve,[$cnf( $equal(join(meet(B,top),complement(join(complement(top),B))),join(meet(B,top),complement(join(zero,B)))) )],[refute_0_1200,refute_0_1201]) ).
cnf(refute_0_1203,plain,
top = join(meet(B,top),complement(join(zero,B))),
inference(resolve,[$cnf( $equal(top,join(meet(B,top),complement(join(complement(top),B)))) )],[refute_0_1188,refute_0_1202]) ).
cnf(refute_0_1204,plain,
top = join(meet(converse(complement(converse(zero))),top),complement(join(zero,converse(complement(converse(zero)))))),
inference(subst,[],[refute_0_1203:[bind(B,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1205,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_1093:[bind(X_82,$fot(zero))]]) ).
cnf(refute_0_1206,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_1207,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
( join(zero,converse(complement(converse(zero)))) != converse(top)
| top != join(meet(converse(complement(converse(zero))),top),complement(join(zero,converse(complement(converse(zero))))))
| top = join(meet(converse(complement(converse(zero))),top),complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(converse(complement(converse(zero))),top),complement(join(zero,converse(complement(converse(zero))))))) ),[1,1,0],$fot(converse(top))]]) ).
cnf(refute_0_1209,plain,
( top != join(meet(converse(complement(converse(zero))),top),complement(join(zero,converse(complement(converse(zero))))))
| top = join(meet(converse(complement(converse(zero))),top),complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_1207,refute_0_1208]) ).
cnf(refute_0_1210,plain,
top = join(meet(converse(complement(converse(zero))),top),complement(converse(top))),
inference(resolve,[$cnf( $equal(top,join(meet(converse(complement(converse(zero))),top),complement(join(zero,converse(complement(converse(zero))))))) )],[refute_0_1204,refute_0_1209]) ).
cnf(refute_0_1211,plain,
meet(converse(complement(converse(zero))),top) = meet(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_144:[bind(A,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1212,plain,
join(complement(converse(top)),meet(converse(complement(converse(zero))),top)) = join(complement(converse(top)),meet(converse(complement(converse(zero))),top)),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(converse(complement(converse(zero))),top)))]]) ).
cnf(refute_0_1213,plain,
( join(complement(converse(top)),meet(converse(complement(converse(zero))),top)) != join(complement(converse(top)),meet(converse(complement(converse(zero))),top))
| meet(converse(complement(converse(zero))),top) != meet(top,converse(complement(converse(zero))))
| join(complement(converse(top)),meet(converse(complement(converse(zero))),top)) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(converse(complement(converse(zero))),top)),join(complement(converse(top)),meet(converse(complement(converse(zero))),top))) ),[1,1],$fot(meet(top,converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1214,plain,
( meet(converse(complement(converse(zero))),top) != meet(top,converse(complement(converse(zero))))
| join(complement(converse(top)),meet(converse(complement(converse(zero))),top)) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(converse(complement(converse(zero))),top)),join(complement(converse(top)),meet(converse(complement(converse(zero))),top))) )],[refute_0_1212,refute_0_1213]) ).
cnf(refute_0_1215,plain,
join(complement(converse(top)),meet(converse(complement(converse(zero))),top)) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(zero))),top),meet(top,converse(complement(converse(zero))))) )],[refute_0_1211,refute_0_1214]) ).
cnf(refute_0_1216,plain,
join(meet(converse(complement(converse(zero))),top),complement(converse(top))) = join(complement(converse(top)),meet(converse(complement(converse(zero))),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(converse(top)))),bind(B,$fot(meet(converse(complement(converse(zero))),top)))]]) ).
cnf(refute_0_1217,plain,
( join(complement(converse(top)),meet(converse(complement(converse(zero))),top)) != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| join(meet(converse(complement(converse(zero))),top),complement(converse(top))) != join(complement(converse(top)),meet(converse(complement(converse(zero))),top))
| join(meet(converse(complement(converse(zero))),top),complement(converse(top))) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(converse(complement(converse(zero))),top),complement(converse(top))))),bind(Y,$fot(join(complement(converse(top)),meet(converse(complement(converse(zero))),top)))),bind(Z,$fot(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_1218,plain,
( join(complement(converse(top)),meet(converse(complement(converse(zero))),top)) != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| join(meet(converse(complement(converse(zero))),top),complement(converse(top))) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(zero))),top),complement(converse(top))),join(complement(converse(top)),meet(converse(complement(converse(zero))),top))) )],[refute_0_1216,refute_0_1217]) ).
cnf(refute_0_1219,plain,
join(meet(converse(complement(converse(zero))),top),complement(converse(top))) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(converse(complement(converse(zero))),top)),join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) )],[refute_0_1215,refute_0_1218]) ).
cnf(refute_0_1220,plain,
( join(meet(converse(complement(converse(zero))),top),complement(converse(top))) != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| top != join(meet(converse(complement(converse(zero))),top),complement(converse(top)))
| top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(converse(complement(converse(zero))),top),complement(converse(top)))) ),[1],$fot(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_1221,plain,
( top != join(meet(converse(complement(converse(zero))),top),complement(converse(top)))
| top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(zero))),top),complement(converse(top))),join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) )],[refute_0_1219,refute_0_1220]) ).
cnf(refute_0_1222,plain,
top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(top,join(meet(converse(complement(converse(zero))),top),complement(converse(top)))) )],[refute_0_1210,refute_0_1221]) ).
cnf(refute_0_1223,plain,
complement(converse(top)) = complement(converse(top)),
introduced(tautology,[refl,[$fot(complement(converse(top)))]]) ).
cnf(refute_0_1224,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_1225,plain,
( converse(top) != top
| complement(converse(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(converse(top))) )],[refute_0_1223,refute_0_1224]) ).
cnf(refute_0_1226,plain,
complement(converse(top)) = complement(top),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1225]) ).
cnf(refute_0_1227,plain,
( complement(converse(top)) != complement(top)
| complement(top) != zero
| complement(converse(top)) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(converse(top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1228,plain,
( complement(top) != zero
| complement(converse(top)) = zero ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(top)) )],[refute_0_1226,refute_0_1227]) ).
cnf(refute_0_1229,plain,
complement(converse(top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_1228]) ).
cnf(refute_0_1230,plain,
join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_1231,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = join(zero,meet(top,converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1232,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = join(zero,meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) )],[refute_0_1230,refute_0_1231]) ).
cnf(refute_0_1233,plain,
join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = join(zero,meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(complement(converse(top)),zero) )],[refute_0_1229,refute_0_1232]) ).
cnf(refute_0_1234,plain,
( join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) != join(zero,meet(top,converse(complement(converse(zero)))))
| top != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| top = join(zero,meet(top,converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) ),[1],$fot(join(zero,meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_1235,plain,
( top != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| top = join(zero,meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),join(zero,meet(top,converse(complement(converse(zero)))))) )],[refute_0_1233,refute_0_1234]) ).
cnf(refute_0_1236,plain,
top = join(zero,meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(top,join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) )],[refute_0_1222,refute_0_1235]) ).
cnf(refute_0_1237,plain,
join(zero,meet(top,converse(complement(converse(zero))))) = meet(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_1238,plain,
( join(zero,meet(top,converse(complement(converse(zero))))) != meet(top,converse(complement(converse(zero))))
| top != join(zero,meet(top,converse(complement(converse(zero)))))
| top = meet(top,converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,meet(top,converse(complement(converse(zero)))))) ),[1],$fot(meet(top,converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1239,plain,
( top != join(zero,meet(top,converse(complement(converse(zero)))))
| top = meet(top,converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,converse(complement(converse(zero))))),meet(top,converse(complement(converse(zero))))) )],[refute_0_1237,refute_0_1238]) ).
cnf(refute_0_1240,plain,
top = meet(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,converse(complement(converse(zero)))))) )],[refute_0_1236,refute_0_1239]) ).
cnf(refute_0_1241,plain,
meet(top,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(subst,[],[refute_0_429:[bind(B,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1242,plain,
( meet(top,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| top != meet(top,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,meet(top,converse(complement(converse(zero))))) ),[1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_1243,plain,
( top != meet(top,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(meet(top,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_1241,refute_0_1242]) ).
cnf(refute_0_1244,plain,
top = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(top,meet(top,converse(complement(converse(zero))))) )],[refute_0_1240,refute_0_1243]) ).
cnf(refute_0_1245,plain,
( top != converse(complement(converse(zero)))
| converse(complement(converse(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1246,plain,
converse(complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,converse(complement(converse(zero)))) )],[refute_0_1244,refute_0_1245]) ).
cnf(refute_0_1247,plain,
( converse(complement(converse(zero))) != top
| converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1248,plain,
( converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),top) )],[refute_0_1246,refute_0_1247]) ).
cnf(refute_0_1249,plain,
converse(top) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) )],[refute_0_1181,refute_0_1248]) ).
cnf(refute_0_1250,plain,
( converse(top) != complement(converse(zero))
| converse(top) != top
| top = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),complement(converse(zero))) ),[0],$fot(top)]]) ).
cnf(refute_0_1251,plain,
( converse(top) != complement(converse(zero))
| top = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1250]) ).
cnf(refute_0_1252,plain,
top = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(top),complement(converse(zero))) )],[refute_0_1249,refute_0_1251]) ).
cnf(refute_0_1253,plain,
( top != complement(converse(zero))
| complement(converse(zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_1254,plain,
complement(converse(zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(converse(zero))) )],[refute_0_1252,refute_0_1253]) ).
cnf(refute_0_1255,plain,
( complement(converse(zero)) != top
| zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1256,plain,
( zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_0_1254,refute_0_1255]) ).
cnf(refute_0_1257,plain,
zero = meet(converse(zero),top),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) )],[refute_0_1180,refute_0_1256]) ).
cnf(refute_0_1258,plain,
meet(top,A) = A,
inference(subst,[],[refute_0_429:[bind(B,$fot(A))]]) ).
cnf(refute_0_1259,plain,
( meet(A,top) != meet(top,A)
| meet(top,A) != A
| meet(A,top) = A ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(A,top),A) ),[0],$fot(meet(top,A))]]) ).
cnf(refute_0_1260,plain,
( meet(A,top) != meet(top,A)
| meet(A,top) = A ),
inference(resolve,[$cnf( $equal(meet(top,A),A) )],[refute_0_1258,refute_0_1259]) ).
cnf(refute_0_1261,plain,
meet(A,top) = A,
inference(resolve,[$cnf( $equal(meet(A,top),meet(top,A)) )],[refute_0_144,refute_0_1260]) ).
cnf(refute_0_1262,plain,
meet(converse(zero),top) = converse(zero),
inference(subst,[],[refute_0_1261:[bind(A,$fot(converse(zero)))]]) ).
cnf(refute_0_1263,plain,
( meet(converse(zero),top) != converse(zero)
| zero != meet(converse(zero),top)
| zero = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),top)) ),[1],$fot(converse(zero))]]) ).
cnf(refute_0_1264,plain,
( zero != meet(converse(zero),top)
| zero = converse(zero) ),
inference(resolve,[$cnf( $equal(meet(converse(zero),top),converse(zero)) )],[refute_0_1262,refute_0_1263]) ).
cnf(refute_0_1265,plain,
zero = converse(zero),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),top)) )],[refute_0_1257,refute_0_1264]) ).
cnf(refute_0_1266,plain,
( zero != converse(zero)
| converse(zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(converse(zero)))]]) ).
cnf(refute_0_1267,plain,
converse(zero) = zero,
inference(resolve,[$cnf( $equal(zero,converse(zero)) )],[refute_0_1265,refute_0_1266]) ).
cnf(refute_0_1268,plain,
( converse(composition(converse(zero),X_23)) != composition(converse(X_23),zero)
| converse(zero) != zero
| converse(composition(zero,X_23)) = composition(converse(X_23),zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(zero),X_23)),composition(converse(X_23),zero)) ),[0,0,0],$fot(zero)]]) ).
cnf(refute_0_1269,plain,
( converse(composition(converse(zero),X_23)) != composition(converse(X_23),zero)
| converse(composition(zero,X_23)) = composition(converse(X_23),zero) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_1267,refute_0_1268]) ).
cnf(refute_0_1270,plain,
converse(composition(zero,X_23)) = composition(converse(X_23),zero),
inference(resolve,[$cnf( $equal(converse(composition(converse(zero),X_23)),composition(converse(X_23),zero)) )],[refute_0_1179,refute_0_1269]) ).
cnf(refute_0_1271,plain,
( converse(composition(zero,X_23)) != composition(converse(X_23),zero)
| composition(converse(X_23),zero) = converse(composition(zero,X_23)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(zero,X_23)))),bind(Y,$fot(composition(converse(X_23),zero)))]]) ).
cnf(refute_0_1272,plain,
composition(converse(X_23),zero) = converse(composition(zero,X_23)),
inference(resolve,[$cnf( $equal(converse(composition(zero,X_23)),composition(converse(X_23),zero)) )],[refute_0_1270,refute_0_1271]) ).
cnf(refute_0_1273,plain,
composition(converse(complement(converse(one))),zero) = converse(composition(zero,complement(converse(one)))),
inference(subst,[],[refute_0_1272:[bind(X_23,$fot(complement(converse(one))))]]) ).
cnf(refute_0_1274,plain,
( composition(converse(complement(converse(one))),zero) != converse(composition(zero,complement(converse(one))))
| converse(composition(zero,complement(converse(one)))) != converse(composition(zero,complement(one)))
| composition(converse(complement(converse(one))),zero) = converse(composition(zero,complement(one))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(converse(complement(converse(one))),zero))),bind(Y,$fot(converse(composition(zero,complement(converse(one)))))),bind(Z,$fot(converse(composition(zero,complement(one)))))]]) ).
cnf(refute_0_1275,plain,
( converse(composition(zero,complement(converse(one)))) != converse(composition(zero,complement(one)))
| composition(converse(complement(converse(one))),zero) = converse(composition(zero,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(converse(one))),zero),converse(composition(zero,complement(converse(one))))) )],[refute_0_1273,refute_0_1274]) ).
cnf(refute_0_1276,plain,
composition(converse(complement(converse(one))),zero) = converse(composition(zero,complement(one))),
inference(resolve,[$cnf( $equal(converse(composition(zero,complement(converse(one)))),converse(composition(zero,complement(one)))) )],[refute_0_1178,refute_0_1275]) ).
cnf(refute_0_1277,plain,
( composition(converse(complement(converse(one))),zero) != converse(composition(zero,complement(one)))
| composition(top,zero) != composition(converse(complement(converse(one))),zero)
| composition(top,zero) = converse(composition(zero,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,zero),composition(converse(complement(converse(one))),zero)) ),[1],$fot(converse(composition(zero,complement(one))))]]) ).
cnf(refute_0_1278,plain,
( composition(top,zero) != composition(converse(complement(converse(one))),zero)
| composition(top,zero) = converse(composition(zero,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(converse(one))),zero),converse(composition(zero,complement(one)))) )],[refute_0_1276,refute_0_1277]) ).
cnf(refute_0_1279,plain,
composition(top,zero) = converse(composition(zero,complement(one))),
inference(resolve,[$cnf( $equal(composition(top,zero),composition(converse(complement(converse(one))),zero)) )],[refute_0_1166,refute_0_1278]) ).
cnf(refute_0_1280,plain,
( composition(top,zero) != converse(composition(zero,complement(one)))
| converse(composition(zero,complement(one))) = composition(top,zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(top,zero))),bind(Y,$fot(converse(composition(zero,complement(one)))))]]) ).
cnf(refute_0_1281,plain,
converse(composition(zero,complement(one))) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),converse(composition(zero,complement(one)))) )],[refute_0_1279,refute_0_1280]) ).
cnf(refute_0_1282,plain,
( converse(composition(zero,complement(one))) != composition(top,zero)
| join(top,composition(converse(composition(zero,complement(one))),complement(composition(composition(zero,complement(one)),zero)))) != top
| join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,composition(converse(composition(zero,complement(one))),complement(composition(composition(zero,complement(one)),zero)))),top) ),[0,1,0],$fot(composition(top,zero))]]) ).
cnf(refute_0_1283,plain,
( join(top,composition(converse(composition(zero,complement(one))),complement(composition(composition(zero,complement(one)),zero)))) != top
| join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) = top ),
inference(resolve,[$cnf( $equal(converse(composition(zero,complement(one))),composition(top,zero)) )],[refute_0_1281,refute_0_1282]) ).
cnf(refute_0_1284,plain,
join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) = top,
inference(resolve,[$cnf( $equal(join(top,composition(converse(composition(zero,complement(one))),complement(composition(composition(zero,complement(one)),zero)))),top) )],[refute_0_665,refute_0_1283]) ).
cnf(refute_0_1285,plain,
composition(join(one,complement(one)),zero) = composition(complement(one),zero),
inference(subst,[],[refute_0_1085:[bind(X_107,$fot(complement(one)))]]) ).
cnf(refute_0_1286,plain,
top = join(one,complement(one)),
inference(subst,[],[def_top_12:[bind(A,$fot(one))]]) ).
cnf(refute_0_1287,plain,
( top != join(one,complement(one))
| join(one,complement(one)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(one,complement(one))))]]) ).
cnf(refute_0_1288,plain,
join(one,complement(one)) = top,
inference(resolve,[$cnf( $equal(top,join(one,complement(one))) )],[refute_0_1286,refute_0_1287]) ).
cnf(refute_0_1289,plain,
( composition(join(one,complement(one)),zero) != composition(complement(one),zero)
| join(one,complement(one)) != top
| composition(top,zero) = composition(complement(one),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,complement(one)),zero),composition(complement(one),zero)) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1290,plain,
( composition(join(one,complement(one)),zero) != composition(complement(one),zero)
| composition(top,zero) = composition(complement(one),zero) ),
inference(resolve,[$cnf( $equal(join(one,complement(one)),top) )],[refute_0_1288,refute_0_1289]) ).
cnf(refute_0_1291,plain,
composition(top,zero) = composition(complement(one),zero),
inference(resolve,[$cnf( $equal(composition(join(one,complement(one)),zero),composition(complement(one),zero)) )],[refute_0_1285,refute_0_1290]) ).
cnf(refute_0_1292,plain,
( composition(top,zero) != composition(complement(one),zero)
| composition(complement(one),zero) = composition(top,zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(top,zero))),bind(Y,$fot(composition(complement(one),zero)))]]) ).
cnf(refute_0_1293,plain,
composition(complement(one),zero) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),composition(complement(one),zero)) )],[refute_0_1291,refute_0_1292]) ).
cnf(refute_0_1294,plain,
composition(zero,composition(complement(one),zero)) = composition(zero,composition(complement(one),zero)),
introduced(tautology,[refl,[$fot(composition(zero,composition(complement(one),zero)))]]) ).
cnf(refute_0_1295,plain,
( composition(complement(one),zero) != composition(top,zero)
| composition(zero,composition(complement(one),zero)) != composition(zero,composition(complement(one),zero))
| composition(zero,composition(complement(one),zero)) = composition(zero,composition(top,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(complement(one),zero)),composition(zero,composition(complement(one),zero))) ),[1,1],$fot(composition(top,zero))]]) ).
cnf(refute_0_1296,plain,
( composition(complement(one),zero) != composition(top,zero)
| composition(zero,composition(complement(one),zero)) = composition(zero,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(one),zero)),composition(zero,composition(complement(one),zero))) )],[refute_0_1294,refute_0_1295]) ).
cnf(refute_0_1297,plain,
composition(zero,composition(complement(one),zero)) = composition(zero,composition(top,zero)),
inference(resolve,[$cnf( $equal(composition(complement(one),zero),composition(top,zero)) )],[refute_0_1293,refute_0_1296]) ).
cnf(refute_0_1298,plain,
( composition(A,composition(B,C)) != composition(composition(A,B),C)
| composition(composition(A,B),C) = composition(A,composition(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(A,composition(B,C)))),bind(Y,$fot(composition(composition(A,B),C)))]]) ).
cnf(refute_0_1299,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(resolve,[$cnf( $equal(composition(A,composition(B,C)),composition(composition(A,B),C)) )],[composition_associativity_5,refute_0_1298]) ).
cnf(refute_0_1300,plain,
composition(composition(zero,complement(one)),zero) = composition(zero,composition(complement(one),zero)),
inference(subst,[],[refute_0_1299:[bind(A,$fot(zero)),bind(B,$fot(complement(one))),bind(C,$fot(zero))]]) ).
cnf(refute_0_1301,plain,
( composition(composition(zero,complement(one)),zero) != composition(zero,composition(complement(one),zero))
| composition(zero,composition(complement(one),zero)) != composition(zero,composition(top,zero))
| composition(composition(zero,complement(one)),zero) = composition(zero,composition(top,zero)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(composition(zero,complement(one)),zero))),bind(Y,$fot(composition(zero,composition(complement(one),zero)))),bind(Z,$fot(composition(zero,composition(top,zero))))]]) ).
cnf(refute_0_1302,plain,
( composition(zero,composition(complement(one),zero)) != composition(zero,composition(top,zero))
| composition(composition(zero,complement(one)),zero) = composition(zero,composition(top,zero)) ),
inference(resolve,[$cnf( $equal(composition(composition(zero,complement(one)),zero),composition(zero,composition(complement(one),zero))) )],[refute_0_1300,refute_0_1301]) ).
cnf(refute_0_1303,plain,
composition(composition(zero,complement(one)),zero) = composition(zero,composition(top,zero)),
inference(resolve,[$cnf( $equal(composition(zero,composition(complement(one),zero)),composition(zero,composition(top,zero))) )],[refute_0_1297,refute_0_1302]) ).
cnf(refute_0_1304,plain,
complement(composition(composition(zero,complement(one)),zero)) = complement(composition(composition(zero,complement(one)),zero)),
introduced(tautology,[refl,[$fot(complement(composition(composition(zero,complement(one)),zero)))]]) ).
cnf(refute_0_1305,plain,
( complement(composition(composition(zero,complement(one)),zero)) != complement(composition(composition(zero,complement(one)),zero))
| composition(composition(zero,complement(one)),zero) != composition(zero,composition(top,zero))
| complement(composition(composition(zero,complement(one)),zero)) = complement(composition(zero,composition(top,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(composition(zero,complement(one)),zero)),complement(composition(composition(zero,complement(one)),zero))) ),[1,0],$fot(composition(zero,composition(top,zero)))]]) ).
cnf(refute_0_1306,plain,
( composition(composition(zero,complement(one)),zero) != composition(zero,composition(top,zero))
| complement(composition(composition(zero,complement(one)),zero)) = complement(composition(zero,composition(top,zero))) ),
inference(resolve,[$cnf( $equal(complement(composition(composition(zero,complement(one)),zero)),complement(composition(composition(zero,complement(one)),zero))) )],[refute_0_1304,refute_0_1305]) ).
cnf(refute_0_1307,plain,
complement(composition(composition(zero,complement(one)),zero)) = complement(composition(zero,composition(top,zero))),
inference(resolve,[$cnf( $equal(composition(composition(zero,complement(one)),zero),composition(zero,composition(top,zero))) )],[refute_0_1303,refute_0_1306]) ).
cnf(refute_0_1308,plain,
composition(zero,complement(composition(composition(zero,complement(one)),zero))) = composition(zero,complement(composition(composition(zero,complement(one)),zero))),
introduced(tautology,[refl,[$fot(composition(zero,complement(composition(composition(zero,complement(one)),zero))))]]) ).
cnf(refute_0_1309,plain,
( complement(composition(composition(zero,complement(one)),zero)) != complement(composition(zero,composition(top,zero)))
| composition(zero,complement(composition(composition(zero,complement(one)),zero))) != composition(zero,complement(composition(composition(zero,complement(one)),zero)))
| composition(zero,complement(composition(composition(zero,complement(one)),zero))) = composition(zero,complement(composition(zero,composition(top,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,complement(composition(composition(zero,complement(one)),zero))),composition(zero,complement(composition(composition(zero,complement(one)),zero)))) ),[1,1],$fot(complement(composition(zero,composition(top,zero))))]]) ).
cnf(refute_0_1310,plain,
( complement(composition(composition(zero,complement(one)),zero)) != complement(composition(zero,composition(top,zero)))
| composition(zero,complement(composition(composition(zero,complement(one)),zero))) = composition(zero,complement(composition(zero,composition(top,zero)))) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(composition(zero,complement(one)),zero))),composition(zero,complement(composition(composition(zero,complement(one)),zero)))) )],[refute_0_1308,refute_0_1309]) ).
cnf(refute_0_1311,plain,
composition(zero,complement(composition(composition(zero,complement(one)),zero))) = composition(zero,complement(composition(zero,composition(top,zero)))),
inference(resolve,[$cnf( $equal(complement(composition(composition(zero,complement(one)),zero)),complement(composition(zero,composition(top,zero)))) )],[refute_0_1307,refute_0_1310]) ).
cnf(refute_0_1312,plain,
composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))) = composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))),
introduced(tautology,[refl,[$fot(composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))))]]) ).
cnf(refute_0_1313,plain,
( composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))) != composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero))))
| composition(zero,complement(composition(composition(zero,complement(one)),zero))) != composition(zero,complement(composition(zero,composition(top,zero))))
| composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))) = composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))),composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero))))) ),[1,1],$fot(composition(zero,complement(composition(zero,composition(top,zero)))))]]) ).
cnf(refute_0_1314,plain,
( composition(zero,complement(composition(composition(zero,complement(one)),zero))) != composition(zero,complement(composition(zero,composition(top,zero))))
| composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))) = composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))),composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero))))) )],[refute_0_1312,refute_0_1313]) ).
cnf(refute_0_1315,plain,
composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))) = composition(top,composition(zero,complement(composition(zero,composition(top,zero))))),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(composition(zero,complement(one)),zero))),composition(zero,complement(composition(zero,composition(top,zero))))) )],[refute_0_1311,refute_0_1314]) ).
cnf(refute_0_1316,plain,
composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))) = composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))),
inference(subst,[],[refute_0_1299:[bind(A,$fot(top)),bind(B,$fot(zero)),bind(C,$fot(complement(composition(composition(zero,complement(one)),zero))))]]) ).
cnf(refute_0_1317,plain,
( composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))) != composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero))))
| composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))) != composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))
| composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))) = composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))))),bind(Y,$fot(composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))))),bind(Z,$fot(composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))]]) ).
cnf(refute_0_1318,plain,
( composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))) != composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))
| composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))) = composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) ),
inference(resolve,[$cnf( $equal(composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))),composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero))))) )],[refute_0_1316,refute_0_1317]) ).
cnf(refute_0_1319,plain,
composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))) = composition(top,composition(zero,complement(composition(zero,composition(top,zero))))),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(composition(zero,complement(one)),zero)))),composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) )],[refute_0_1315,refute_0_1318]) ).
cnf(refute_0_1320,plain,
join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) = join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))),
introduced(tautology,[refl,[$fot(join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))))]]) ).
cnf(refute_0_1321,plain,
( composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))) != composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))
| join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) != join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))))
| join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) = join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))),join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))))) ),[1,1],$fot(composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))]]) ).
cnf(refute_0_1322,plain,
( composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))) != composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))
| join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) = join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) ),
inference(resolve,[$cnf( $equal(join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))),join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))))) )],[refute_0_1320,refute_0_1321]) ).
cnf(refute_0_1323,plain,
join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) = join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))),
inference(resolve,[$cnf( $equal(composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero))),composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) )],[refute_0_1319,refute_0_1322]) ).
cnf(refute_0_1324,plain,
( join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) != join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))
| join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) != top
| join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))),top) ),[0],$fot(join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))]]) ).
cnf(refute_0_1325,plain,
( join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))) != top
| join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) = top ),
inference(resolve,[$cnf( $equal(join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))),join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) )],[refute_0_1323,refute_0_1324]) ).
cnf(refute_0_1326,plain,
join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) = top,
inference(resolve,[$cnf( $equal(join(top,composition(composition(top,zero),complement(composition(composition(zero,complement(one)),zero)))),top) )],[refute_0_1284,refute_0_1325]) ).
cnf(refute_0_1327,plain,
( join(X_118,join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) != join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))
| join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) != top
| join(X_118,top) = join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_118,join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_1328,plain,
( join(X_118,join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) != join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))
| join(X_118,top) = join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) ),
inference(resolve,[$cnf( $equal(join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))),top) )],[refute_0_1326,refute_0_1327]) ).
cnf(refute_0_1329,plain,
join(X_118,top) = join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),
inference(resolve,[$cnf( $equal(join(X_118,join(top,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))) )],[refute_0_657,refute_0_1328]) ).
cnf(refute_0_1330,plain,
composition(join(zero,join(one,one)),zero) = composition(zero,zero),
inference(subst,[],[refute_0_770:[bind(X_104,$fot(zero))]]) ).
cnf(refute_0_1331,plain,
join(one,one) = join(zero,join(one,one)),
inference(subst,[],[refute_0_416:[bind(X_10,$fot(join(one,one)))]]) ).
cnf(refute_0_1332,plain,
( join(one,one) != join(zero,join(one,one))
| join(zero,join(one,one)) = join(one,one) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,one))),bind(Y,$fot(join(zero,join(one,one))))]]) ).
cnf(refute_0_1333,plain,
join(zero,join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(join(one,one),join(zero,join(one,one))) )],[refute_0_1331,refute_0_1332]) ).
cnf(refute_0_1334,plain,
( composition(join(zero,join(one,one)),zero) != composition(zero,zero)
| join(zero,join(one,one)) != join(one,one)
| composition(join(one,one),zero) = composition(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(zero,join(one,one)),zero),composition(zero,zero)) ),[0,0],$fot(join(one,one))]]) ).
cnf(refute_0_1335,plain,
( composition(join(zero,join(one,one)),zero) != composition(zero,zero)
| composition(join(one,one),zero) = composition(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,join(one,one)),join(one,one)) )],[refute_0_1333,refute_0_1334]) ).
cnf(refute_0_1336,plain,
composition(join(one,one),zero) = composition(zero,zero),
inference(resolve,[$cnf( $equal(composition(join(zero,join(one,one)),zero),composition(zero,zero)) )],[refute_0_1330,refute_0_1335]) ).
cnf(refute_0_1337,plain,
( composition(join(one,one),zero) != composition(zero,zero)
| composition(join(one,one),zero) != zero
| zero = composition(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),zero),composition(zero,zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_1338,plain,
( composition(join(one,one),zero) != composition(zero,zero)
| zero = composition(zero,zero) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),zero),zero) )],[refute_0_763,refute_0_1337]) ).
cnf(refute_0_1339,plain,
zero = composition(zero,zero),
inference(resolve,[$cnf( $equal(composition(join(one,one),zero),composition(zero,zero)) )],[refute_0_1336,refute_0_1338]) ).
cnf(refute_0_1340,plain,
( zero != composition(zero,zero)
| composition(zero,zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(zero,zero)))]]) ).
cnf(refute_0_1341,plain,
composition(zero,zero) = zero,
inference(resolve,[$cnf( $equal(zero,composition(zero,zero)) )],[refute_0_1339,refute_0_1340]) ).
cnf(refute_0_1342,plain,
join(zero,composition(converse(converse(A)),complement(composition(converse(A),top)))) = zero,
inference(subst,[],[refute_0_685:[bind(X_45,$fot(converse(A)))]]) ).
cnf(refute_0_1343,plain,
( converse(converse(A)) != A
| join(zero,composition(converse(converse(A)),complement(composition(converse(A),top)))) != zero
| join(zero,composition(A,complement(composition(converse(A),top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(converse(A)),complement(composition(converse(A),top)))),zero) ),[0,1,0],$fot(A)]]) ).
cnf(refute_0_1344,plain,
( join(zero,composition(converse(converse(A)),complement(composition(converse(A),top)))) != zero
| join(zero,composition(A,complement(composition(converse(A),top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1343]) ).
cnf(refute_0_1345,plain,
join(zero,composition(A,complement(composition(converse(A),top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(converse(A)),complement(composition(converse(A),top)))),zero) )],[refute_0_1342,refute_0_1344]) ).
cnf(refute_0_1346,plain,
join(zero,composition(top,complement(composition(converse(top),top)))) = zero,
inference(subst,[],[refute_0_1345:[bind(A,$fot(top))]]) ).
cnf(refute_0_1347,plain,
( converse(top) != top
| join(zero,composition(top,complement(composition(converse(top),top)))) != zero
| join(zero,composition(top,complement(composition(top,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(top,complement(composition(converse(top),top)))),zero) ),[0,1,1,0,0],$fot(top)]]) ).
cnf(refute_0_1348,plain,
( join(zero,composition(top,complement(composition(converse(top),top)))) != zero
| join(zero,composition(top,complement(composition(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1347]) ).
cnf(refute_0_1349,plain,
join(zero,composition(top,complement(composition(top,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(converse(top),top)))),zero) )],[refute_0_1346,refute_0_1348]) ).
cnf(refute_0_1350,plain,
join(zero,composition(top,complement(composition(top,top)))) = composition(top,complement(composition(top,top))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(composition(top,complement(composition(top,top)))))]]) ).
cnf(refute_0_1351,plain,
( join(zero,composition(top,complement(composition(top,top)))) != composition(top,complement(composition(top,top)))
| join(zero,composition(top,complement(composition(top,top)))) != zero
| composition(top,complement(composition(top,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) ),[0],$fot(composition(top,complement(composition(top,top))))]]) ).
cnf(refute_0_1352,plain,
( join(zero,composition(top,complement(composition(top,top)))) != zero
| composition(top,complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),composition(top,complement(composition(top,top)))) )],[refute_0_1350,refute_0_1351]) ).
cnf(refute_0_1353,plain,
composition(top,complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) )],[refute_0_1349,refute_0_1352]) ).
cnf(refute_0_1354,plain,
composition(join(top,one),complement(composition(top,top))) = join(complement(composition(top,top)),composition(top,complement(composition(top,top)))),
inference(subst,[],[refute_0_676:[bind(X_104,$fot(top)),bind(X_106,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1355,plain,
composition(join(top,X_105),complement(composition(top,top))) = join(composition(top,complement(composition(top,top))),composition(X_105,complement(composition(top,top)))),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(top)),bind(B,$fot(X_105)),bind(C,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1356,plain,
( composition(join(top,X_105),complement(composition(top,top))) != join(composition(top,complement(composition(top,top))),composition(X_105,complement(composition(top,top))))
| composition(top,complement(composition(top,top))) != zero
| composition(join(top,X_105),complement(composition(top,top))) = join(zero,composition(X_105,complement(composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,X_105),complement(composition(top,top))),join(composition(top,complement(composition(top,top))),composition(X_105,complement(composition(top,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1357,plain,
( composition(join(top,X_105),complement(composition(top,top))) != join(composition(top,complement(composition(top,top))),composition(X_105,complement(composition(top,top))))
| composition(join(top,X_105),complement(composition(top,top))) = join(zero,composition(X_105,complement(composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1353,refute_0_1356]) ).
cnf(refute_0_1358,plain,
composition(join(top,X_105),complement(composition(top,top))) = join(zero,composition(X_105,complement(composition(top,top)))),
inference(resolve,[$cnf( $equal(composition(join(top,X_105),complement(composition(top,top))),join(composition(top,complement(composition(top,top))),composition(X_105,complement(composition(top,top))))) )],[refute_0_1355,refute_0_1357]) ).
cnf(refute_0_1359,plain,
join(zero,composition(X_105,complement(composition(top,top)))) = composition(X_105,complement(composition(top,top))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(composition(X_105,complement(composition(top,top)))))]]) ).
cnf(refute_0_1360,plain,
( composition(join(top,X_105),complement(composition(top,top))) != join(zero,composition(X_105,complement(composition(top,top))))
| join(zero,composition(X_105,complement(composition(top,top)))) != composition(X_105,complement(composition(top,top)))
| composition(join(top,X_105),complement(composition(top,top))) = composition(X_105,complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(top,X_105),complement(composition(top,top))),composition(X_105,complement(composition(top,top)))) ),[0],$fot(join(zero,composition(X_105,complement(composition(top,top)))))]]) ).
cnf(refute_0_1361,plain,
( composition(join(top,X_105),complement(composition(top,top))) != join(zero,composition(X_105,complement(composition(top,top))))
| composition(join(top,X_105),complement(composition(top,top))) = composition(X_105,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X_105,complement(composition(top,top)))),composition(X_105,complement(composition(top,top)))) )],[refute_0_1359,refute_0_1360]) ).
cnf(refute_0_1362,plain,
composition(join(top,X_105),complement(composition(top,top))) = composition(X_105,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(join(top,X_105),complement(composition(top,top))),join(zero,composition(X_105,complement(composition(top,top))))) )],[refute_0_1358,refute_0_1361]) ).
cnf(refute_0_1363,plain,
composition(join(top,one),complement(composition(top,top))) = composition(one,complement(composition(top,top))),
inference(subst,[],[refute_0_1362:[bind(X_105,$fot(one))]]) ).
cnf(refute_0_1364,plain,
( composition(join(top,one),complement(composition(top,top))) != composition(one,complement(composition(top,top)))
| composition(join(top,one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| composition(one,complement(composition(top,top))) = join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),join(complement(composition(top,top)),composition(top,complement(composition(top,top))))) ),[0],$fot(composition(one,complement(composition(top,top))))]]) ).
cnf(refute_0_1365,plain,
( composition(join(top,one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| composition(one,complement(composition(top,top))) = join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),composition(one,complement(composition(top,top)))) )],[refute_0_1363,refute_0_1364]) ).
cnf(refute_0_1366,plain,
composition(one,complement(composition(top,top))) = join(complement(composition(top,top)),composition(top,complement(composition(top,top)))),
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),join(complement(composition(top,top)),composition(top,complement(composition(top,top))))) )],[refute_0_1354,refute_0_1365]) ).
cnf(refute_0_1367,plain,
composition(one,complement(composition(top,top))) = complement(composition(top,top)),
inference(subst,[],[refute_0_198:[bind(X_24,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1368,plain,
( composition(one,complement(composition(top,top))) != complement(composition(top,top))
| composition(one,complement(composition(top,top))) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| complement(composition(top,top)) = join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(one,complement(composition(top,top))),join(complement(composition(top,top)),composition(top,complement(composition(top,top))))) ),[0],$fot(complement(composition(top,top)))]]) ).
cnf(refute_0_1369,plain,
( composition(one,complement(composition(top,top))) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| complement(composition(top,top)) = join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(one,complement(composition(top,top))),complement(composition(top,top))) )],[refute_0_1367,refute_0_1368]) ).
cnf(refute_0_1370,plain,
composition(join(join(top,X_123),one),complement(composition(top,top))) = join(complement(composition(top,top)),composition(join(top,X_123),complement(composition(top,top)))),
inference(subst,[],[refute_0_676:[bind(X_104,$fot(join(top,X_123))),bind(X_106,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1371,plain,
composition(join(top,X_123),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))),
inference(subst,[],[refute_0_1362:[bind(X_105,$fot(X_123))]]) ).
cnf(refute_0_1372,plain,
( composition(join(join(top,X_123),one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(join(top,X_123),complement(composition(top,top))))
| composition(join(top,X_123),complement(composition(top,top))) != composition(X_123,complement(composition(top,top)))
| composition(join(join(top,X_123),one),complement(composition(top,top))) = join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(top,X_123),one),complement(composition(top,top))),join(complement(composition(top,top)),composition(join(top,X_123),complement(composition(top,top))))) ),[1,1],$fot(composition(X_123,complement(composition(top,top))))]]) ).
cnf(refute_0_1373,plain,
( composition(join(join(top,X_123),one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(join(top,X_123),complement(composition(top,top))))
| composition(join(join(top,X_123),one),complement(composition(top,top))) = join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(join(top,X_123),complement(composition(top,top))),composition(X_123,complement(composition(top,top)))) )],[refute_0_1371,refute_0_1372]) ).
cnf(refute_0_1374,plain,
composition(join(join(top,X_123),one),complement(composition(top,top))) = join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))),
inference(resolve,[$cnf( $equal(composition(join(join(top,X_123),one),complement(composition(top,top))),join(complement(composition(top,top)),composition(join(top,X_123),complement(composition(top,top))))) )],[refute_0_1370,refute_0_1373]) ).
cnf(refute_0_1375,plain,
converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A),
inference(subst,[],[refute_0_797:[bind(X_4,$fot(join(one,join(one,join(top,complement(join(one,join(one,top))))))))]]) ).
cnf(refute_0_1376,plain,
top = join(join(one,join(one,top)),converse(complement(converse(join(one,join(one,top)))))),
inference(subst,[],[refute_0_1160:[bind(X_82,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_1377,plain,
converse(join(one,join(one,top))) = join(one,converse(join(one,top))),
inference(subst,[],[refute_0_690:[bind(B,$fot(join(one,top)))]]) ).
cnf(refute_0_1378,plain,
converse(join(one,top)) = join(one,converse(top)),
inference(subst,[],[refute_0_690:[bind(B,$fot(top))]]) ).
cnf(refute_0_1379,plain,
( converse(join(one,top)) != join(one,converse(top))
| converse(top) != top
| converse(join(one,top)) = join(one,top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,top)),join(one,converse(top))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1380,plain,
( converse(join(one,top)) != join(one,converse(top))
| converse(join(one,top)) = join(one,top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1379]) ).
cnf(refute_0_1381,plain,
converse(join(one,top)) = join(one,top),
inference(resolve,[$cnf( $equal(converse(join(one,top)),join(one,converse(top))) )],[refute_0_1378,refute_0_1380]) ).
cnf(refute_0_1382,plain,
( converse(join(one,join(one,top))) != join(one,converse(join(one,top)))
| converse(join(one,top)) != join(one,top)
| converse(join(one,join(one,top))) = join(one,join(one,top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,top))),join(one,converse(join(one,top)))) ),[1,1],$fot(join(one,top))]]) ).
cnf(refute_0_1383,plain,
( converse(join(one,join(one,top))) != join(one,converse(join(one,top)))
| converse(join(one,join(one,top))) = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),join(one,top)) )],[refute_0_1381,refute_0_1382]) ).
cnf(refute_0_1384,plain,
converse(join(one,join(one,top))) = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,top))),join(one,converse(join(one,top)))) )],[refute_0_1377,refute_0_1383]) ).
cnf(refute_0_1385,plain,
( converse(join(one,join(one,top))) != join(one,join(one,top))
| top != join(join(one,join(one,top)),converse(complement(converse(join(one,join(one,top))))))
| top = join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(one,join(one,top)),converse(complement(converse(join(one,join(one,top))))))) ),[1,1,0,0],$fot(join(one,join(one,top)))]]) ).
cnf(refute_0_1386,plain,
( top != join(join(one,join(one,top)),converse(complement(converse(join(one,join(one,top))))))
| top = join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,top))),join(one,join(one,top))) )],[refute_0_1384,refute_0_1385]) ).
cnf(refute_0_1387,plain,
top = join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))),
inference(resolve,[$cnf( $equal(top,join(join(one,join(one,top)),converse(complement(converse(join(one,join(one,top))))))) )],[refute_0_1376,refute_0_1386]) ).
cnf(refute_0_1388,plain,
join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))) = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(one,join(top,complement(join(one,join(one,top)))))))]]) ).
cnf(refute_0_1389,plain,
join(one,converse(join(top,complement(join(one,join(one,top)))))) = converse(join(one,join(top,complement(join(one,join(one,top)))))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(top,complement(join(one,join(one,top))))))]]) ).
cnf(refute_0_1390,plain,
converse(join(converse(top),X_5)) = join(top,converse(X_5)),
inference(subst,[],[refute_0_775:[bind(A,$fot(top))]]) ).
cnf(refute_0_1391,plain,
( converse(join(converse(top),X_5)) != join(top,converse(X_5))
| converse(top) != top
| converse(join(top,X_5)) = join(top,converse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),X_5)),join(top,converse(X_5))) ),[0,0,0],$fot(top)]]) ).
cnf(refute_0_1392,plain,
( converse(join(converse(top),X_5)) != join(top,converse(X_5))
| converse(join(top,X_5)) = join(top,converse(X_5)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1391]) ).
cnf(refute_0_1393,plain,
converse(join(top,X_5)) = join(top,converse(X_5)),
inference(resolve,[$cnf( $equal(converse(join(converse(top),X_5)),join(top,converse(X_5))) )],[refute_0_1390,refute_0_1392]) ).
cnf(refute_0_1394,plain,
( converse(join(top,X_5)) != join(top,converse(X_5))
| join(top,converse(X_5)) = converse(join(top,X_5)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(top,X_5)))),bind(Y,$fot(join(top,converse(X_5))))]]) ).
cnf(refute_0_1395,plain,
join(top,converse(X_5)) = converse(join(top,X_5)),
inference(resolve,[$cnf( $equal(converse(join(top,X_5)),join(top,converse(X_5))) )],[refute_0_1393,refute_0_1394]) ).
cnf(refute_0_1396,plain,
join(top,converse(complement(join(one,join(one,top))))) = converse(join(top,complement(join(one,join(one,top))))),
inference(subst,[],[refute_0_1395:[bind(X_5,$fot(complement(join(one,join(one,top)))))]]) ).
cnf(refute_0_1397,plain,
join(one,join(top,converse(complement(join(one,join(one,top)))))) = join(one,join(top,converse(complement(join(one,join(one,top)))))),
introduced(tautology,[refl,[$fot(join(one,join(top,converse(complement(join(one,join(one,top)))))))]]) ).
cnf(refute_0_1398,plain,
( join(one,join(top,converse(complement(join(one,join(one,top)))))) != join(one,join(top,converse(complement(join(one,join(one,top))))))
| join(top,converse(complement(join(one,join(one,top))))) != converse(join(top,complement(join(one,join(one,top)))))
| join(one,join(top,converse(complement(join(one,join(one,top)))))) = join(one,converse(join(top,complement(join(one,join(one,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(top,converse(complement(join(one,join(one,top)))))),join(one,join(top,converse(complement(join(one,join(one,top))))))) ),[1,1],$fot(converse(join(top,complement(join(one,join(one,top))))))]]) ).
cnf(refute_0_1399,plain,
( join(top,converse(complement(join(one,join(one,top))))) != converse(join(top,complement(join(one,join(one,top)))))
| join(one,join(top,converse(complement(join(one,join(one,top)))))) = join(one,converse(join(top,complement(join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(one,join(top,converse(complement(join(one,join(one,top)))))),join(one,join(top,converse(complement(join(one,join(one,top))))))) )],[refute_0_1397,refute_0_1398]) ).
cnf(refute_0_1400,plain,
join(one,join(top,converse(complement(join(one,join(one,top)))))) = join(one,converse(join(top,complement(join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(join(top,converse(complement(join(one,join(one,top))))),converse(join(top,complement(join(one,join(one,top)))))) )],[refute_0_1396,refute_0_1399]) ).
cnf(refute_0_1401,plain,
( join(one,converse(join(top,complement(join(one,join(one,top)))))) != converse(join(one,join(top,complement(join(one,join(one,top))))))
| join(one,join(top,converse(complement(join(one,join(one,top)))))) != join(one,converse(join(top,complement(join(one,join(one,top))))))
| join(one,join(top,converse(complement(join(one,join(one,top)))))) = converse(join(one,join(top,complement(join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(top,converse(complement(join(one,join(one,top)))))))),bind(Y,$fot(join(one,converse(join(top,complement(join(one,join(one,top)))))))),bind(Z,$fot(converse(join(one,join(top,complement(join(one,join(one,top))))))))]]) ).
cnf(refute_0_1402,plain,
( join(one,converse(join(top,complement(join(one,join(one,top)))))) != converse(join(one,join(top,complement(join(one,join(one,top))))))
| join(one,join(top,converse(complement(join(one,join(one,top)))))) = converse(join(one,join(top,complement(join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(one,join(top,converse(complement(join(one,join(one,top)))))),join(one,converse(join(top,complement(join(one,join(one,top))))))) )],[refute_0_1400,refute_0_1401]) ).
cnf(refute_0_1403,plain,
join(one,join(top,converse(complement(join(one,join(one,top)))))) = converse(join(one,join(top,complement(join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(top,complement(join(one,join(one,top)))))),converse(join(one,join(top,complement(join(one,join(one,top))))))) )],[refute_0_1389,refute_0_1402]) ).
cnf(refute_0_1404,plain,
join(join(one,top),converse(complement(join(one,join(one,top))))) = join(one,join(top,converse(complement(join(one,join(one,top)))))),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(top)),bind(C,$fot(converse(complement(join(one,join(one,top))))))]]) ).
cnf(refute_0_1405,plain,
( join(join(one,top),converse(complement(join(one,join(one,top))))) != join(one,join(top,converse(complement(join(one,join(one,top))))))
| join(one,join(top,converse(complement(join(one,join(one,top)))))) != converse(join(one,join(top,complement(join(one,join(one,top))))))
| join(join(one,top),converse(complement(join(one,join(one,top))))) = converse(join(one,join(top,complement(join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,top),converse(complement(join(one,join(one,top))))))),bind(Y,$fot(join(one,join(top,converse(complement(join(one,join(one,top)))))))),bind(Z,$fot(converse(join(one,join(top,complement(join(one,join(one,top))))))))]]) ).
cnf(refute_0_1406,plain,
( join(one,join(top,converse(complement(join(one,join(one,top)))))) != converse(join(one,join(top,complement(join(one,join(one,top))))))
| join(join(one,top),converse(complement(join(one,join(one,top))))) = converse(join(one,join(top,complement(join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(join(one,top),converse(complement(join(one,join(one,top))))),join(one,join(top,converse(complement(join(one,join(one,top))))))) )],[refute_0_1404,refute_0_1405]) ).
cnf(refute_0_1407,plain,
join(join(one,top),converse(complement(join(one,join(one,top))))) = converse(join(one,join(top,complement(join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(join(one,join(top,converse(complement(join(one,join(one,top)))))),converse(join(one,join(top,complement(join(one,join(one,top))))))) )],[refute_0_1403,refute_0_1406]) ).
cnf(refute_0_1408,plain,
join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) = join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))),
introduced(tautology,[refl,[$fot(join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))))]]) ).
cnf(refute_0_1409,plain,
( join(join(one,top),converse(complement(join(one,join(one,top))))) != converse(join(one,join(top,complement(join(one,join(one,top))))))
| join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) != join(one,join(join(one,top),converse(complement(join(one,join(one,top))))))
| join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) = join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))),join(one,join(join(one,top),converse(complement(join(one,join(one,top))))))) ),[1,1],$fot(converse(join(one,join(top,complement(join(one,join(one,top)))))))]]) ).
cnf(refute_0_1410,plain,
( join(join(one,top),converse(complement(join(one,join(one,top))))) != converse(join(one,join(top,complement(join(one,join(one,top))))))
| join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) = join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))),join(one,join(join(one,top),converse(complement(join(one,join(one,top))))))) )],[refute_0_1408,refute_0_1409]) ).
cnf(refute_0_1411,plain,
join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) = join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))),
inference(resolve,[$cnf( $equal(join(join(one,top),converse(complement(join(one,join(one,top))))),converse(join(one,join(top,complement(join(one,join(one,top))))))) )],[refute_0_1407,refute_0_1410]) ).
cnf(refute_0_1412,plain,
( join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))) != converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))
| join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) != join(one,converse(join(one,join(top,complement(join(one,join(one,top)))))))
| join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))))),bind(Y,$fot(join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))))),bind(Z,$fot(converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))))]]) ).
cnf(refute_0_1413,plain,
( join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))) != converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))
| join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))),join(one,converse(join(one,join(top,complement(join(one,join(one,top)))))))) )],[refute_0_1411,refute_0_1412]) ).
cnf(refute_0_1414,plain,
join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(top,complement(join(one,join(one,top))))))),converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))) )],[refute_0_1388,refute_0_1413]) ).
cnf(refute_0_1415,plain,
join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) = join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(join(one,top))),bind(C,$fot(converse(complement(join(one,join(one,top))))))]]) ).
cnf(refute_0_1416,plain,
( join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) != join(one,join(join(one,top),converse(complement(join(one,join(one,top))))))
| join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) != converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))
| join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))))),bind(Y,$fot(join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))))),bind(Z,$fot(converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))))]]) ).
cnf(refute_0_1417,plain,
( join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))) != converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))
| join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))),join(one,join(join(one,top),converse(complement(join(one,join(one,top))))))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),
inference(resolve,[$cnf( $equal(join(one,join(join(one,top),converse(complement(join(one,join(one,top)))))),converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))) )],[refute_0_1414,refute_0_1417]) ).
cnf(refute_0_1419,plain,
( join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))) != converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))
| top != join(join(one,join(one,top)),converse(complement(join(one,join(one,top)))))
| top = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(one,join(one,top)),converse(complement(join(one,join(one,top)))))) ),[1],$fot(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))))]]) ).
cnf(refute_0_1420,plain,
( top != join(join(one,join(one,top)),converse(complement(join(one,join(one,top)))))
| top = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,top)),converse(complement(join(one,join(one,top))))),converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))) )],[refute_0_1418,refute_0_1419]) ).
cnf(refute_0_1421,plain,
top = converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),
inference(resolve,[$cnf( $equal(top,join(join(one,join(one,top)),converse(complement(join(one,join(one,top)))))) )],[refute_0_1387,refute_0_1420]) ).
cnf(refute_0_1422,plain,
( top != converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))
| converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))))]]) ).
cnf(refute_0_1423,plain,
converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) = top,
inference(resolve,[$cnf( $equal(top,converse(join(one,join(one,join(top,complement(join(one,join(one,top)))))))) )],[refute_0_1421,refute_0_1422]) ).
cnf(refute_0_1424,plain,
( converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) != join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A)
| converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))) != top
| converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))),join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1425,plain,
( converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) != join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A)
| converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(top,A) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),top) )],[refute_0_1423,refute_0_1424]) ).
cnf(refute_0_1426,plain,
converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(top,A),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))),join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A)) )],[refute_0_1375,refute_0_1425]) ).
cnf(refute_0_1427,plain,
join(one,join(converse(X_28),C)) = join(join(one,converse(X_28)),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(one)),bind(B,$fot(converse(X_28)))]]) ).
cnf(refute_0_1428,plain,
converse(join(one,X_28)) = join(one,converse(X_28)),
inference(subst,[],[refute_0_690:[bind(B,$fot(X_28))]]) ).
cnf(refute_0_1429,plain,
( converse(join(one,X_28)) != join(one,converse(X_28))
| join(one,converse(X_28)) = converse(join(one,X_28)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(one,X_28)))),bind(Y,$fot(join(one,converse(X_28))))]]) ).
cnf(refute_0_1430,plain,
join(one,converse(X_28)) = converse(join(one,X_28)),
inference(resolve,[$cnf( $equal(converse(join(one,X_28)),join(one,converse(X_28))) )],[refute_0_1428,refute_0_1429]) ).
cnf(refute_0_1431,plain,
( join(one,converse(X_28)) != converse(join(one,X_28))
| join(one,join(converse(X_28),C)) != join(join(one,converse(X_28)),C)
| join(one,join(converse(X_28),C)) = join(converse(join(one,X_28)),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(X_28),C)),join(join(one,converse(X_28)),C)) ),[1,0],$fot(converse(join(one,X_28)))]]) ).
cnf(refute_0_1432,plain,
( join(one,join(converse(X_28),C)) != join(join(one,converse(X_28)),C)
| join(one,join(converse(X_28),C)) = join(converse(join(one,X_28)),C) ),
inference(resolve,[$cnf( $equal(join(one,converse(X_28)),converse(join(one,X_28))) )],[refute_0_1430,refute_0_1431]) ).
cnf(refute_0_1433,plain,
join(one,join(converse(X_28),C)) = join(converse(join(one,X_28)),C),
inference(resolve,[$cnf( $equal(join(one,join(converse(X_28),C)),join(join(one,converse(X_28)),C)) )],[refute_0_1427,refute_0_1432]) ).
cnf(refute_0_1434,plain,
( join(one,join(converse(X_28),C)) != join(converse(join(one,X_28)),C)
| join(converse(join(one,X_28)),C) = join(one,join(converse(X_28),C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(converse(X_28),C)))),bind(Y,$fot(join(converse(join(one,X_28)),C)))]]) ).
cnf(refute_0_1435,plain,
join(converse(join(one,X_28)),C) = join(one,join(converse(X_28),C)),
inference(resolve,[$cnf( $equal(join(one,join(converse(X_28),C)),join(converse(join(one,X_28)),C)) )],[refute_0_1433,refute_0_1434]) ).
cnf(refute_0_1436,plain,
join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A) = join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)),
inference(subst,[],[refute_0_1435:[bind(C,$fot(A)),bind(X_28,$fot(join(top,complement(join(one,join(one,top))))))]]) ).
cnf(refute_0_1437,plain,
join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) = join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)),
introduced(tautology,[refl,[$fot(join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)))]]) ).
cnf(refute_0_1438,plain,
( join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A) != join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))
| join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) != join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))
| join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) = join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)),join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))) ),[1,1],$fot(join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))]]) ).
cnf(refute_0_1439,plain,
( join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A) != join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))
| join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) = join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) ),
inference(resolve,[$cnf( $equal(join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)),join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))) )],[refute_0_1437,refute_0_1438]) ).
cnf(refute_0_1440,plain,
join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) = join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),
inference(resolve,[$cnf( $equal(join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A),join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) )],[refute_0_1436,refute_0_1439]) ).
cnf(refute_0_1441,plain,
join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A) = join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)),
inference(subst,[],[refute_0_1435:[bind(C,$fot(A)),bind(X_28,$fot(join(one,join(top,complement(join(one,join(one,top)))))))]]) ).
cnf(refute_0_1442,plain,
( converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) != join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A)
| join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A) != join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))
| converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))))),bind(Y,$fot(join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A))),bind(Z,$fot(join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))))]]) ).
cnf(refute_0_1443,plain,
( join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A) != join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))
| converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) ),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))),join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A)) )],[refute_0_1375,refute_0_1442]) ).
cnf(refute_0_1444,plain,
converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)),
inference(resolve,[$cnf( $equal(join(converse(join(one,join(one,join(top,complement(join(one,join(one,top))))))),A),join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))) )],[refute_0_1441,refute_0_1443]) ).
cnf(refute_0_1445,plain,
( converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) != join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))
| join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) != join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))
| converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))))),bind(Y,$fot(join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)))),bind(Z,$fot(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))))]]) ).
cnf(refute_0_1446,plain,
( join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)) != join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))
| converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) ),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))),join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A))) )],[refute_0_1444,refute_0_1445]) ).
cnf(refute_0_1447,plain,
converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) = join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),
inference(resolve,[$cnf( $equal(join(one,join(converse(join(one,join(top,complement(join(one,join(one,top)))))),A)),join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))) )],[refute_0_1440,refute_0_1446]) ).
cnf(refute_0_1448,plain,
( converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) != join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))
| converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) != join(top,A)
| join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) = join(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))),join(top,A)) ),[0],$fot(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))))]]) ).
cnf(refute_0_1449,plain,
( converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))) != join(top,A)
| join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) = join(top,A) ),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))),join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))) )],[refute_0_1447,refute_0_1448]) ).
cnf(refute_0_1450,plain,
join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) = join(top,A),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,join(top,complement(join(one,join(one,top)))))),converse(A))),join(top,A)) )],[refute_0_1426,refute_0_1449]) ).
cnf(refute_0_1451,plain,
join(top,complement(join(one,join(one,top)))) = complement(meet(zero,join(one,join(one,top)))),
inference(subst,[],[refute_0_655:[bind(X_79,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_1452,plain,
converse(join(top,complement(join(one,join(one,top))))) = converse(join(top,complement(join(one,join(one,top))))),
introduced(tautology,[refl,[$fot(converse(join(top,complement(join(one,join(one,top))))))]]) ).
cnf(refute_0_1453,plain,
( converse(join(top,complement(join(one,join(one,top))))) != converse(join(top,complement(join(one,join(one,top)))))
| join(top,complement(join(one,join(one,top)))) != complement(meet(zero,join(one,join(one,top))))
| converse(join(top,complement(join(one,join(one,top))))) = converse(complement(meet(zero,join(one,join(one,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,complement(join(one,join(one,top))))),converse(join(top,complement(join(one,join(one,top)))))) ),[1,0],$fot(complement(meet(zero,join(one,join(one,top)))))]]) ).
cnf(refute_0_1454,plain,
( join(top,complement(join(one,join(one,top)))) != complement(meet(zero,join(one,join(one,top))))
| converse(join(top,complement(join(one,join(one,top))))) = converse(complement(meet(zero,join(one,join(one,top))))) ),
inference(resolve,[$cnf( $equal(converse(join(top,complement(join(one,join(one,top))))),converse(join(top,complement(join(one,join(one,top)))))) )],[refute_0_1452,refute_0_1453]) ).
cnf(refute_0_1455,plain,
converse(join(top,complement(join(one,join(one,top))))) = converse(complement(meet(zero,join(one,join(one,top))))),
inference(resolve,[$cnf( $equal(join(top,complement(join(one,join(one,top)))),complement(meet(zero,join(one,join(one,top))))) )],[refute_0_1451,refute_0_1454]) ).
cnf(refute_0_1456,plain,
join(converse(join(top,complement(join(one,join(one,top))))),A) = join(converse(join(top,complement(join(one,join(one,top))))),A),
introduced(tautology,[refl,[$fot(join(converse(join(top,complement(join(one,join(one,top))))),A))]]) ).
cnf(refute_0_1457,plain,
( converse(join(top,complement(join(one,join(one,top))))) != converse(complement(meet(zero,join(one,join(one,top)))))
| join(converse(join(top,complement(join(one,join(one,top))))),A) != join(converse(join(top,complement(join(one,join(one,top))))),A)
| join(converse(join(top,complement(join(one,join(one,top))))),A) = join(converse(complement(meet(zero,join(one,join(one,top))))),A) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(join(top,complement(join(one,join(one,top))))),A),join(converse(join(top,complement(join(one,join(one,top))))),A)) ),[1,0],$fot(converse(complement(meet(zero,join(one,join(one,top))))))]]) ).
cnf(refute_0_1458,plain,
( converse(join(top,complement(join(one,join(one,top))))) != converse(complement(meet(zero,join(one,join(one,top)))))
| join(converse(join(top,complement(join(one,join(one,top))))),A) = join(converse(complement(meet(zero,join(one,join(one,top))))),A) ),
inference(resolve,[$cnf( $equal(join(converse(join(top,complement(join(one,join(one,top))))),A),join(converse(join(top,complement(join(one,join(one,top))))),A)) )],[refute_0_1456,refute_0_1457]) ).
cnf(refute_0_1459,plain,
join(converse(join(top,complement(join(one,join(one,top))))),A) = join(converse(complement(meet(zero,join(one,join(one,top))))),A),
inference(resolve,[$cnf( $equal(converse(join(top,complement(join(one,join(one,top))))),converse(complement(meet(zero,join(one,join(one,top)))))) )],[refute_0_1455,refute_0_1458]) ).
cnf(refute_0_1460,plain,
join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)) = join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)),
introduced(tautology,[refl,[$fot(join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))]]) ).
cnf(refute_0_1461,plain,
( join(converse(join(top,complement(join(one,join(one,top))))),A) != join(converse(complement(meet(zero,join(one,join(one,top))))),A)
| join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)) != join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))
| join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)) = join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)),join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) ),[1,1],$fot(join(converse(complement(meet(zero,join(one,join(one,top))))),A))]]) ).
cnf(refute_0_1462,plain,
( join(converse(join(top,complement(join(one,join(one,top))))),A) != join(converse(complement(meet(zero,join(one,join(one,top))))),A)
| join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)) = join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) ),
inference(resolve,[$cnf( $equal(join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)),join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)) = join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)),
inference(resolve,[$cnf( $equal(join(converse(join(top,complement(join(one,join(one,top))))),A),join(converse(complement(meet(zero,join(one,join(one,top))))),A)) )],[refute_0_1459,refute_0_1462]) ).
cnf(refute_0_1464,plain,
join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) = join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))))]]) ).
cnf(refute_0_1465,plain,
( join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)) != join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))
| join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) != join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))
| join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) = join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))) ),[1,1],$fot(join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)))]]) ).
cnf(refute_0_1466,plain,
( join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)) != join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))
| join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) = join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)))) )],[refute_0_1464,refute_0_1465]) ).
cnf(refute_0_1467,plain,
join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) = join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))),
inference(resolve,[$cnf( $equal(join(one,join(converse(join(top,complement(join(one,join(one,top))))),A)),join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) )],[refute_0_1463,refute_0_1466]) ).
cnf(refute_0_1468,plain,
( join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) != join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)))
| join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) != join(top,A)
| join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) = join(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),join(top,A)) ),[0],$fot(join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))))]]) ).
cnf(refute_0_1469,plain,
( join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))) != join(top,A)
| join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) = join(top,A) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)))) )],[refute_0_1467,refute_0_1468]) ).
cnf(refute_0_1470,plain,
join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) = join(top,A),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(join(top,complement(join(one,join(one,top))))),A))),join(top,A)) )],[refute_0_1450,refute_0_1469]) ).
cnf(refute_0_1471,plain,
meet(top,zero) = zero,
inference(subst,[],[refute_0_429:[bind(B,$fot(zero))]]) ).
cnf(refute_0_1472,plain,
meet(A,join(zero,zero)) = complement(join(complement(A),complement(join(zero,zero)))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(zero,zero)))]]) ).
cnf(refute_0_1473,plain,
meet(top,top) = complement(join(zero,complement(top))),
inference(subst,[],[refute_0_130:[bind(B,$fot(top))]]) ).
cnf(refute_0_1474,plain,
( complement(top) != zero
| meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_1475,plain,
( meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_1474]) ).
cnf(refute_0_1476,plain,
meet(top,top) = complement(join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) )],[refute_0_1473,refute_0_1475]) ).
cnf(refute_0_1477,plain,
meet(top,complement(zero)) = meet(top,complement(zero)),
introduced(tautology,[refl,[$fot(meet(top,complement(zero)))]]) ).
cnf(refute_0_1478,plain,
( complement(zero) != top
| meet(top,complement(zero)) != meet(top,complement(zero))
| meet(top,complement(zero)) = meet(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(zero)),meet(top,complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1479,plain,
( complement(zero) != top
| meet(top,complement(zero)) = meet(top,top) ),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),meet(top,complement(zero))) )],[refute_0_1477,refute_0_1478]) ).
cnf(refute_0_1480,plain,
meet(top,complement(zero)) = meet(top,top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_1479]) ).
cnf(refute_0_1481,plain,
( meet(top,complement(zero)) != meet(top,top)
| top != meet(top,complement(zero))
| top = meet(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,meet(top,complement(zero))) ),[1],$fot(meet(top,top))]]) ).
cnf(refute_0_1482,plain,
( top != meet(top,complement(zero))
| top = meet(top,top) ),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),meet(top,top)) )],[refute_0_1480,refute_0_1481]) ).
cnf(refute_0_1483,plain,
top = meet(top,top),
inference(resolve,[$cnf( $equal(top,meet(top,complement(zero))) )],[refute_0_598,refute_0_1482]) ).
cnf(refute_0_1484,plain,
( top != meet(top,top)
| meet(top,top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(meet(top,top)))]]) ).
cnf(refute_0_1485,plain,
meet(top,top) = top,
inference(resolve,[$cnf( $equal(top,meet(top,top)) )],[refute_0_1483,refute_0_1484]) ).
cnf(refute_0_1486,plain,
( meet(top,top) != complement(join(zero,zero))
| meet(top,top) != top
| top = complement(join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) ),[0],$fot(top)]]) ).
cnf(refute_0_1487,plain,
( meet(top,top) != complement(join(zero,zero))
| top = complement(join(zero,zero)) ),
inference(resolve,[$cnf( $equal(meet(top,top),top) )],[refute_0_1485,refute_0_1486]) ).
cnf(refute_0_1488,plain,
top = complement(join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) )],[refute_0_1476,refute_0_1487]) ).
cnf(refute_0_1489,plain,
( top != complement(join(zero,zero))
| complement(join(zero,zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(complement(join(zero,zero))))]]) ).
cnf(refute_0_1490,plain,
complement(join(zero,zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(join(zero,zero))) )],[refute_0_1488,refute_0_1489]) ).
cnf(refute_0_1491,plain,
( complement(join(zero,zero)) != top
| meet(A,join(zero,zero)) != complement(join(complement(A),complement(join(zero,zero))))
| meet(A,join(zero,zero)) = complement(join(complement(A),top)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,zero)),complement(join(complement(A),complement(join(zero,zero))))) ),[1,0,1],$fot(top)]]) ).
cnf(refute_0_1492,plain,
( meet(A,join(zero,zero)) != complement(join(complement(A),complement(join(zero,zero))))
| meet(A,join(zero,zero)) = complement(join(complement(A),top)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),top) )],[refute_0_1490,refute_0_1491]) ).
cnf(refute_0_1493,plain,
meet(A,join(zero,zero)) = complement(join(complement(A),top)),
inference(resolve,[$cnf( $equal(meet(A,join(zero,zero)),complement(join(complement(A),complement(join(zero,zero))))) )],[refute_0_1472,refute_0_1492]) ).
cnf(refute_0_1494,plain,
( meet(zero,B) != complement(join(top,complement(B)))
| complement(join(top,complement(B))) = meet(zero,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(zero,B))),bind(Y,$fot(complement(join(top,complement(B)))))]]) ).
cnf(refute_0_1495,plain,
complement(join(top,complement(B))) = meet(zero,B),
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(top,complement(B)))) )],[refute_0_621,refute_0_1494]) ).
cnf(refute_0_1496,plain,
complement(join(top,complement(A))) = meet(zero,A),
inference(subst,[],[refute_0_1495:[bind(B,$fot(A))]]) ).
cnf(refute_0_1497,plain,
join(complement(A),top) = join(top,complement(A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(A)))]]) ).
cnf(refute_0_1498,plain,
complement(join(complement(A),top)) = complement(join(complement(A),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),top)))]]) ).
cnf(refute_0_1499,plain,
( complement(join(complement(A),top)) != complement(join(complement(A),top))
| join(complement(A),top) != join(top,complement(A))
| complement(join(complement(A),top)) = complement(join(top,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),top)),complement(join(complement(A),top))) ),[1,0],$fot(join(top,complement(A)))]]) ).
cnf(refute_0_1500,plain,
( join(complement(A),top) != join(top,complement(A))
| complement(join(complement(A),top)) = complement(join(top,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),complement(join(complement(A),top))) )],[refute_0_1498,refute_0_1499]) ).
cnf(refute_0_1501,plain,
complement(join(complement(A),top)) = complement(join(top,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),top),join(top,complement(A))) )],[refute_0_1497,refute_0_1500]) ).
cnf(refute_0_1502,plain,
( complement(join(complement(A),top)) != complement(join(top,complement(A)))
| complement(join(top,complement(A))) != meet(zero,A)
| complement(join(complement(A),top)) = meet(zero,A) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(join(complement(A),top)))),bind(Y,$fot(complement(join(top,complement(A))))),bind(Z,$fot(meet(zero,A)))]]) ).
cnf(refute_0_1503,plain,
( complement(join(top,complement(A))) != meet(zero,A)
| complement(join(complement(A),top)) = meet(zero,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),complement(join(top,complement(A)))) )],[refute_0_1501,refute_0_1502]) ).
cnf(refute_0_1504,plain,
complement(join(complement(A),top)) = meet(zero,A),
inference(resolve,[$cnf( $equal(complement(join(top,complement(A))),meet(zero,A)) )],[refute_0_1496,refute_0_1503]) ).
cnf(refute_0_1505,plain,
( complement(join(complement(A),top)) != meet(zero,A)
| meet(A,join(zero,zero)) != complement(join(complement(A),top))
| meet(A,join(zero,zero)) = meet(zero,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,zero)),complement(join(complement(A),top))) ),[1],$fot(meet(zero,A))]]) ).
cnf(refute_0_1506,plain,
( meet(A,join(zero,zero)) != complement(join(complement(A),top))
| meet(A,join(zero,zero)) = meet(zero,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),meet(zero,A)) )],[refute_0_1504,refute_0_1505]) ).
cnf(refute_0_1507,plain,
meet(A,join(zero,zero)) = meet(zero,A),
inference(resolve,[$cnf( $equal(meet(A,join(zero,zero)),complement(join(complement(A),top))) )],[refute_0_1493,refute_0_1506]) ).
cnf(refute_0_1508,plain,
join(zero,zero) = join(meet(join(zero,zero),B),complement(join(complement(join(zero,zero)),B))),
inference(subst,[],[refute_0_38:[bind(A,$fot(join(zero,zero)))]]) ).
cnf(refute_0_1509,plain,
( complement(join(zero,zero)) != top
| join(zero,zero) != join(meet(join(zero,zero),B),complement(join(complement(join(zero,zero)),B)))
| join(zero,zero) = join(meet(join(zero,zero),B),complement(join(top,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),join(meet(join(zero,zero),B),complement(join(complement(join(zero,zero)),B)))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_1510,plain,
( join(zero,zero) != join(meet(join(zero,zero),B),complement(join(complement(join(zero,zero)),B)))
| join(zero,zero) = join(meet(join(zero,zero),B),complement(join(top,B))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),top) )],[refute_0_1490,refute_0_1509]) ).
cnf(refute_0_1511,plain,
join(zero,zero) = join(meet(join(zero,zero),B),complement(join(top,B))),
inference(resolve,[$cnf( $equal(join(zero,zero),join(meet(join(zero,zero),B),complement(join(complement(join(zero,zero)),B)))) )],[refute_0_1508,refute_0_1510]) ).
cnf(refute_0_1512,plain,
zero = join(meet(zero,B),complement(join(complement(zero),B))),
inference(subst,[],[refute_0_38:[bind(A,$fot(zero))]]) ).
cnf(refute_0_1513,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_1514,plain,
( zero != join(meet(zero,B),complement(join(complement(zero),B)))
| zero = join(meet(zero,B),complement(join(top,B))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_1513]) ).
cnf(refute_0_1515,plain,
zero = join(meet(zero,B),complement(join(top,B))),
inference(resolve,[$cnf( $equal(zero,join(meet(zero,B),complement(join(complement(zero),B)))) )],[refute_0_1512,refute_0_1514]) ).
cnf(refute_0_1516,plain,
( zero != join(meet(zero,B),complement(join(top,B)))
| join(meet(zero,B),complement(join(top,B))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(join(meet(zero,B),complement(join(top,B)))))]]) ).
cnf(refute_0_1517,plain,
join(meet(zero,B),complement(join(top,B))) = zero,
inference(resolve,[$cnf( $equal(zero,join(meet(zero,B),complement(join(top,B)))) )],[refute_0_1515,refute_0_1516]) ).
cnf(refute_0_1518,plain,
join(complement(join(top,B)),meet(zero,B)) = join(meet(zero,B),complement(join(top,B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(zero,B))),bind(B,$fot(complement(join(top,B))))]]) ).
cnf(refute_0_1519,plain,
( join(complement(join(top,B)),meet(zero,B)) != join(meet(zero,B),complement(join(top,B)))
| join(meet(zero,B),complement(join(top,B))) != zero
| join(complement(join(top,B)),meet(zero,B)) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(top,B)),meet(zero,B)))),bind(Y,$fot(join(meet(zero,B),complement(join(top,B))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1520,plain,
( join(meet(zero,B),complement(join(top,B))) != zero
| join(complement(join(top,B)),meet(zero,B)) = zero ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(zero,B)),join(meet(zero,B),complement(join(top,B)))) )],[refute_0_1518,refute_0_1519]) ).
cnf(refute_0_1521,plain,
join(complement(join(top,B)),meet(zero,B)) = zero,
inference(resolve,[$cnf( $equal(join(meet(zero,B),complement(join(top,B))),zero) )],[refute_0_1517,refute_0_1520]) ).
cnf(refute_0_1522,plain,
meet(join(zero,zero),B) = complement(join(complement(join(zero,zero)),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(zero,zero)))]]) ).
cnf(refute_0_1523,plain,
( complement(join(zero,zero)) != top
| meet(join(zero,zero),B) != complement(join(complement(join(zero,zero)),complement(B)))
| meet(join(zero,zero),B) = complement(join(top,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,zero),B),complement(join(complement(join(zero,zero)),complement(B)))) ),[1,0,0],$fot(top)]]) ).
cnf(refute_0_1524,plain,
( meet(join(zero,zero),B) != complement(join(complement(join(zero,zero)),complement(B)))
| meet(join(zero,zero),B) = complement(join(top,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),top) )],[refute_0_1490,refute_0_1523]) ).
cnf(refute_0_1525,plain,
meet(join(zero,zero),B) = complement(join(top,complement(B))),
inference(resolve,[$cnf( $equal(meet(join(zero,zero),B),complement(join(complement(join(zero,zero)),complement(B)))) )],[refute_0_1522,refute_0_1524]) ).
cnf(refute_0_1526,plain,
( complement(join(top,complement(B))) != meet(zero,B)
| meet(join(zero,zero),B) != complement(join(top,complement(B)))
| meet(join(zero,zero),B) = meet(zero,B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,zero),B),complement(join(top,complement(B)))) ),[1],$fot(meet(zero,B))]]) ).
cnf(refute_0_1527,plain,
( meet(join(zero,zero),B) != complement(join(top,complement(B)))
| meet(join(zero,zero),B) = meet(zero,B) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),meet(zero,B)) )],[refute_0_1495,refute_0_1526]) ).
cnf(refute_0_1528,plain,
meet(join(zero,zero),B) = meet(zero,B),
inference(resolve,[$cnf( $equal(meet(join(zero,zero),B),complement(join(top,complement(B)))) )],[refute_0_1525,refute_0_1527]) ).
cnf(refute_0_1529,plain,
join(complement(join(top,B)),meet(join(zero,zero),B)) = join(complement(join(top,B)),meet(join(zero,zero),B)),
introduced(tautology,[refl,[$fot(join(complement(join(top,B)),meet(join(zero,zero),B)))]]) ).
cnf(refute_0_1530,plain,
( join(complement(join(top,B)),meet(join(zero,zero),B)) != join(complement(join(top,B)),meet(join(zero,zero),B))
| meet(join(zero,zero),B) != meet(zero,B)
| join(complement(join(top,B)),meet(join(zero,zero),B)) = join(complement(join(top,B)),meet(zero,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(top,B)),meet(join(zero,zero),B)),join(complement(join(top,B)),meet(join(zero,zero),B))) ),[1,1],$fot(meet(zero,B))]]) ).
cnf(refute_0_1531,plain,
( meet(join(zero,zero),B) != meet(zero,B)
| join(complement(join(top,B)),meet(join(zero,zero),B)) = join(complement(join(top,B)),meet(zero,B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(join(zero,zero),B)),join(complement(join(top,B)),meet(join(zero,zero),B))) )],[refute_0_1529,refute_0_1530]) ).
cnf(refute_0_1532,plain,
join(complement(join(top,B)),meet(join(zero,zero),B)) = join(complement(join(top,B)),meet(zero,B)),
inference(resolve,[$cnf( $equal(meet(join(zero,zero),B),meet(zero,B)) )],[refute_0_1528,refute_0_1531]) ).
cnf(refute_0_1533,plain,
( join(complement(join(top,B)),meet(join(zero,zero),B)) != join(complement(join(top,B)),meet(zero,B))
| join(complement(join(top,B)),meet(zero,B)) != zero
| join(complement(join(top,B)),meet(join(zero,zero),B)) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(top,B)),meet(join(zero,zero),B)))),bind(Y,$fot(join(complement(join(top,B)),meet(zero,B)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1534,plain,
( join(complement(join(top,B)),meet(zero,B)) != zero
| join(complement(join(top,B)),meet(join(zero,zero),B)) = zero ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(join(zero,zero),B)),join(complement(join(top,B)),meet(zero,B))) )],[refute_0_1532,refute_0_1533]) ).
cnf(refute_0_1535,plain,
join(complement(join(top,B)),meet(join(zero,zero),B)) = zero,
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(zero,B)),zero) )],[refute_0_1521,refute_0_1534]) ).
cnf(refute_0_1536,plain,
join(meet(join(zero,zero),B),complement(join(top,B))) = join(complement(join(top,B)),meet(join(zero,zero),B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(top,B)))),bind(B,$fot(meet(join(zero,zero),B)))]]) ).
cnf(refute_0_1537,plain,
( join(complement(join(top,B)),meet(join(zero,zero),B)) != zero
| join(meet(join(zero,zero),B),complement(join(top,B))) != join(complement(join(top,B)),meet(join(zero,zero),B))
| join(meet(join(zero,zero),B),complement(join(top,B))) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(join(zero,zero),B),complement(join(top,B))))),bind(Y,$fot(join(complement(join(top,B)),meet(join(zero,zero),B)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1538,plain,
( join(complement(join(top,B)),meet(join(zero,zero),B)) != zero
| join(meet(join(zero,zero),B),complement(join(top,B))) = zero ),
inference(resolve,[$cnf( $equal(join(meet(join(zero,zero),B),complement(join(top,B))),join(complement(join(top,B)),meet(join(zero,zero),B))) )],[refute_0_1536,refute_0_1537]) ).
cnf(refute_0_1539,plain,
join(meet(join(zero,zero),B),complement(join(top,B))) = zero,
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(join(zero,zero),B)),zero) )],[refute_0_1535,refute_0_1538]) ).
cnf(refute_0_1540,plain,
( join(meet(join(zero,zero),B),complement(join(top,B))) != zero
| join(zero,zero) != join(meet(join(zero,zero),B),complement(join(top,B)))
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),join(meet(join(zero,zero),B),complement(join(top,B)))) ),[1],$fot(zero)]]) ).
cnf(refute_0_1541,plain,
( join(zero,zero) != join(meet(join(zero,zero),B),complement(join(top,B)))
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(meet(join(zero,zero),B),complement(join(top,B))),zero) )],[refute_0_1539,refute_0_1540]) ).
cnf(refute_0_1542,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(zero,zero),join(meet(join(zero,zero),B),complement(join(top,B)))) )],[refute_0_1511,refute_0_1541]) ).
cnf(refute_0_1543,plain,
meet(A,join(zero,zero)) = meet(A,join(zero,zero)),
introduced(tautology,[refl,[$fot(meet(A,join(zero,zero)))]]) ).
cnf(refute_0_1544,plain,
( join(zero,zero) != zero
| meet(A,join(zero,zero)) != meet(A,join(zero,zero))
| meet(A,join(zero,zero)) = meet(A,zero) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,zero)),meet(A,join(zero,zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1545,plain,
( join(zero,zero) != zero
| meet(A,join(zero,zero)) = meet(A,zero) ),
inference(resolve,[$cnf( $equal(meet(A,join(zero,zero)),meet(A,join(zero,zero))) )],[refute_0_1543,refute_0_1544]) ).
cnf(refute_0_1546,plain,
meet(A,join(zero,zero)) = meet(A,zero),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_1542,refute_0_1545]) ).
cnf(refute_0_1547,plain,
( meet(A,join(zero,zero)) != meet(A,zero)
| meet(A,join(zero,zero)) != meet(zero,A)
| meet(A,zero) = meet(zero,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,zero)),meet(zero,A)) ),[0],$fot(meet(A,zero))]]) ).
cnf(refute_0_1548,plain,
( meet(A,join(zero,zero)) != meet(zero,A)
| meet(A,zero) = meet(zero,A) ),
inference(resolve,[$cnf( $equal(meet(A,join(zero,zero)),meet(A,zero)) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
meet(A,zero) = meet(zero,A),
inference(resolve,[$cnf( $equal(meet(A,join(zero,zero)),meet(zero,A)) )],[refute_0_1507,refute_0_1548]) ).
cnf(refute_0_1550,plain,
( meet(A,zero) != meet(zero,A)
| meet(zero,A) = meet(A,zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,zero))),bind(Y,$fot(meet(zero,A)))]]) ).
cnf(refute_0_1551,plain,
meet(zero,A) = meet(A,zero),
inference(resolve,[$cnf( $equal(meet(A,zero),meet(zero,A)) )],[refute_0_1549,refute_0_1550]) ).
cnf(refute_0_1552,plain,
meet(zero,top) = meet(top,zero),
inference(subst,[],[refute_0_1551:[bind(A,$fot(top))]]) ).
cnf(refute_0_1553,plain,
( meet(top,zero) != zero
| meet(zero,top) != meet(top,zero)
| meet(zero,top) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(zero,top))),bind(Y,$fot(meet(top,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1554,plain,
( meet(top,zero) != zero
| meet(zero,top) = zero ),
inference(resolve,[$cnf( $equal(meet(zero,top),meet(top,zero)) )],[refute_0_1552,refute_0_1553]) ).
cnf(refute_0_1555,plain,
meet(zero,top) = zero,
inference(resolve,[$cnf( $equal(meet(top,zero),zero) )],[refute_0_1471,refute_0_1554]) ).
cnf(refute_0_1556,plain,
converse(top) = join(join(one,join(one,one)),converse(complement(converse(join(one,join(one,one)))))),
inference(subst,[],[refute_0_1093:[bind(X_82,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1557,plain,
( converse(join(one,join(one,one))) != join(one,join(one,one))
| converse(top) != join(join(one,join(one,one)),converse(complement(converse(join(one,join(one,one))))))
| converse(top) = join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(join(one,join(one,one)),converse(complement(converse(join(one,join(one,one))))))) ),[1,1,0,0],$fot(join(one,join(one,one)))]]) ).
cnf(refute_0_1558,plain,
( converse(top) != join(join(one,join(one,one)),converse(complement(converse(join(one,join(one,one))))))
| converse(top) = join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_948,refute_0_1557]) ).
cnf(refute_0_1559,plain,
converse(top) = join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,join(one,one)),converse(complement(converse(join(one,join(one,one))))))) )],[refute_0_1556,refute_0_1558]) ).
cnf(refute_0_1560,plain,
join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(one,join(one,complement(join(one,join(one,one)))))))]]) ).
cnf(refute_0_1561,plain,
join(one,converse(join(one,complement(join(one,join(one,one)))))) = converse(join(one,join(one,complement(join(one,join(one,one)))))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(one,complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_1562,plain,
join(one,converse(complement(join(one,join(one,one))))) = converse(join(one,complement(join(one,join(one,one))))),
inference(subst,[],[refute_0_803:[bind(B,$fot(complement(join(one,join(one,one)))))]]) ).
cnf(refute_0_1563,plain,
join(one,join(one,converse(complement(join(one,join(one,one)))))) = join(one,join(one,converse(complement(join(one,join(one,one)))))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(complement(join(one,join(one,one)))))))]]) ).
cnf(refute_0_1564,plain,
( join(one,converse(complement(join(one,join(one,one))))) != converse(join(one,complement(join(one,join(one,one)))))
| join(one,join(one,converse(complement(join(one,join(one,one)))))) != join(one,join(one,converse(complement(join(one,join(one,one))))))
| join(one,join(one,converse(complement(join(one,join(one,one)))))) = join(one,converse(join(one,complement(join(one,join(one,one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(complement(join(one,join(one,one)))))),join(one,join(one,converse(complement(join(one,join(one,one))))))) ),[1,1],$fot(converse(join(one,complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_1565,plain,
( join(one,converse(complement(join(one,join(one,one))))) != converse(join(one,complement(join(one,join(one,one)))))
| join(one,join(one,converse(complement(join(one,join(one,one)))))) = join(one,converse(join(one,complement(join(one,join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,join(one,one)))))),join(one,join(one,converse(complement(join(one,join(one,one))))))) )],[refute_0_1563,refute_0_1564]) ).
cnf(refute_0_1566,plain,
join(one,join(one,converse(complement(join(one,join(one,one)))))) = join(one,converse(join(one,complement(join(one,join(one,one)))))),
inference(resolve,[$cnf( $equal(join(one,converse(complement(join(one,join(one,one))))),converse(join(one,complement(join(one,join(one,one)))))) )],[refute_0_1562,refute_0_1565]) ).
cnf(refute_0_1567,plain,
( join(one,converse(join(one,complement(join(one,join(one,one)))))) != converse(join(one,join(one,complement(join(one,join(one,one))))))
| join(one,join(one,converse(complement(join(one,join(one,one)))))) != join(one,converse(join(one,complement(join(one,join(one,one))))))
| join(one,join(one,converse(complement(join(one,join(one,one)))))) = converse(join(one,join(one,complement(join(one,join(one,one)))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,converse(complement(join(one,join(one,one)))))))),bind(Y,$fot(join(one,converse(join(one,complement(join(one,join(one,one)))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,join(one,one))))))))]]) ).
cnf(refute_0_1568,plain,
( join(one,converse(join(one,complement(join(one,join(one,one)))))) != converse(join(one,join(one,complement(join(one,join(one,one))))))
| join(one,join(one,converse(complement(join(one,join(one,one)))))) = converse(join(one,join(one,complement(join(one,join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,join(one,one)))))),join(one,converse(join(one,complement(join(one,join(one,one))))))) )],[refute_0_1566,refute_0_1567]) ).
cnf(refute_0_1569,plain,
join(one,join(one,converse(complement(join(one,join(one,one)))))) = converse(join(one,join(one,complement(join(one,join(one,one)))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,complement(join(one,join(one,one)))))),converse(join(one,join(one,complement(join(one,join(one,one))))))) )],[refute_0_1561,refute_0_1568]) ).
cnf(refute_0_1570,plain,
join(join(one,one),converse(complement(join(one,join(one,one))))) = join(one,join(one,converse(complement(join(one,join(one,one)))))),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(converse(complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_1571,plain,
( join(join(one,one),converse(complement(join(one,join(one,one))))) != join(one,join(one,converse(complement(join(one,join(one,one))))))
| join(one,join(one,converse(complement(join(one,join(one,one)))))) != converse(join(one,join(one,complement(join(one,join(one,one))))))
| join(join(one,one),converse(complement(join(one,join(one,one))))) = converse(join(one,join(one,complement(join(one,join(one,one)))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,one),converse(complement(join(one,join(one,one))))))),bind(Y,$fot(join(one,join(one,converse(complement(join(one,join(one,one)))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,join(one,one))))))))]]) ).
cnf(refute_0_1572,plain,
( join(one,join(one,converse(complement(join(one,join(one,one)))))) != converse(join(one,join(one,complement(join(one,join(one,one))))))
| join(join(one,one),converse(complement(join(one,join(one,one))))) = converse(join(one,join(one,complement(join(one,join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,join(one,one))))),join(one,join(one,converse(complement(join(one,join(one,one))))))) )],[refute_0_1570,refute_0_1571]) ).
cnf(refute_0_1573,plain,
join(join(one,one),converse(complement(join(one,join(one,one))))) = converse(join(one,join(one,complement(join(one,join(one,one)))))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,join(one,one)))))),converse(join(one,join(one,complement(join(one,join(one,one))))))) )],[refute_0_1569,refute_0_1572]) ).
cnf(refute_0_1574,plain,
join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) = join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))),
introduced(tautology,[refl,[$fot(join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))))]]) ).
cnf(refute_0_1575,plain,
( join(join(one,one),converse(complement(join(one,join(one,one))))) != converse(join(one,join(one,complement(join(one,join(one,one))))))
| join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) != join(one,join(join(one,one),converse(complement(join(one,join(one,one))))))
| join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) = join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))),join(one,join(join(one,one),converse(complement(join(one,join(one,one))))))) ),[1,1],$fot(converse(join(one,join(one,complement(join(one,join(one,one)))))))]]) ).
cnf(refute_0_1576,plain,
( join(join(one,one),converse(complement(join(one,join(one,one))))) != converse(join(one,join(one,complement(join(one,join(one,one))))))
| join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) = join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))),join(one,join(join(one,one),converse(complement(join(one,join(one,one))))))) )],[refute_0_1574,refute_0_1575]) ).
cnf(refute_0_1577,plain,
join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) = join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,join(one,one))))),converse(join(one,join(one,complement(join(one,join(one,one))))))) )],[refute_0_1573,refute_0_1576]) ).
cnf(refute_0_1578,plain,
( join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) != join(one,converse(join(one,join(one,complement(join(one,join(one,one)))))))
| join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))))),bind(Y,$fot(join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))))),bind(Z,$fot(converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))))]]) ).
cnf(refute_0_1579,plain,
( join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))),join(one,converse(join(one,join(one,complement(join(one,join(one,one)))))))) )],[refute_0_1577,refute_0_1578]) ).
cnf(refute_0_1580,plain,
join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,complement(join(one,join(one,one))))))),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) )],[refute_0_1560,refute_0_1579]) ).
cnf(refute_0_1581,plain,
join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) = join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(join(one,one))),bind(C,$fot(converse(complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_1582,plain,
( join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) != join(one,join(join(one,one),converse(complement(join(one,join(one,one))))))
| join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))))),bind(Y,$fot(join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))))),bind(Z,$fot(converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))))]]) ).
cnf(refute_0_1583,plain,
( join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))),join(one,join(join(one,one),converse(complement(join(one,join(one,one))))))) )],[refute_0_1581,refute_0_1582]) ).
cnf(refute_0_1584,plain,
join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),converse(complement(join(one,join(one,one)))))),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) )],[refute_0_1580,refute_0_1583]) ).
cnf(refute_0_1585,plain,
( converse(top) != join(join(one,join(one,one)),converse(complement(join(one,join(one,one)))))
| join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| converse(top) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) ),[0],$fot(join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_1586,plain,
( converse(top) != join(join(one,join(one,one)),converse(complement(join(one,join(one,one)))))
| converse(top) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,one)),converse(complement(join(one,join(one,one))))),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) )],[refute_0_1584,refute_0_1585]) ).
cnf(refute_0_1587,plain,
converse(top) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,join(one,one)),converse(complement(join(one,join(one,one)))))) )],[refute_0_1559,refute_0_1586]) ).
cnf(refute_0_1588,plain,
( converse(top) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| converse(top) != top
| top = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) ),[0],$fot(top)]]) ).
cnf(refute_0_1589,plain,
( converse(top) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| top = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1588]) ).
cnf(refute_0_1590,plain,
top = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),
inference(resolve,[$cnf( $equal(converse(top),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) )],[refute_0_1587,refute_0_1589]) ).
cnf(refute_0_1591,plain,
composition(join(join(one,one),one),X_106) = join(X_106,composition(join(one,one),X_106)),
inference(subst,[],[refute_0_676:[bind(X_104,$fot(join(one,one)))]]) ).
cnf(refute_0_1592,plain,
composition(join(one,one),X_111) = join(X_111,composition(one,X_111)),
inference(subst,[],[refute_0_676:[bind(X_104,$fot(one)),bind(X_106,$fot(X_111))]]) ).
cnf(refute_0_1593,plain,
X_111 = composition(one,X_111),
inference(subst,[],[refute_0_190:[bind(X_24,$fot(X_111))]]) ).
cnf(refute_0_1594,plain,
( X_111 != composition(one,X_111)
| composition(one,X_111) = X_111 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_111)),bind(Y,$fot(composition(one,X_111)))]]) ).
cnf(refute_0_1595,plain,
composition(one,X_111) = X_111,
inference(resolve,[$cnf( $equal(X_111,composition(one,X_111)) )],[refute_0_1593,refute_0_1594]) ).
cnf(refute_0_1596,plain,
( composition(join(one,one),X_111) != join(X_111,composition(one,X_111))
| composition(one,X_111) != X_111
| composition(join(one,one),X_111) = join(X_111,X_111) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_111),join(X_111,composition(one,X_111))) ),[1,1],$fot(X_111)]]) ).
cnf(refute_0_1597,plain,
( composition(join(one,one),X_111) != join(X_111,composition(one,X_111))
| composition(join(one,one),X_111) = join(X_111,X_111) ),
inference(resolve,[$cnf( $equal(composition(one,X_111),X_111) )],[refute_0_1595,refute_0_1596]) ).
cnf(refute_0_1598,plain,
composition(join(one,one),X_111) = join(X_111,X_111),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_111),join(X_111,composition(one,X_111))) )],[refute_0_1592,refute_0_1597]) ).
cnf(refute_0_1599,plain,
composition(join(one,one),X_106) = join(X_106,X_106),
inference(subst,[],[refute_0_1598:[bind(X_111,$fot(X_106))]]) ).
cnf(refute_0_1600,plain,
( composition(join(join(one,one),one),X_106) != join(X_106,composition(join(one,one),X_106))
| composition(join(one,one),X_106) != join(X_106,X_106)
| composition(join(join(one,one),one),X_106) = join(X_106,join(X_106,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,one),one),X_106),join(X_106,composition(join(one,one),X_106))) ),[1,1],$fot(join(X_106,X_106))]]) ).
cnf(refute_0_1601,plain,
( composition(join(join(one,one),one),X_106) != join(X_106,composition(join(one,one),X_106))
| composition(join(join(one,one),one),X_106) = join(X_106,join(X_106,X_106)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_106),join(X_106,X_106)) )],[refute_0_1599,refute_0_1600]) ).
cnf(refute_0_1602,plain,
composition(join(join(one,one),one),X_106) = join(X_106,join(X_106,X_106)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_106),join(X_106,composition(join(one,one),X_106))) )],[refute_0_1591,refute_0_1601]) ).
cnf(refute_0_1603,plain,
composition(join(join(one,one),one),X_106) = composition(join(one,join(one,one)),X_106),
inference(subst,[],[refute_0_874:[bind(X_110,$fot(join(one,one))),bind(X_111,$fot(X_106))]]) ).
cnf(refute_0_1604,plain,
( composition(join(join(one,one),one),X_106) != composition(join(one,join(one,one)),X_106)
| composition(join(join(one,one),one),X_106) != join(X_106,join(X_106,X_106))
| composition(join(one,join(one,one)),X_106) = join(X_106,join(X_106,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,one),one),X_106),join(X_106,join(X_106,X_106))) ),[0],$fot(composition(join(one,join(one,one)),X_106))]]) ).
cnf(refute_0_1605,plain,
( composition(join(join(one,one),one),X_106) != join(X_106,join(X_106,X_106))
| composition(join(one,join(one,one)),X_106) = join(X_106,join(X_106,X_106)) ),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_106),composition(join(one,join(one,one)),X_106)) )],[refute_0_1603,refute_0_1604]) ).
cnf(refute_0_1606,plain,
composition(join(one,join(one,one)),X_106) = join(X_106,join(X_106,X_106)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_106),join(X_106,join(X_106,X_106))) )],[refute_0_1602,refute_0_1605]) ).
cnf(refute_0_1607,plain,
join(complement(X_46),composition(converse(join(one,one)),complement(composition(join(one,one),X_46)))) = complement(X_46),
inference(subst,[],[refute_0_160:[bind(A,$fot(join(one,one))),bind(B,$fot(X_46))]]) ).
cnf(refute_0_1608,plain,
( converse(join(one,one)) != join(one,one)
| join(complement(X_46),composition(converse(join(one,one)),complement(composition(join(one,one),X_46)))) != complement(X_46)
| join(complement(X_46),composition(join(one,one),complement(composition(join(one,one),X_46)))) = complement(X_46) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_46),composition(converse(join(one,one)),complement(composition(join(one,one),X_46)))),complement(X_46)) ),[0,1,0],$fot(join(one,one))]]) ).
cnf(refute_0_1609,plain,
( join(complement(X_46),composition(converse(join(one,one)),complement(composition(join(one,one),X_46)))) != complement(X_46)
| join(complement(X_46),composition(join(one,one),complement(composition(join(one,one),X_46)))) = complement(X_46) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_1608]) ).
cnf(refute_0_1610,plain,
join(complement(X_46),composition(join(one,one),complement(composition(join(one,one),X_46)))) = complement(X_46),
inference(resolve,[$cnf( $equal(join(complement(X_46),composition(converse(join(one,one)),complement(composition(join(one,one),X_46)))),complement(X_46)) )],[refute_0_1607,refute_0_1609]) ).
cnf(refute_0_1611,plain,
join(complement(complement(X_10)),composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = complement(complement(X_10)),
inference(subst,[],[refute_0_1610:[bind(X_46,$fot(complement(X_10)))]]) ).
cnf(refute_0_1612,plain,
( complement(complement(X_10)) != X_10
| join(complement(complement(X_10)),composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != complement(complement(X_10))
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = complement(complement(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_10)),composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),complement(complement(X_10))) ),[0,0],$fot(X_10)]]) ).
cnf(refute_0_1613,plain,
( join(complement(complement(X_10)),composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != complement(complement(X_10))
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_10)),X_10) )],[refute_0_397,refute_0_1612]) ).
cnf(refute_0_1614,plain,
join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = complement(complement(X_10)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_10)),composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),complement(complement(X_10))) )],[refute_0_1611,refute_0_1613]) ).
cnf(refute_0_1615,plain,
composition(join(join(one,one),one),X_10) = composition(join(one,join(one,one)),X_10),
inference(subst,[],[refute_0_874:[bind(X_110,$fot(join(one,one))),bind(X_111,$fot(X_10))]]) ).
cnf(refute_0_1616,plain,
join(X_10,composition(join(one,one),X_10)) = composition(join(join(one,one),one),X_10),
inference(subst,[],[refute_0_868:[bind(X_104,$fot(join(one,one))),bind(X_106,$fot(X_10))]]) ).
cnf(refute_0_1617,plain,
( composition(join(join(one,one),one),X_10) != composition(join(one,join(one,one)),X_10)
| join(X_10,composition(join(one,one),X_10)) != composition(join(join(one,one),one),X_10)
| join(X_10,composition(join(one,one),X_10)) = composition(join(one,join(one,one)),X_10) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(X_10,composition(join(one,one),X_10)))),bind(Y,$fot(composition(join(join(one,one),one),X_10))),bind(Z,$fot(composition(join(one,join(one,one)),X_10)))]]) ).
cnf(refute_0_1618,plain,
( composition(join(join(one,one),one),X_10) != composition(join(one,join(one,one)),X_10)
| join(X_10,composition(join(one,one),X_10)) = composition(join(one,join(one,one)),X_10) ),
inference(resolve,[$cnf( $equal(join(X_10,composition(join(one,one),X_10)),composition(join(join(one,one),one),X_10)) )],[refute_0_1616,refute_0_1617]) ).
cnf(refute_0_1619,plain,
join(X_10,composition(join(one,one),X_10)) = composition(join(one,join(one,one)),X_10),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_10),composition(join(one,join(one,one)),X_10)) )],[refute_0_1615,refute_0_1618]) ).
cnf(refute_0_1620,plain,
A = join(meet(complement(A),A),complement(join(complement(A),complement(A)))),
inference(subst,[],[refute_0_469:[bind(B,$fot(complement(A)))]]) ).
cnf(refute_0_1621,plain,
composition(join(one,one),complement(A)) = join(complement(A),complement(A)),
inference(subst,[],[refute_0_1598:[bind(X_111,$fot(complement(A)))]]) ).
cnf(refute_0_1622,plain,
( composition(join(one,one),complement(A)) != join(complement(A),complement(A))
| join(complement(A),complement(A)) = composition(join(one,one),complement(A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),complement(A)))),bind(Y,$fot(join(complement(A),complement(A))))]]) ).
cnf(refute_0_1623,plain,
join(complement(A),complement(A)) = composition(join(one,one),complement(A)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(A)),join(complement(A),complement(A))) )],[refute_0_1621,refute_0_1622]) ).
cnf(refute_0_1624,plain,
( A != join(meet(complement(A),A),complement(join(complement(A),complement(A))))
| join(complement(A),complement(A)) != composition(join(one,one),complement(A))
| A = join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) ),
introduced(tautology,[equality,[$cnf( $equal(A,join(meet(complement(A),A),complement(join(complement(A),complement(A))))) ),[1,1,0],$fot(composition(join(one,one),complement(A)))]]) ).
cnf(refute_0_1625,plain,
( A != join(meet(complement(A),A),complement(join(complement(A),complement(A))))
| A = join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) ),
inference(resolve,[$cnf( $equal(join(complement(A),complement(A)),composition(join(one,one),complement(A))) )],[refute_0_1623,refute_0_1624]) ).
cnf(refute_0_1626,plain,
A = join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))),
inference(resolve,[$cnf( $equal(A,join(meet(complement(A),A),complement(join(complement(A),complement(A))))) )],[refute_0_1620,refute_0_1625]) ).
cnf(refute_0_1627,plain,
join(zero,complement(composition(join(one,one),complement(A)))) = complement(composition(join(one,one),complement(A))),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(complement(composition(join(one,one),complement(A)))))]]) ).
cnf(refute_0_1628,plain,
meet(complement(A),A) = meet(A,complement(A)),
inference(subst,[],[refute_0_274:[bind(X_17,$fot(A)),bind(X_18,$fot(complement(A)))]]) ).
cnf(refute_0_1629,plain,
( meet(A,complement(A)) != zero
| meet(complement(A),A) != meet(A,complement(A))
| meet(complement(A),A) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(complement(A),A))),bind(Y,$fot(meet(A,complement(A)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1630,plain,
( meet(A,complement(A)) != zero
| meet(complement(A),A) = zero ),
inference(resolve,[$cnf( $equal(meet(complement(A),A),meet(A,complement(A))) )],[refute_0_1628,refute_0_1629]) ).
cnf(refute_0_1631,plain,
meet(complement(A),A) = zero,
inference(resolve,[$cnf( $equal(meet(A,complement(A)),zero) )],[refute_0_220,refute_0_1630]) ).
cnf(refute_0_1632,plain,
join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) = join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))),
introduced(tautology,[refl,[$fot(join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))))]]) ).
cnf(refute_0_1633,plain,
( join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) != join(meet(complement(A),A),complement(composition(join(one,one),complement(A))))
| meet(complement(A),A) != zero
| join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) = join(zero,complement(composition(join(one,one),complement(A)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))),join(meet(complement(A),A),complement(composition(join(one,one),complement(A))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1634,plain,
( meet(complement(A),A) != zero
| join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) = join(zero,complement(composition(join(one,one),complement(A)))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))),join(meet(complement(A),A),complement(composition(join(one,one),complement(A))))) )],[refute_0_1632,refute_0_1633]) ).
cnf(refute_0_1635,plain,
join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) = join(zero,complement(composition(join(one,one),complement(A)))),
inference(resolve,[$cnf( $equal(meet(complement(A),A),zero) )],[refute_0_1631,refute_0_1634]) ).
cnf(refute_0_1636,plain,
( join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) != join(zero,complement(composition(join(one,one),complement(A))))
| join(zero,complement(composition(join(one,one),complement(A)))) != complement(composition(join(one,one),complement(A)))
| join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) = complement(composition(join(one,one),complement(A))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))))),bind(Y,$fot(join(zero,complement(composition(join(one,one),complement(A)))))),bind(Z,$fot(complement(composition(join(one,one),complement(A)))))]]) ).
cnf(refute_0_1637,plain,
( join(zero,complement(composition(join(one,one),complement(A)))) != complement(composition(join(one,one),complement(A)))
| join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) = complement(composition(join(one,one),complement(A))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))),join(zero,complement(composition(join(one,one),complement(A))))) )],[refute_0_1635,refute_0_1636]) ).
cnf(refute_0_1638,plain,
join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) = complement(composition(join(one,one),complement(A))),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(join(one,one),complement(A)))),complement(composition(join(one,one),complement(A)))) )],[refute_0_1627,refute_0_1637]) ).
cnf(refute_0_1639,plain,
( A != join(meet(complement(A),A),complement(composition(join(one,one),complement(A))))
| join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))) != complement(composition(join(one,one),complement(A)))
| A = complement(composition(join(one,one),complement(A))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,complement(composition(join(one,one),complement(A)))) ),[0],$fot(join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))))]]) ).
cnf(refute_0_1640,plain,
( A != join(meet(complement(A),A),complement(composition(join(one,one),complement(A))))
| A = complement(composition(join(one,one),complement(A))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(A),A),complement(composition(join(one,one),complement(A)))),complement(composition(join(one,one),complement(A)))) )],[refute_0_1638,refute_0_1639]) ).
cnf(refute_0_1641,plain,
A = complement(composition(join(one,one),complement(A))),
inference(resolve,[$cnf( $equal(A,join(meet(complement(A),A),complement(composition(join(one,one),complement(A))))) )],[refute_0_1626,refute_0_1640]) ).
cnf(refute_0_1642,plain,
( A != complement(composition(join(one,one),complement(A)))
| complement(composition(join(one,one),complement(A))) = A ),
inference(subst,[],[refute_0_2:[bind(X,$fot(A)),bind(Y,$fot(complement(composition(join(one,one),complement(A)))))]]) ).
cnf(refute_0_1643,plain,
complement(composition(join(one,one),complement(A))) = A,
inference(resolve,[$cnf( $equal(A,complement(composition(join(one,one),complement(A)))) )],[refute_0_1641,refute_0_1642]) ).
cnf(refute_0_1644,plain,
complement(composition(join(one,one),complement(X_10))) = X_10,
inference(subst,[],[refute_0_1643:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_1645,plain,
composition(join(one,one),complement(composition(join(one,one),complement(X_10)))) = composition(join(one,one),complement(composition(join(one,one),complement(X_10)))),
introduced(tautology,[refl,[$fot(composition(join(one,one),complement(composition(join(one,one),complement(X_10)))))]]) ).
cnf(refute_0_1646,plain,
( complement(composition(join(one,one),complement(X_10))) != X_10
| composition(join(one,one),complement(composition(join(one,one),complement(X_10)))) != composition(join(one,one),complement(composition(join(one,one),complement(X_10))))
| composition(join(one,one),complement(composition(join(one,one),complement(X_10)))) = composition(join(one,one),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),complement(X_10)))),composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_1647,plain,
( complement(composition(join(one,one),complement(X_10))) != X_10
| composition(join(one,one),complement(composition(join(one,one),complement(X_10)))) = composition(join(one,one),X_10) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),complement(X_10)))),composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) )],[refute_0_1645,refute_0_1646]) ).
cnf(refute_0_1648,plain,
composition(join(one,one),complement(composition(join(one,one),complement(X_10)))) = composition(join(one,one),X_10),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(X_10))),X_10) )],[refute_0_1644,refute_0_1647]) ).
cnf(refute_0_1649,plain,
join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),
introduced(tautology,[refl,[$fot(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))))]]) ).
cnf(refute_0_1650,plain,
( composition(join(one,one),complement(composition(join(one,one),complement(X_10)))) != composition(join(one,one),X_10)
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10)))))
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = join(X_10,composition(join(one,one),X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10)))))) ),[1,1],$fot(composition(join(one,one),X_10))]]) ).
cnf(refute_0_1651,plain,
( composition(join(one,one),complement(composition(join(one,one),complement(X_10)))) != composition(join(one,one),X_10)
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = join(X_10,composition(join(one,one),X_10)) ),
inference(resolve,[$cnf( $equal(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10)))))) )],[refute_0_1649,refute_0_1650]) ).
cnf(refute_0_1652,plain,
join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = join(X_10,composition(join(one,one),X_10)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),complement(X_10)))),composition(join(one,one),X_10)) )],[refute_0_1648,refute_0_1651]) ).
cnf(refute_0_1653,plain,
( join(X_10,composition(join(one,one),X_10)) != composition(join(one,join(one,one)),X_10)
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != join(X_10,composition(join(one,one),X_10))
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = composition(join(one,join(one,one)),X_10) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))))),bind(Y,$fot(join(X_10,composition(join(one,one),X_10)))),bind(Z,$fot(composition(join(one,join(one,one)),X_10)))]]) ).
cnf(refute_0_1654,plain,
( join(X_10,composition(join(one,one),X_10)) != composition(join(one,join(one,one)),X_10)
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = composition(join(one,join(one,one)),X_10) ),
inference(resolve,[$cnf( $equal(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),join(X_10,composition(join(one,one),X_10))) )],[refute_0_1652,refute_0_1653]) ).
cnf(refute_0_1655,plain,
join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) = composition(join(one,join(one,one)),X_10),
inference(resolve,[$cnf( $equal(join(X_10,composition(join(one,one),X_10)),composition(join(one,join(one,one)),X_10)) )],[refute_0_1619,refute_0_1654]) ).
cnf(refute_0_1656,plain,
( join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != complement(complement(X_10))
| join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != composition(join(one,join(one,one)),X_10)
| composition(join(one,join(one,one)),X_10) = complement(complement(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),complement(complement(X_10))) ),[0],$fot(composition(join(one,join(one,one)),X_10))]]) ).
cnf(refute_0_1657,plain,
( join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != complement(complement(X_10))
| composition(join(one,join(one,one)),X_10) = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),composition(join(one,join(one,one)),X_10)) )],[refute_0_1655,refute_0_1656]) ).
cnf(refute_0_1658,plain,
( complement(complement(X_10)) != X_10
| composition(join(one,join(one,one)),X_10) != complement(complement(X_10))
| composition(join(one,join(one,one)),X_10) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,one)),X_10),complement(complement(X_10))) ),[1],$fot(X_10)]]) ).
cnf(refute_0_1659,plain,
( composition(join(one,join(one,one)),X_10) != complement(complement(X_10))
| composition(join(one,join(one,one)),X_10) = X_10 ),
inference(resolve,[$cnf( $equal(complement(complement(X_10)),X_10) )],[refute_0_397,refute_0_1658]) ).
cnf(refute_0_1660,plain,
( join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))) != complement(complement(X_10))
| composition(join(one,join(one,one)),X_10) = X_10 ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),X_10),complement(complement(X_10))) )],[refute_0_1657,refute_0_1659]) ).
cnf(refute_0_1661,plain,
composition(join(one,join(one,one)),X_10) = X_10,
inference(resolve,[$cnf( $equal(join(X_10,composition(join(one,one),complement(composition(join(one,one),complement(X_10))))),complement(complement(X_10))) )],[refute_0_1614,refute_0_1660]) ).
cnf(refute_0_1662,plain,
composition(join(one,join(one,one)),X_106) = X_106,
inference(subst,[],[refute_0_1661:[bind(X_10,$fot(X_106))]]) ).
cnf(refute_0_1663,plain,
( composition(join(one,join(one,one)),X_106) != X_106
| composition(join(one,join(one,one)),X_106) != join(X_106,join(X_106,X_106))
| X_106 = join(X_106,join(X_106,X_106)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,one)),X_106),join(X_106,join(X_106,X_106))) ),[0],$fot(X_106)]]) ).
cnf(refute_0_1664,plain,
( composition(join(one,join(one,one)),X_106) != join(X_106,join(X_106,X_106))
| X_106 = join(X_106,join(X_106,X_106)) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),X_106),X_106) )],[refute_0_1662,refute_0_1663]) ).
cnf(refute_0_1665,plain,
X_106 = join(X_106,join(X_106,X_106)),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),X_106),join(X_106,join(X_106,X_106))) )],[refute_0_1606,refute_0_1664]) ).
cnf(refute_0_1666,plain,
( X_106 != join(X_106,join(X_106,X_106))
| join(X_106,join(X_106,X_106)) = X_106 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_106)),bind(Y,$fot(join(X_106,join(X_106,X_106))))]]) ).
cnf(refute_0_1667,plain,
join(X_106,join(X_106,X_106)) = X_106,
inference(resolve,[$cnf( $equal(X_106,join(X_106,join(X_106,X_106))) )],[refute_0_1665,refute_0_1666]) ).
cnf(refute_0_1668,plain,
join(one,join(one,one)) = one,
inference(subst,[],[refute_0_1667:[bind(X_106,$fot(one))]]) ).
cnf(refute_0_1669,plain,
complement(join(one,join(one,one))) = complement(join(one,join(one,one))),
introduced(tautology,[refl,[$fot(complement(join(one,join(one,one))))]]) ).
cnf(refute_0_1670,plain,
( complement(join(one,join(one,one))) != complement(join(one,join(one,one)))
| join(one,join(one,one)) != one
| complement(join(one,join(one,one))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(one,join(one,one))),complement(join(one,join(one,one)))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1671,plain,
( join(one,join(one,one)) != one
| complement(join(one,join(one,one))) = complement(one) ),
inference(resolve,[$cnf( $equal(complement(join(one,join(one,one))),complement(join(one,join(one,one)))) )],[refute_0_1669,refute_0_1670]) ).
cnf(refute_0_1672,plain,
complement(join(one,join(one,one))) = complement(one),
inference(resolve,[$cnf( $equal(join(one,join(one,one)),one) )],[refute_0_1668,refute_0_1671]) ).
cnf(refute_0_1673,plain,
join(one,complement(join(one,join(one,one)))) = join(one,complement(join(one,join(one,one)))),
introduced(tautology,[refl,[$fot(join(one,complement(join(one,join(one,one)))))]]) ).
cnf(refute_0_1674,plain,
( complement(join(one,join(one,one))) != complement(one)
| join(one,complement(join(one,join(one,one)))) != join(one,complement(join(one,join(one,one))))
| join(one,complement(join(one,join(one,one)))) = join(one,complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(one,join(one,one)))),join(one,complement(join(one,join(one,one))))) ),[1,1],$fot(complement(one))]]) ).
cnf(refute_0_1675,plain,
( complement(join(one,join(one,one))) != complement(one)
| join(one,complement(join(one,join(one,one)))) = join(one,complement(one)) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,join(one,one)))),join(one,complement(join(one,join(one,one))))) )],[refute_0_1673,refute_0_1674]) ).
cnf(refute_0_1676,plain,
join(one,complement(join(one,join(one,one)))) = join(one,complement(one)),
inference(resolve,[$cnf( $equal(complement(join(one,join(one,one))),complement(one)) )],[refute_0_1672,refute_0_1675]) ).
cnf(refute_0_1677,plain,
( join(one,complement(join(one,join(one,one)))) != join(one,complement(one))
| join(one,complement(one)) != top
| join(one,complement(join(one,join(one,one)))) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,complement(join(one,join(one,one)))))),bind(Y,$fot(join(one,complement(one)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1678,plain,
( join(one,complement(one)) != top
| join(one,complement(join(one,join(one,one)))) = top ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,join(one,one)))),join(one,complement(one))) )],[refute_0_1676,refute_0_1677]) ).
cnf(refute_0_1679,plain,
join(one,complement(join(one,join(one,one)))) = top,
inference(resolve,[$cnf( $equal(join(one,complement(one)),top) )],[refute_0_1288,refute_0_1678]) ).
cnf(refute_0_1680,plain,
join(one,join(one,complement(join(one,join(one,one))))) = join(one,join(one,complement(join(one,join(one,one))))),
introduced(tautology,[refl,[$fot(join(one,join(one,complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_1681,plain,
( join(one,complement(join(one,join(one,one)))) != top
| join(one,join(one,complement(join(one,join(one,one))))) != join(one,join(one,complement(join(one,join(one,one)))))
| join(one,join(one,complement(join(one,join(one,one))))) = join(one,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,complement(join(one,join(one,one))))),join(one,join(one,complement(join(one,join(one,one)))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1682,plain,
( join(one,complement(join(one,join(one,one)))) != top
| join(one,join(one,complement(join(one,join(one,one))))) = join(one,top) ),
inference(resolve,[$cnf( $equal(join(one,join(one,complement(join(one,join(one,one))))),join(one,join(one,complement(join(one,join(one,one)))))) )],[refute_0_1680,refute_0_1681]) ).
cnf(refute_0_1683,plain,
join(one,join(one,complement(join(one,join(one,one))))) = join(one,top),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,join(one,one)))),top) )],[refute_0_1679,refute_0_1682]) ).
cnf(refute_0_1684,plain,
join(one,join(one,join(one,complement(join(one,join(one,one)))))) = join(one,join(one,join(one,complement(join(one,join(one,one)))))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(one,complement(join(one,join(one,one)))))))]]) ).
cnf(refute_0_1685,plain,
( join(one,join(one,complement(join(one,join(one,one))))) != join(one,top)
| join(one,join(one,join(one,complement(join(one,join(one,one)))))) != join(one,join(one,join(one,complement(join(one,join(one,one))))))
| join(one,join(one,join(one,complement(join(one,join(one,one)))))) = join(one,join(one,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(one,complement(join(one,join(one,one)))))),join(one,join(one,join(one,complement(join(one,join(one,one))))))) ),[1,1],$fot(join(one,top))]]) ).
cnf(refute_0_1686,plain,
( join(one,join(one,complement(join(one,join(one,one))))) != join(one,top)
| join(one,join(one,join(one,complement(join(one,join(one,one)))))) = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,complement(join(one,join(one,one)))))),join(one,join(one,join(one,complement(join(one,join(one,one))))))) )],[refute_0_1684,refute_0_1685]) ).
cnf(refute_0_1687,plain,
join(one,join(one,join(one,complement(join(one,join(one,one)))))) = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(join(one,join(one,complement(join(one,join(one,one))))),join(one,top)) )],[refute_0_1683,refute_0_1686]) ).
cnf(refute_0_1688,plain,
converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) = converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))))]]) ).
cnf(refute_0_1689,plain,
( converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| join(one,join(one,join(one,complement(join(one,join(one,one)))))) != join(one,join(one,top))
| converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) = converse(join(one,join(one,top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) ),[1,0],$fot(join(one,join(one,top)))]]) ).
cnf(refute_0_1690,plain,
( join(one,join(one,join(one,complement(join(one,join(one,one)))))) != join(one,join(one,top))
| converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) = converse(join(one,join(one,top))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) )],[refute_0_1688,refute_0_1689]) ).
cnf(refute_0_1691,plain,
converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) = converse(join(one,join(one,top))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,complement(join(one,join(one,one)))))),join(one,join(one,top))) )],[refute_0_1687,refute_0_1690]) ).
cnf(refute_0_1692,plain,
( converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) != converse(join(one,join(one,top)))
| converse(join(one,join(one,top))) != join(one,join(one,top))
| converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) = join(one,join(one,top)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))))),bind(Y,$fot(converse(join(one,join(one,top))))),bind(Z,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_1693,plain,
( converse(join(one,join(one,top))) != join(one,join(one,top))
| converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),converse(join(one,join(one,top)))) )],[refute_0_1691,refute_0_1692]) ).
cnf(refute_0_1694,plain,
converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,top))),join(one,join(one,top))) )],[refute_0_1384,refute_0_1693]) ).
cnf(refute_0_1695,plain,
( converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))) != join(one,join(one,top))
| top != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| top = join(one,join(one,top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) ),[1],$fot(join(one,join(one,top)))]]) ).
cnf(refute_0_1696,plain,
( top != converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))
| top = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,complement(join(one,join(one,one))))))),join(one,join(one,top))) )],[refute_0_1694,refute_0_1695]) ).
cnf(refute_0_1697,plain,
top = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(top,converse(join(one,join(one,join(one,complement(join(one,join(one,one)))))))) )],[refute_0_1590,refute_0_1696]) ).
cnf(refute_0_1698,plain,
( top != join(one,join(one,top))
| join(one,join(one,top)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_1699,plain,
join(one,join(one,top)) = top,
inference(resolve,[$cnf( $equal(top,join(one,join(one,top))) )],[refute_0_1697,refute_0_1698]) ).
cnf(refute_0_1700,plain,
meet(zero,join(one,join(one,top))) = meet(zero,join(one,join(one,top))),
introduced(tautology,[refl,[$fot(meet(zero,join(one,join(one,top))))]]) ).
cnf(refute_0_1701,plain,
( join(one,join(one,top)) != top
| meet(zero,join(one,join(one,top))) != meet(zero,join(one,join(one,top)))
| meet(zero,join(one,join(one,top))) = meet(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(one,join(one,top))),meet(zero,join(one,join(one,top)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1702,plain,
( join(one,join(one,top)) != top
| meet(zero,join(one,join(one,top))) = meet(zero,top) ),
inference(resolve,[$cnf( $equal(meet(zero,join(one,join(one,top))),meet(zero,join(one,join(one,top)))) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
meet(zero,join(one,join(one,top))) = meet(zero,top),
inference(resolve,[$cnf( $equal(join(one,join(one,top)),top) )],[refute_0_1699,refute_0_1702]) ).
cnf(refute_0_1704,plain,
( meet(zero,join(one,join(one,top))) != meet(zero,top)
| meet(zero,top) != zero
| meet(zero,join(one,join(one,top))) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(zero,join(one,join(one,top))))),bind(Y,$fot(meet(zero,top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1705,plain,
( meet(zero,top) != zero
| meet(zero,join(one,join(one,top))) = zero ),
inference(resolve,[$cnf( $equal(meet(zero,join(one,join(one,top))),meet(zero,top)) )],[refute_0_1703,refute_0_1704]) ).
cnf(refute_0_1706,plain,
meet(zero,join(one,join(one,top))) = zero,
inference(resolve,[$cnf( $equal(meet(zero,top),zero) )],[refute_0_1555,refute_0_1705]) ).
cnf(refute_0_1707,plain,
complement(meet(zero,join(one,join(one,top)))) = complement(meet(zero,join(one,join(one,top)))),
introduced(tautology,[refl,[$fot(complement(meet(zero,join(one,join(one,top)))))]]) ).
cnf(refute_0_1708,plain,
( complement(meet(zero,join(one,join(one,top)))) != complement(meet(zero,join(one,join(one,top))))
| meet(zero,join(one,join(one,top))) != zero
| complement(meet(zero,join(one,join(one,top)))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(zero,join(one,join(one,top)))),complement(meet(zero,join(one,join(one,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1709,plain,
( meet(zero,join(one,join(one,top))) != zero
| complement(meet(zero,join(one,join(one,top)))) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(meet(zero,join(one,join(one,top)))),complement(meet(zero,join(one,join(one,top))))) )],[refute_0_1707,refute_0_1708]) ).
cnf(refute_0_1710,plain,
complement(meet(zero,join(one,join(one,top)))) = complement(zero),
inference(resolve,[$cnf( $equal(meet(zero,join(one,join(one,top))),zero) )],[refute_0_1706,refute_0_1709]) ).
cnf(refute_0_1711,plain,
( complement(meet(zero,join(one,join(one,top)))) != complement(zero)
| complement(zero) != top
| complement(meet(zero,join(one,join(one,top)))) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(meet(zero,join(one,join(one,top)))))),bind(Y,$fot(complement(zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1712,plain,
( complement(zero) != top
| complement(meet(zero,join(one,join(one,top)))) = top ),
inference(resolve,[$cnf( $equal(complement(meet(zero,join(one,join(one,top)))),complement(zero)) )],[refute_0_1710,refute_0_1711]) ).
cnf(refute_0_1713,plain,
complement(meet(zero,join(one,join(one,top)))) = top,
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_1712]) ).
cnf(refute_0_1714,plain,
converse(complement(meet(zero,join(one,join(one,top))))) = converse(complement(meet(zero,join(one,join(one,top))))),
introduced(tautology,[refl,[$fot(converse(complement(meet(zero,join(one,join(one,top))))))]]) ).
cnf(refute_0_1715,plain,
( complement(meet(zero,join(one,join(one,top)))) != top
| converse(complement(meet(zero,join(one,join(one,top))))) != converse(complement(meet(zero,join(one,join(one,top)))))
| converse(complement(meet(zero,join(one,join(one,top))))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(meet(zero,join(one,join(one,top))))),converse(complement(meet(zero,join(one,join(one,top)))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1716,plain,
( complement(meet(zero,join(one,join(one,top)))) != top
| converse(complement(meet(zero,join(one,join(one,top))))) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(complement(meet(zero,join(one,join(one,top))))),converse(complement(meet(zero,join(one,join(one,top)))))) )],[refute_0_1714,refute_0_1715]) ).
cnf(refute_0_1717,plain,
converse(complement(meet(zero,join(one,join(one,top))))) = converse(top),
inference(resolve,[$cnf( $equal(complement(meet(zero,join(one,join(one,top)))),top) )],[refute_0_1713,refute_0_1716]) ).
cnf(refute_0_1718,plain,
( converse(complement(meet(zero,join(one,join(one,top))))) != converse(top)
| converse(top) != top
| converse(complement(meet(zero,join(one,join(one,top))))) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(complement(meet(zero,join(one,join(one,top))))))),bind(Y,$fot(converse(top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1719,plain,
( converse(top) != top
| converse(complement(meet(zero,join(one,join(one,top))))) = top ),
inference(resolve,[$cnf( $equal(converse(complement(meet(zero,join(one,join(one,top))))),converse(top)) )],[refute_0_1717,refute_0_1718]) ).
cnf(refute_0_1720,plain,
converse(complement(meet(zero,join(one,join(one,top))))) = top,
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_1157,refute_0_1719]) ).
cnf(refute_0_1721,plain,
join(converse(complement(meet(zero,join(one,join(one,top))))),A) = join(converse(complement(meet(zero,join(one,join(one,top))))),A),
introduced(tautology,[refl,[$fot(join(converse(complement(meet(zero,join(one,join(one,top))))),A))]]) ).
cnf(refute_0_1722,plain,
( converse(complement(meet(zero,join(one,join(one,top))))) != top
| join(converse(complement(meet(zero,join(one,join(one,top))))),A) != join(converse(complement(meet(zero,join(one,join(one,top))))),A)
| join(converse(complement(meet(zero,join(one,join(one,top))))),A) = join(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(meet(zero,join(one,join(one,top))))),A),join(converse(complement(meet(zero,join(one,join(one,top))))),A)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1723,plain,
( converse(complement(meet(zero,join(one,join(one,top))))) != top
| join(converse(complement(meet(zero,join(one,join(one,top))))),A) = join(top,A) ),
inference(resolve,[$cnf( $equal(join(converse(complement(meet(zero,join(one,join(one,top))))),A),join(converse(complement(meet(zero,join(one,join(one,top))))),A)) )],[refute_0_1721,refute_0_1722]) ).
cnf(refute_0_1724,plain,
join(converse(complement(meet(zero,join(one,join(one,top))))),A) = join(top,A),
inference(resolve,[$cnf( $equal(converse(complement(meet(zero,join(one,join(one,top))))),top) )],[refute_0_1720,refute_0_1723]) ).
cnf(refute_0_1725,plain,
join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) = join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)),
introduced(tautology,[refl,[$fot(join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)))]]) ).
cnf(refute_0_1726,plain,
( join(converse(complement(meet(zero,join(one,join(one,top))))),A) != join(top,A)
| join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) != join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))
| join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) = join(one,join(top,A)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)),join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) ),[1,1],$fot(join(top,A))]]) ).
cnf(refute_0_1727,plain,
( join(converse(complement(meet(zero,join(one,join(one,top))))),A) != join(top,A)
| join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) = join(one,join(top,A)) ),
inference(resolve,[$cnf( $equal(join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)),join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) )],[refute_0_1725,refute_0_1726]) ).
cnf(refute_0_1728,plain,
join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) = join(one,join(top,A)),
inference(resolve,[$cnf( $equal(join(converse(complement(meet(zero,join(one,join(one,top))))),A),join(top,A)) )],[refute_0_1724,refute_0_1727]) ).
cnf(refute_0_1729,plain,
join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) = join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))))]]) ).
cnf(refute_0_1730,plain,
( join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) != join(one,join(top,A))
| join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) != join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)))
| join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) = join(one,join(one,join(top,A))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))),join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)))) ),[1,1],$fot(join(one,join(top,A)))]]) ).
cnf(refute_0_1731,plain,
( join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)) != join(one,join(top,A))
| join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) = join(one,join(one,join(top,A))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))),join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)))) )],[refute_0_1729,refute_0_1730]) ).
cnf(refute_0_1732,plain,
join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) = join(one,join(one,join(top,A))),
inference(resolve,[$cnf( $equal(join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A)),join(one,join(top,A))) )],[refute_0_1728,refute_0_1731]) ).
cnf(refute_0_1733,plain,
( join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) != join(one,join(one,join(top,A)))
| join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) != join(top,A)
| join(one,join(one,join(top,A))) = join(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))),join(top,A)) ),[0],$fot(join(one,join(one,join(top,A))))]]) ).
cnf(refute_0_1734,plain,
( join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))) != join(top,A)
| join(one,join(one,join(top,A))) = join(top,A) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))),join(one,join(one,join(top,A)))) )],[refute_0_1732,refute_0_1733]) ).
cnf(refute_0_1735,plain,
join(one,join(one,join(top,A))) = join(top,A),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(complement(meet(zero,join(one,join(one,top))))),A))),join(top,A)) )],[refute_0_1470,refute_0_1734]) ).
cnf(refute_0_1736,plain,
join(A,join(X_14,X_15)) = join(join(X_14,X_15),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_14,X_15)))]]) ).
cnf(refute_0_1737,plain,
join(X_14,join(X_15,A)) = join(join(X_14,X_15),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(A))]]) ).
cnf(refute_0_1738,plain,
( join(X_14,join(X_15,A)) != join(join(X_14,X_15),A)
| join(join(X_14,X_15),A) = join(X_14,join(X_15,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_14,join(X_15,A)))),bind(Y,$fot(join(join(X_14,X_15),A)))]]) ).
cnf(refute_0_1739,plain,
join(join(X_14,X_15),A) = join(X_14,join(X_15,A)),
inference(resolve,[$cnf( $equal(join(X_14,join(X_15,A)),join(join(X_14,X_15),A)) )],[refute_0_1737,refute_0_1738]) ).
cnf(refute_0_1740,plain,
( join(A,join(X_14,X_15)) != join(join(X_14,X_15),A)
| join(join(X_14,X_15),A) != join(X_14,join(X_15,A))
| join(A,join(X_14,X_15)) = join(X_14,join(X_15,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_14,X_15)),join(X_14,join(X_15,A))) ),[0],$fot(join(join(X_14,X_15),A))]]) ).
cnf(refute_0_1741,plain,
( join(A,join(X_14,X_15)) != join(join(X_14,X_15),A)
| join(A,join(X_14,X_15)) = join(X_14,join(X_15,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_14,X_15),A),join(X_14,join(X_15,A))) )],[refute_0_1739,refute_0_1740]) ).
cnf(refute_0_1742,plain,
join(A,join(X_14,X_15)) = join(X_14,join(X_15,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_14,X_15)),join(join(X_14,X_15),A)) )],[refute_0_1736,refute_0_1741]) ).
cnf(refute_0_1743,plain,
( join(A,join(X_14,X_15)) != join(X_14,join(X_15,A))
| join(X_14,join(X_15,A)) = join(A,join(X_14,X_15)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(X_14,X_15)))),bind(Y,$fot(join(X_14,join(X_15,A))))]]) ).
cnf(refute_0_1744,plain,
join(X_14,join(X_15,A)) = join(A,join(X_14,X_15)),
inference(resolve,[$cnf( $equal(join(A,join(X_14,X_15)),join(X_14,join(X_15,A))) )],[refute_0_1742,refute_0_1743]) ).
cnf(refute_0_1745,plain,
join(top,join(A,one)) = join(one,join(top,A)),
inference(subst,[],[refute_0_1744:[bind(A,$fot(one)),bind(X_14,$fot(top)),bind(X_15,$fot(A))]]) ).
cnf(refute_0_1746,plain,
join(join(top,A),one) = join(top,join(A,one)),
inference(subst,[],[refute_0_86:[bind(A,$fot(top)),bind(B,$fot(A)),bind(C,$fot(one))]]) ).
cnf(refute_0_1747,plain,
( join(join(top,A),one) != join(top,join(A,one))
| join(top,join(A,one)) != join(one,join(top,A))
| join(join(top,A),one) = join(one,join(top,A)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(top,A),one))),bind(Y,$fot(join(top,join(A,one)))),bind(Z,$fot(join(one,join(top,A))))]]) ).
cnf(refute_0_1748,plain,
( join(top,join(A,one)) != join(one,join(top,A))
| join(join(top,A),one) = join(one,join(top,A)) ),
inference(resolve,[$cnf( $equal(join(join(top,A),one),join(top,join(A,one))) )],[refute_0_1746,refute_0_1747]) ).
cnf(refute_0_1749,plain,
join(join(top,A),one) = join(one,join(top,A)),
inference(resolve,[$cnf( $equal(join(top,join(A,one)),join(one,join(top,A))) )],[refute_0_1745,refute_0_1748]) ).
cnf(refute_0_1750,plain,
converse(join(converse(X_82),join(one,join(one,one)))) = join(X_82,converse(join(one,join(one,one)))),
inference(subst,[],[refute_0_775:[bind(A,$fot(X_82)),bind(X_5,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1751,plain,
( converse(join(converse(X_82),join(one,join(one,one)))) != join(X_82,converse(join(one,join(one,one))))
| converse(join(one,join(one,one))) != join(one,join(one,one))
| converse(join(converse(X_82),join(one,join(one,one)))) = join(X_82,join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_82),join(one,join(one,one)))),join(X_82,converse(join(one,join(one,one))))) ),[1,1],$fot(join(one,join(one,one)))]]) ).
cnf(refute_0_1752,plain,
( converse(join(converse(X_82),join(one,join(one,one)))) != join(X_82,converse(join(one,join(one,one))))
| converse(join(converse(X_82),join(one,join(one,one)))) = join(X_82,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_948,refute_0_1751]) ).
cnf(refute_0_1753,plain,
converse(join(converse(X_82),join(one,join(one,one)))) = join(X_82,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,join(one,one)))),join(X_82,converse(join(one,join(one,one))))) )],[refute_0_1750,refute_0_1752]) ).
cnf(refute_0_1754,plain,
converse(converse(join(one,join(one,join(one,X_82))))) = join(one,join(one,join(one,X_82))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(one,join(one,join(one,X_82)))))]]) ).
cnf(refute_0_1755,plain,
join(one,converse(join(one,join(one,X_82)))) = converse(join(one,join(one,join(one,X_82)))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(one,join(one,X_82))))]]) ).
cnf(refute_0_1756,plain,
join(one,converse(join(one,X_82))) = converse(join(one,join(one,X_82))),
inference(subst,[],[refute_0_803:[bind(B,$fot(join(one,X_82)))]]) ).
cnf(refute_0_1757,plain,
join(one,converse(X_82)) = converse(join(one,X_82)),
inference(subst,[],[refute_0_803:[bind(B,$fot(X_82))]]) ).
cnf(refute_0_1758,plain,
join(one,join(one,converse(X_82))) = join(one,join(one,converse(X_82))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(X_82))))]]) ).
cnf(refute_0_1759,plain,
( join(one,converse(X_82)) != converse(join(one,X_82))
| join(one,join(one,converse(X_82))) != join(one,join(one,converse(X_82)))
| join(one,join(one,converse(X_82))) = join(one,converse(join(one,X_82))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(X_82))),join(one,join(one,converse(X_82)))) ),[1,1],$fot(converse(join(one,X_82)))]]) ).
cnf(refute_0_1760,plain,
( join(one,converse(X_82)) != converse(join(one,X_82))
| join(one,join(one,converse(X_82))) = join(one,converse(join(one,X_82))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(X_82))),join(one,join(one,converse(X_82)))) )],[refute_0_1758,refute_0_1759]) ).
cnf(refute_0_1761,plain,
join(one,join(one,converse(X_82))) = join(one,converse(join(one,X_82))),
inference(resolve,[$cnf( $equal(join(one,converse(X_82)),converse(join(one,X_82))) )],[refute_0_1757,refute_0_1760]) ).
cnf(refute_0_1762,plain,
( join(one,converse(join(one,X_82))) != converse(join(one,join(one,X_82)))
| join(one,join(one,converse(X_82))) != join(one,converse(join(one,X_82)))
| join(one,join(one,converse(X_82))) = converse(join(one,join(one,X_82))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,converse(X_82))))),bind(Y,$fot(join(one,converse(join(one,X_82))))),bind(Z,$fot(converse(join(one,join(one,X_82)))))]]) ).
cnf(refute_0_1763,plain,
( join(one,converse(join(one,X_82))) != converse(join(one,join(one,X_82)))
| join(one,join(one,converse(X_82))) = converse(join(one,join(one,X_82))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(X_82))),join(one,converse(join(one,X_82)))) )],[refute_0_1761,refute_0_1762]) ).
cnf(refute_0_1764,plain,
join(one,join(one,converse(X_82))) = converse(join(one,join(one,X_82))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,X_82))),converse(join(one,join(one,X_82)))) )],[refute_0_1756,refute_0_1763]) ).
cnf(refute_0_1765,plain,
join(one,join(converse(X_82),one)) = join(one,join(one,converse(X_82))),
inference(subst,[],[refute_0_497:[bind(X_14,$fot(one)),bind(X_15,$fot(converse(X_82))),bind(X_16,$fot(one))]]) ).
cnf(refute_0_1766,plain,
( join(one,join(converse(X_82),one)) != join(one,join(one,converse(X_82)))
| join(one,join(one,converse(X_82))) != converse(join(one,join(one,X_82)))
| join(one,join(converse(X_82),one)) = converse(join(one,join(one,X_82))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(converse(X_82),one)))),bind(Y,$fot(join(one,join(one,converse(X_82))))),bind(Z,$fot(converse(join(one,join(one,X_82)))))]]) ).
cnf(refute_0_1767,plain,
( join(one,join(one,converse(X_82))) != converse(join(one,join(one,X_82)))
| join(one,join(converse(X_82),one)) = converse(join(one,join(one,X_82))) ),
inference(resolve,[$cnf( $equal(join(one,join(converse(X_82),one)),join(one,join(one,converse(X_82)))) )],[refute_0_1765,refute_0_1766]) ).
cnf(refute_0_1768,plain,
join(one,join(converse(X_82),one)) = converse(join(one,join(one,X_82))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(X_82))),converse(join(one,join(one,X_82)))) )],[refute_0_1764,refute_0_1767]) ).
cnf(refute_0_1769,plain,
join(one,join(one,join(converse(X_82),one))) = join(one,join(one,join(converse(X_82),one))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(converse(X_82),one))))]]) ).
cnf(refute_0_1770,plain,
( join(one,join(converse(X_82),one)) != converse(join(one,join(one,X_82)))
| join(one,join(one,join(converse(X_82),one))) != join(one,join(one,join(converse(X_82),one)))
| join(one,join(one,join(converse(X_82),one))) = join(one,converse(join(one,join(one,X_82)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(converse(X_82),one))),join(one,join(one,join(converse(X_82),one)))) ),[1,1],$fot(converse(join(one,join(one,X_82))))]]) ).
cnf(refute_0_1771,plain,
( join(one,join(converse(X_82),one)) != converse(join(one,join(one,X_82)))
| join(one,join(one,join(converse(X_82),one))) = join(one,converse(join(one,join(one,X_82)))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(X_82),one))),join(one,join(one,join(converse(X_82),one)))) )],[refute_0_1769,refute_0_1770]) ).
cnf(refute_0_1772,plain,
join(one,join(one,join(converse(X_82),one))) = join(one,converse(join(one,join(one,X_82)))),
inference(resolve,[$cnf( $equal(join(one,join(converse(X_82),one)),converse(join(one,join(one,X_82)))) )],[refute_0_1768,refute_0_1771]) ).
cnf(refute_0_1773,plain,
( join(one,converse(join(one,join(one,X_82)))) != converse(join(one,join(one,join(one,X_82))))
| join(one,join(one,join(converse(X_82),one))) != join(one,converse(join(one,join(one,X_82))))
| join(one,join(one,join(converse(X_82),one))) = converse(join(one,join(one,join(one,X_82)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,join(converse(X_82),one))))),bind(Y,$fot(join(one,converse(join(one,join(one,X_82)))))),bind(Z,$fot(converse(join(one,join(one,join(one,X_82))))))]]) ).
cnf(refute_0_1774,plain,
( join(one,converse(join(one,join(one,X_82)))) != converse(join(one,join(one,join(one,X_82))))
| join(one,join(one,join(converse(X_82),one))) = converse(join(one,join(one,join(one,X_82)))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(X_82),one))),join(one,converse(join(one,join(one,X_82))))) )],[refute_0_1772,refute_0_1773]) ).
cnf(refute_0_1775,plain,
join(one,join(one,join(converse(X_82),one))) = converse(join(one,join(one,join(one,X_82)))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,X_82)))),converse(join(one,join(one,join(one,X_82))))) )],[refute_0_1755,refute_0_1774]) ).
cnf(refute_0_1776,plain,
converse(join(one,join(one,join(converse(X_82),one)))) = converse(join(one,join(one,join(converse(X_82),one)))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,join(converse(X_82),one)))))]]) ).
cnf(refute_0_1777,plain,
( converse(join(one,join(one,join(converse(X_82),one)))) != converse(join(one,join(one,join(converse(X_82),one))))
| join(one,join(one,join(converse(X_82),one))) != converse(join(one,join(one,join(one,X_82))))
| converse(join(one,join(one,join(converse(X_82),one)))) = converse(converse(join(one,join(one,join(one,X_82))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(converse(X_82),one)))),converse(join(one,join(one,join(converse(X_82),one))))) ),[1,0],$fot(converse(join(one,join(one,join(one,X_82)))))]]) ).
cnf(refute_0_1778,plain,
( join(one,join(one,join(converse(X_82),one))) != converse(join(one,join(one,join(one,X_82))))
| converse(join(one,join(one,join(converse(X_82),one)))) = converse(converse(join(one,join(one,join(one,X_82))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(converse(X_82),one)))),converse(join(one,join(one,join(converse(X_82),one))))) )],[refute_0_1776,refute_0_1777]) ).
cnf(refute_0_1779,plain,
converse(join(one,join(one,join(converse(X_82),one)))) = converse(converse(join(one,join(one,join(one,X_82))))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(converse(X_82),one))),converse(join(one,join(one,join(one,X_82))))) )],[refute_0_1775,refute_0_1778]) ).
cnf(refute_0_1780,plain,
( converse(converse(join(one,join(one,join(one,X_82))))) != join(one,join(one,join(one,X_82)))
| converse(join(one,join(one,join(converse(X_82),one)))) != converse(converse(join(one,join(one,join(one,X_82)))))
| converse(join(one,join(one,join(converse(X_82),one)))) = join(one,join(one,join(one,X_82))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(one,join(one,join(converse(X_82),one)))))),bind(Y,$fot(converse(converse(join(one,join(one,join(one,X_82))))))),bind(Z,$fot(join(one,join(one,join(one,X_82)))))]]) ).
cnf(refute_0_1781,plain,
( converse(converse(join(one,join(one,join(one,X_82))))) != join(one,join(one,join(one,X_82)))
| converse(join(one,join(one,join(converse(X_82),one)))) = join(one,join(one,join(one,X_82))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(converse(X_82),one)))),converse(converse(join(one,join(one,join(one,X_82)))))) )],[refute_0_1779,refute_0_1780]) ).
cnf(refute_0_1782,plain,
converse(join(one,join(one,join(converse(X_82),one)))) = join(one,join(one,join(one,X_82))),
inference(resolve,[$cnf( $equal(converse(converse(join(one,join(one,join(one,X_82))))),join(one,join(one,join(one,X_82)))) )],[refute_0_1754,refute_0_1781]) ).
cnf(refute_0_1783,plain,
converse(join(join(A,B),join(one,one))) = converse(join(one,join(one,join(A,B)))),
inference(subst,[],[refute_0_825:[bind(X_42,$fot(join(A,B)))]]) ).
cnf(refute_0_1784,plain,
join(A,join(B,join(one,one))) = join(join(A,B),join(one,one)),
inference(subst,[],[maddux2_join_associativity_2:[bind(C,$fot(join(one,one)))]]) ).
cnf(refute_0_1785,plain,
( join(A,join(B,join(one,one))) != join(join(A,B),join(one,one))
| join(join(A,B),join(one,one)) = join(A,join(B,join(one,one))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,join(one,one))))),bind(Y,$fot(join(join(A,B),join(one,one))))]]) ).
cnf(refute_0_1786,plain,
join(join(A,B),join(one,one)) = join(A,join(B,join(one,one))),
inference(resolve,[$cnf( $equal(join(A,join(B,join(one,one))),join(join(A,B),join(one,one))) )],[refute_0_1784,refute_0_1785]) ).
cnf(refute_0_1787,plain,
( converse(join(join(A,B),join(one,one))) != converse(join(one,join(one,join(A,B))))
| join(join(A,B),join(one,one)) != join(A,join(B,join(one,one)))
| converse(join(A,join(B,join(one,one)))) = converse(join(one,join(one,join(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(A,B),join(one,one))),converse(join(one,join(one,join(A,B))))) ),[0,0],$fot(join(A,join(B,join(one,one))))]]) ).
cnf(refute_0_1788,plain,
( converse(join(join(A,B),join(one,one))) != converse(join(one,join(one,join(A,B))))
| converse(join(A,join(B,join(one,one)))) = converse(join(one,join(one,join(A,B)))) ),
inference(resolve,[$cnf( $equal(join(join(A,B),join(one,one)),join(A,join(B,join(one,one)))) )],[refute_0_1786,refute_0_1787]) ).
cnf(refute_0_1789,plain,
converse(join(A,join(B,join(one,one)))) = converse(join(one,join(one,join(A,B)))),
inference(resolve,[$cnf( $equal(converse(join(join(A,B),join(one,one))),converse(join(one,join(one,join(A,B))))) )],[refute_0_1783,refute_0_1788]) ).
cnf(refute_0_1790,plain,
converse(join(converse(X_82),join(one,join(one,one)))) = converse(join(one,join(one,join(converse(X_82),one)))),
inference(subst,[],[refute_0_1789:[bind(A,$fot(converse(X_82))),bind(B,$fot(one))]]) ).
cnf(refute_0_1791,plain,
( converse(join(converse(X_82),join(one,join(one,one)))) != converse(join(one,join(one,join(converse(X_82),one))))
| converse(join(one,join(one,join(converse(X_82),one)))) != join(one,join(one,join(one,X_82)))
| converse(join(converse(X_82),join(one,join(one,one)))) = join(one,join(one,join(one,X_82))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(converse(X_82),join(one,join(one,one)))))),bind(Y,$fot(converse(join(one,join(one,join(converse(X_82),one)))))),bind(Z,$fot(join(one,join(one,join(one,X_82)))))]]) ).
cnf(refute_0_1792,plain,
( converse(join(one,join(one,join(converse(X_82),one)))) != join(one,join(one,join(one,X_82)))
| converse(join(converse(X_82),join(one,join(one,one)))) = join(one,join(one,join(one,X_82))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,join(one,one)))),converse(join(one,join(one,join(converse(X_82),one))))) )],[refute_0_1790,refute_0_1791]) ).
cnf(refute_0_1793,plain,
converse(join(converse(X_82),join(one,join(one,one)))) = join(one,join(one,join(one,X_82))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(converse(X_82),one)))),join(one,join(one,join(one,X_82)))) )],[refute_0_1782,refute_0_1792]) ).
cnf(refute_0_1794,plain,
( converse(join(converse(X_82),join(one,join(one,one)))) != join(X_82,join(one,join(one,one)))
| converse(join(converse(X_82),join(one,join(one,one)))) != join(one,join(one,join(one,X_82)))
| join(one,join(one,join(one,X_82))) = join(X_82,join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_82),join(one,join(one,one)))),join(X_82,join(one,join(one,one)))) ),[0],$fot(join(one,join(one,join(one,X_82))))]]) ).
cnf(refute_0_1795,plain,
( converse(join(converse(X_82),join(one,join(one,one)))) != join(X_82,join(one,join(one,one)))
| join(one,join(one,join(one,X_82))) = join(X_82,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,join(one,one)))),join(one,join(one,join(one,X_82)))) )],[refute_0_1793,refute_0_1794]) ).
cnf(refute_0_1796,plain,
join(one,join(one,join(one,X_82))) = join(X_82,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,join(one,one)))),join(X_82,join(one,join(one,one)))) )],[refute_0_1753,refute_0_1795]) ).
cnf(refute_0_1797,plain,
join(X_82,join(one,join(one,one))) = join(X_82,join(one,join(one,one))),
introduced(tautology,[refl,[$fot(join(X_82,join(one,join(one,one))))]]) ).
cnf(refute_0_1798,plain,
( join(X_82,join(one,join(one,one))) != join(X_82,join(one,join(one,one)))
| join(one,join(one,one)) != one
| join(X_82,join(one,join(one,one))) = join(X_82,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_82,join(one,join(one,one))),join(X_82,join(one,join(one,one)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1799,plain,
( join(one,join(one,one)) != one
| join(X_82,join(one,join(one,one))) = join(X_82,one) ),
inference(resolve,[$cnf( $equal(join(X_82,join(one,join(one,one))),join(X_82,join(one,join(one,one)))) )],[refute_0_1797,refute_0_1798]) ).
cnf(refute_0_1800,plain,
join(X_82,join(one,join(one,one))) = join(X_82,one),
inference(resolve,[$cnf( $equal(join(one,join(one,one)),one) )],[refute_0_1668,refute_0_1799]) ).
cnf(refute_0_1801,plain,
( join(X_82,join(one,join(one,one))) != join(X_82,one)
| join(one,join(one,join(one,X_82))) != join(X_82,join(one,join(one,one)))
| join(one,join(one,join(one,X_82))) = join(X_82,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(one,X_82))),join(X_82,join(one,join(one,one)))) ),[1],$fot(join(X_82,one))]]) ).
cnf(refute_0_1802,plain,
( join(one,join(one,join(one,X_82))) != join(X_82,join(one,join(one,one)))
| join(one,join(one,join(one,X_82))) = join(X_82,one) ),
inference(resolve,[$cnf( $equal(join(X_82,join(one,join(one,one))),join(X_82,one)) )],[refute_0_1800,refute_0_1801]) ).
cnf(refute_0_1803,plain,
join(one,join(one,join(one,X_82))) = join(X_82,one),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,X_82))),join(X_82,join(one,join(one,one)))) )],[refute_0_1796,refute_0_1802]) ).
cnf(refute_0_1804,plain,
join(one,join(join(one,join(one,join(X_114,one))),C)) = join(join(one,join(one,join(one,join(X_114,one)))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(one)),bind(B,$fot(join(one,join(one,join(X_114,one)))))]]) ).
cnf(refute_0_1805,plain,
join(A,join(one,join(one,join(one,one)))) = join(join(A,one),join(one,join(one,one))),
inference(subst,[],[maddux2_join_associativity_2:[bind(B,$fot(one)),bind(C,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1806,plain,
( join(A,join(one,join(one,join(one,one)))) != join(join(A,one),join(one,join(one,one)))
| join(one,join(one,join(one,one))) != one
| join(A,one) = join(join(A,one),join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(one,join(one,join(one,one)))),join(join(A,one),join(one,join(one,one)))) ),[0,1],$fot(one)]]) ).
cnf(refute_0_1807,plain,
( join(A,join(one,join(one,join(one,one)))) != join(join(A,one),join(one,join(one,one)))
| join(A,one) = join(join(A,one),join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),one) )],[refute_0_1065,refute_0_1806]) ).
cnf(refute_0_1808,plain,
join(A,one) = join(join(A,one),join(one,join(one,one))),
inference(resolve,[$cnf( $equal(join(A,join(one,join(one,join(one,one)))),join(join(A,one),join(one,join(one,one)))) )],[refute_0_1805,refute_0_1807]) ).
cnf(refute_0_1809,plain,
join(one,join(join(A,B),one)) = join(join(A,B),join(one,one)),
inference(subst,[],[refute_0_842:[bind(X_82,$fot(join(A,B)))]]) ).
cnf(refute_0_1810,plain,
( join(join(A,B),one) != join(A,join(B,one))
| join(one,join(join(A,B),one)) != join(join(A,B),join(one,one))
| join(one,join(A,join(B,one))) = join(join(A,B),join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(A,B),one)),join(join(A,B),join(one,one))) ),[0,1],$fot(join(A,join(B,one)))]]) ).
cnf(refute_0_1811,plain,
( join(one,join(join(A,B),one)) != join(join(A,B),join(one,one))
| join(one,join(A,join(B,one))) = join(join(A,B),join(one,one)) ),
inference(resolve,[$cnf( $equal(join(join(A,B),one),join(A,join(B,one))) )],[refute_0_855,refute_0_1810]) ).
cnf(refute_0_1812,plain,
join(one,join(A,join(B,one))) = join(join(A,B),join(one,one)),
inference(resolve,[$cnf( $equal(join(one,join(join(A,B),one)),join(join(A,B),join(one,one))) )],[refute_0_1809,refute_0_1811]) ).
cnf(refute_0_1813,plain,
join(join(one,one),B) = join(B,join(one,one)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(one,one)))]]) ).
cnf(refute_0_1814,plain,
join(one,join(B,one)) = join(B,join(one,one)),
inference(subst,[],[refute_0_842:[bind(X_82,$fot(B))]]) ).
cnf(refute_0_1815,plain,
( join(one,join(B,one)) != join(B,join(one,one))
| join(B,join(one,one)) = join(one,join(B,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(B,one)))),bind(Y,$fot(join(B,join(one,one))))]]) ).
cnf(refute_0_1816,plain,
join(B,join(one,one)) = join(one,join(B,one)),
inference(resolve,[$cnf( $equal(join(one,join(B,one)),join(B,join(one,one))) )],[refute_0_1814,refute_0_1815]) ).
cnf(refute_0_1817,plain,
( join(B,join(one,one)) != join(one,join(B,one))
| join(join(one,one),B) != join(B,join(one,one))
| join(join(one,one),B) = join(one,join(B,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(one,one),B),join(B,join(one,one))) ),[1],$fot(join(one,join(B,one)))]]) ).
cnf(refute_0_1818,plain,
( join(join(one,one),B) != join(B,join(one,one))
| join(join(one,one),B) = join(one,join(B,one)) ),
inference(resolve,[$cnf( $equal(join(B,join(one,one)),join(one,join(B,one))) )],[refute_0_1816,refute_0_1817]) ).
cnf(refute_0_1819,plain,
join(join(one,one),B) = join(one,join(B,one)),
inference(resolve,[$cnf( $equal(join(join(one,one),B),join(B,join(one,one))) )],[refute_0_1813,refute_0_1818]) ).
cnf(refute_0_1820,plain,
join(join(one,one),B) = join(one,join(one,B)),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(B))]]) ).
cnf(refute_0_1821,plain,
( join(join(one,one),B) != join(one,join(B,one))
| join(join(one,one),B) != join(one,join(one,B))
| join(one,join(one,B)) = join(one,join(B,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(one,one),B),join(one,join(B,one))) ),[0],$fot(join(one,join(one,B)))]]) ).
cnf(refute_0_1822,plain,
( join(join(one,one),B) != join(one,join(B,one))
| join(one,join(one,B)) = join(one,join(B,one)) ),
inference(resolve,[$cnf( $equal(join(join(one,one),B),join(one,join(one,B))) )],[refute_0_1820,refute_0_1821]) ).
cnf(refute_0_1823,plain,
join(one,join(one,B)) = join(one,join(B,one)),
inference(resolve,[$cnf( $equal(join(join(one,one),B),join(one,join(B,one))) )],[refute_0_1819,refute_0_1822]) ).
cnf(refute_0_1824,plain,
( join(one,join(one,B)) != join(one,join(B,one))
| join(one,join(B,one)) = join(one,join(one,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(one,B)))),bind(Y,$fot(join(one,join(B,one))))]]) ).
cnf(refute_0_1825,plain,
join(one,join(B,one)) = join(one,join(one,B)),
inference(resolve,[$cnf( $equal(join(one,join(one,B)),join(one,join(B,one))) )],[refute_0_1823,refute_0_1824]) ).
cnf(refute_0_1826,plain,
join(one,join(join(A,B),one)) = join(one,join(one,join(A,B))),
inference(subst,[],[refute_0_1825:[bind(B,$fot(join(A,B)))]]) ).
cnf(refute_0_1827,plain,
( join(one,join(X_82,one)) != join(X_82,join(one,one))
| join(X_82,join(one,one)) = join(one,join(X_82,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(X_82,one)))),bind(Y,$fot(join(X_82,join(one,one))))]]) ).
cnf(refute_0_1828,plain,
join(X_82,join(one,one)) = join(one,join(X_82,one)),
inference(resolve,[$cnf( $equal(join(one,join(X_82,one)),join(X_82,join(one,one))) )],[refute_0_842,refute_0_1827]) ).
cnf(refute_0_1829,plain,
join(join(A,B),join(one,one)) = join(one,join(join(A,B),one)),
inference(subst,[],[refute_0_1828:[bind(X_82,$fot(join(A,B)))]]) ).
cnf(refute_0_1830,plain,
( join(join(A,B),join(one,one)) != join(one,join(join(A,B),one))
| join(one,join(join(A,B),one)) != join(one,join(one,join(A,B)))
| join(join(A,B),join(one,one)) = join(one,join(one,join(A,B))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(A,B),join(one,one)))),bind(Y,$fot(join(one,join(join(A,B),one)))),bind(Z,$fot(join(one,join(one,join(A,B)))))]]) ).
cnf(refute_0_1831,plain,
( join(one,join(join(A,B),one)) != join(one,join(one,join(A,B)))
| join(join(A,B),join(one,one)) = join(one,join(one,join(A,B))) ),
inference(resolve,[$cnf( $equal(join(join(A,B),join(one,one)),join(one,join(join(A,B),one))) )],[refute_0_1829,refute_0_1830]) ).
cnf(refute_0_1832,plain,
join(join(A,B),join(one,one)) = join(one,join(one,join(A,B))),
inference(resolve,[$cnf( $equal(join(one,join(join(A,B),one)),join(one,join(one,join(A,B)))) )],[refute_0_1826,refute_0_1831]) ).
cnf(refute_0_1833,plain,
( join(join(A,B),join(one,one)) != join(one,join(one,join(A,B)))
| join(one,join(A,join(B,one))) != join(join(A,B),join(one,one))
| join(one,join(A,join(B,one))) = join(one,join(one,join(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(A,join(B,one))),join(join(A,B),join(one,one))) ),[1],$fot(join(one,join(one,join(A,B))))]]) ).
cnf(refute_0_1834,plain,
( join(one,join(A,join(B,one))) != join(join(A,B),join(one,one))
| join(one,join(A,join(B,one))) = join(one,join(one,join(A,B))) ),
inference(resolve,[$cnf( $equal(join(join(A,B),join(one,one)),join(one,join(one,join(A,B)))) )],[refute_0_1832,refute_0_1833]) ).
cnf(refute_0_1835,plain,
join(one,join(A,join(B,one))) = join(one,join(one,join(A,B))),
inference(resolve,[$cnf( $equal(join(one,join(A,join(B,one))),join(join(A,B),join(one,one))) )],[refute_0_1812,refute_0_1834]) ).
cnf(refute_0_1836,plain,
join(one,join(one,join(join(A,one),one))) = join(one,join(one,join(one,join(A,one)))),
inference(subst,[],[refute_0_1835:[bind(A,$fot(one)),bind(B,$fot(join(A,one)))]]) ).
cnf(refute_0_1837,plain,
converse(join(converse(X_82),join(one,one))) = converse(join(one,join(one,converse(X_82)))),
inference(subst,[],[refute_0_825:[bind(X_42,$fot(converse(X_82)))]]) ).
cnf(refute_0_1838,plain,
( converse(join(converse(X_82),join(one,one))) != converse(join(one,join(one,converse(X_82))))
| converse(join(converse(X_82),join(one,one))) != join(X_82,converse(join(one,one)))
| join(X_82,converse(join(one,one))) = converse(join(one,join(one,converse(X_82)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),converse(join(one,join(one,converse(X_82))))) ),[0],$fot(join(X_82,converse(join(one,one))))]]) ).
cnf(refute_0_1839,plain,
( converse(join(converse(X_82),join(one,one))) != converse(join(one,join(one,converse(X_82))))
| join(X_82,converse(join(one,one))) = converse(join(one,join(one,converse(X_82)))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),join(X_82,converse(join(one,one)))) )],[refute_0_776,refute_0_1838]) ).
cnf(refute_0_1840,plain,
join(X_82,converse(join(one,one))) = converse(join(one,join(one,converse(X_82)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_82),join(one,one))),converse(join(one,join(one,converse(X_82))))) )],[refute_0_1837,refute_0_1839]) ).
cnf(refute_0_1841,plain,
join(X_82,converse(join(one,one))) = join(X_82,converse(join(one,one))),
introduced(tautology,[refl,[$fot(join(X_82,converse(join(one,one))))]]) ).
cnf(refute_0_1842,plain,
( converse(join(one,one)) != join(one,one)
| join(X_82,converse(join(one,one))) != join(X_82,converse(join(one,one)))
| join(X_82,converse(join(one,one))) = join(X_82,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_82,converse(join(one,one))),join(X_82,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_0_1843,plain,
( converse(join(one,one)) != join(one,one)
| join(X_82,converse(join(one,one))) = join(X_82,join(one,one)) ),
inference(resolve,[$cnf( $equal(join(X_82,converse(join(one,one))),join(X_82,converse(join(one,one)))) )],[refute_0_1841,refute_0_1842]) ).
cnf(refute_0_1844,plain,
join(X_82,converse(join(one,one))) = join(X_82,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_694,refute_0_1843]) ).
cnf(refute_0_1845,plain,
( join(X_82,converse(join(one,one))) != converse(join(one,join(one,converse(X_82))))
| join(X_82,converse(join(one,one))) != join(X_82,join(one,one))
| join(X_82,join(one,one)) = converse(join(one,join(one,converse(X_82)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_82,converse(join(one,one))),converse(join(one,join(one,converse(X_82))))) ),[0],$fot(join(X_82,join(one,one)))]]) ).
cnf(refute_0_1846,plain,
( join(X_82,converse(join(one,one))) != converse(join(one,join(one,converse(X_82))))
| join(X_82,join(one,one)) = converse(join(one,join(one,converse(X_82)))) ),
inference(resolve,[$cnf( $equal(join(X_82,converse(join(one,one))),join(X_82,join(one,one))) )],[refute_0_1844,refute_0_1845]) ).
cnf(refute_0_1847,plain,
join(converse(one),X_82) = join(converse(one),X_82),
introduced(tautology,[refl,[$fot(join(converse(one),X_82))]]) ).
cnf(refute_0_1848,plain,
( converse(one) != one
| join(converse(one),X_82) != join(converse(one),X_82)
| join(converse(one),X_82) = join(one,X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),X_82),join(converse(one),X_82)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1849,plain,
( converse(one) != one
| join(converse(one),X_82) = join(one,X_82) ),
inference(resolve,[$cnf( $equal(join(converse(one),X_82),join(converse(one),X_82)) )],[refute_0_1847,refute_0_1848]) ).
cnf(refute_0_1850,plain,
join(converse(one),X_82) = join(one,X_82),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_183,refute_0_1849]) ).
cnf(refute_0_1851,plain,
join(one,join(converse(one),X_82)) = join(one,join(converse(one),X_82)),
introduced(tautology,[refl,[$fot(join(one,join(converse(one),X_82)))]]) ).
cnf(refute_0_1852,plain,
( join(converse(one),X_82) != join(one,X_82)
| join(one,join(converse(one),X_82)) != join(one,join(converse(one),X_82))
| join(one,join(converse(one),X_82)) = join(one,join(one,X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(one),X_82)),join(one,join(converse(one),X_82))) ),[1,1],$fot(join(one,X_82))]]) ).
cnf(refute_0_1853,plain,
( join(converse(one),X_82) != join(one,X_82)
| join(one,join(converse(one),X_82)) = join(one,join(one,X_82)) ),
inference(resolve,[$cnf( $equal(join(one,join(converse(one),X_82)),join(one,join(converse(one),X_82))) )],[refute_0_1851,refute_0_1852]) ).
cnf(refute_0_1854,plain,
join(one,join(converse(one),X_82)) = join(one,join(one,X_82)),
inference(resolve,[$cnf( $equal(join(converse(one),X_82),join(one,X_82)) )],[refute_0_1850,refute_0_1853]) ).
cnf(refute_0_1855,plain,
join(converse(join(one,one)),X_82) = join(one,join(converse(one),X_82)),
inference(subst,[],[refute_0_1435:[bind(C,$fot(X_82)),bind(X_28,$fot(one))]]) ).
cnf(refute_0_1856,plain,
converse(join(A,join(X_42,converse(X_41)))) = join(converse(A),converse(join(X_42,converse(X_41)))),
inference(subst,[],[converse_additivity_9:[bind(B,$fot(join(X_42,converse(X_41))))]]) ).
cnf(refute_0_1857,plain,
converse(join(X_42,converse(X_41))) = join(converse(X_42),X_41),
inference(subst,[],[refute_0_797:[bind(A,$fot(X_41)),bind(X_4,$fot(X_42))]]) ).
cnf(refute_0_1858,plain,
( converse(join(A,join(X_42,converse(X_41)))) != join(converse(A),converse(join(X_42,converse(X_41))))
| converse(join(X_42,converse(X_41))) != join(converse(X_42),X_41)
| converse(join(A,join(X_42,converse(X_41)))) = join(converse(A),join(converse(X_42),X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(A,join(X_42,converse(X_41)))),join(converse(A),converse(join(X_42,converse(X_41))))) ),[1,1],$fot(join(converse(X_42),X_41))]]) ).
cnf(refute_0_1859,plain,
( converse(join(A,join(X_42,converse(X_41)))) != join(converse(A),converse(join(X_42,converse(X_41))))
| converse(join(A,join(X_42,converse(X_41)))) = join(converse(A),join(converse(X_42),X_41)) ),
inference(resolve,[$cnf( $equal(converse(join(X_42,converse(X_41))),join(converse(X_42),X_41)) )],[refute_0_1857,refute_0_1858]) ).
cnf(refute_0_1860,plain,
converse(join(A,join(X_42,converse(X_41)))) = join(converse(A),join(converse(X_42),X_41)),
inference(resolve,[$cnf( $equal(converse(join(A,join(X_42,converse(X_41)))),join(converse(A),converse(join(X_42,converse(X_41))))) )],[refute_0_1856,refute_0_1859]) ).
cnf(refute_0_1861,plain,
join(converse(A),join(converse(B),X_16)) = join(join(converse(A),converse(B)),X_16),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(converse(A))),bind(B,$fot(converse(B))),bind(C,$fot(X_16))]]) ).
cnf(refute_0_1862,plain,
( join(converse(A),converse(B)) != converse(join(A,B))
| join(converse(A),join(converse(B),X_16)) != join(join(converse(A),converse(B)),X_16)
| join(converse(A),join(converse(B),X_16)) = join(converse(join(A,B)),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(A),join(converse(B),X_16)),join(join(converse(A),converse(B)),X_16)) ),[1,0],$fot(converse(join(A,B)))]]) ).
cnf(refute_0_1863,plain,
( join(converse(A),join(converse(B),X_16)) != join(join(converse(A),converse(B)),X_16)
| join(converse(A),join(converse(B),X_16)) = join(converse(join(A,B)),X_16) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),converse(join(A,B))) )],[refute_0_1099,refute_0_1862]) ).
cnf(refute_0_1864,plain,
join(converse(A),join(converse(B),X_16)) = join(converse(join(A,B)),X_16),
inference(resolve,[$cnf( $equal(join(converse(A),join(converse(B),X_16)),join(join(converse(A),converse(B)),X_16)) )],[refute_0_1861,refute_0_1863]) ).
cnf(refute_0_1865,plain,
join(converse(A),join(converse(X_42),X_41)) = join(converse(join(A,X_42)),X_41),
inference(subst,[],[refute_0_1864:[bind(B,$fot(X_42)),bind(X_16,$fot(X_41))]]) ).
cnf(refute_0_1866,plain,
( converse(join(A,join(X_42,converse(X_41)))) != join(converse(A),join(converse(X_42),X_41))
| join(converse(A),join(converse(X_42),X_41)) != join(converse(join(A,X_42)),X_41)
| converse(join(A,join(X_42,converse(X_41)))) = join(converse(join(A,X_42)),X_41) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(A,join(X_42,converse(X_41)))),join(converse(join(A,X_42)),X_41)) ),[0],$fot(join(converse(A),join(converse(X_42),X_41)))]]) ).
cnf(refute_0_1867,plain,
( converse(join(A,join(X_42,converse(X_41)))) != join(converse(A),join(converse(X_42),X_41))
| converse(join(A,join(X_42,converse(X_41)))) = join(converse(join(A,X_42)),X_41) ),
inference(resolve,[$cnf( $equal(join(converse(A),join(converse(X_42),X_41)),join(converse(join(A,X_42)),X_41)) )],[refute_0_1865,refute_0_1866]) ).
cnf(refute_0_1868,plain,
converse(join(A,join(X_42,converse(X_41)))) = join(converse(join(A,X_42)),X_41),
inference(resolve,[$cnf( $equal(converse(join(A,join(X_42,converse(X_41)))),join(converse(A),join(converse(X_42),X_41))) )],[refute_0_1860,refute_0_1867]) ).
cnf(refute_0_1869,plain,
converse(join(one,join(one,converse(X_82)))) = join(converse(join(one,one)),X_82),
inference(subst,[],[refute_0_1868:[bind(A,$fot(one)),bind(X_41,$fot(X_82)),bind(X_42,$fot(one))]]) ).
cnf(refute_0_1870,plain,
( converse(join(one,join(one,converse(X_82)))) != join(converse(join(one,one)),X_82)
| join(converse(join(one,one)),X_82) != join(one,join(converse(one),X_82))
| converse(join(one,join(one,converse(X_82)))) = join(one,join(converse(one),X_82)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(one,join(one,converse(X_82)))))),bind(Y,$fot(join(converse(join(one,one)),X_82))),bind(Z,$fot(join(one,join(converse(one),X_82))))]]) ).
cnf(refute_0_1871,plain,
( join(converse(join(one,one)),X_82) != join(one,join(converse(one),X_82))
| converse(join(one,join(one,converse(X_82)))) = join(one,join(converse(one),X_82)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,converse(X_82)))),join(converse(join(one,one)),X_82)) )],[refute_0_1869,refute_0_1870]) ).
cnf(refute_0_1872,plain,
converse(join(one,join(one,converse(X_82)))) = join(one,join(converse(one),X_82)),
inference(resolve,[$cnf( $equal(join(converse(join(one,one)),X_82),join(one,join(converse(one),X_82))) )],[refute_0_1855,refute_0_1871]) ).
cnf(refute_0_1873,plain,
( converse(join(one,join(one,converse(X_82)))) != join(one,join(converse(one),X_82))
| join(one,join(converse(one),X_82)) != join(one,join(one,X_82))
| converse(join(one,join(one,converse(X_82)))) = join(one,join(one,X_82)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(join(one,join(one,converse(X_82)))))),bind(Y,$fot(join(one,join(converse(one),X_82)))),bind(Z,$fot(join(one,join(one,X_82))))]]) ).
cnf(refute_0_1874,plain,
( join(one,join(converse(one),X_82)) != join(one,join(one,X_82))
| converse(join(one,join(one,converse(X_82)))) = join(one,join(one,X_82)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,converse(X_82)))),join(one,join(converse(one),X_82))) )],[refute_0_1872,refute_0_1873]) ).
cnf(refute_0_1875,plain,
converse(join(one,join(one,converse(X_82)))) = join(one,join(one,X_82)),
inference(resolve,[$cnf( $equal(join(one,join(converse(one),X_82)),join(one,join(one,X_82))) )],[refute_0_1854,refute_0_1874]) ).
cnf(refute_0_1876,plain,
( converse(join(one,join(one,converse(X_82)))) != join(one,join(one,X_82))
| join(X_82,join(one,one)) != converse(join(one,join(one,converse(X_82))))
| join(X_82,join(one,one)) = join(one,join(one,X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_82,join(one,one)),converse(join(one,join(one,converse(X_82))))) ),[1],$fot(join(one,join(one,X_82)))]]) ).
cnf(refute_0_1877,plain,
( join(X_82,join(one,one)) != converse(join(one,join(one,converse(X_82))))
| join(X_82,join(one,one)) = join(one,join(one,X_82)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,converse(X_82)))),join(one,join(one,X_82))) )],[refute_0_1875,refute_0_1876]) ).
cnf(refute_0_1878,plain,
( join(X_82,converse(join(one,one))) != converse(join(one,join(one,converse(X_82))))
| join(X_82,join(one,one)) = join(one,join(one,X_82)) ),
inference(resolve,[$cnf( $equal(join(X_82,join(one,one)),converse(join(one,join(one,converse(X_82))))) )],[refute_0_1846,refute_0_1877]) ).
cnf(refute_0_1879,plain,
join(X_82,join(one,one)) = join(one,join(one,X_82)),
inference(resolve,[$cnf( $equal(join(X_82,converse(join(one,one))),converse(join(one,join(one,converse(X_82))))) )],[refute_0_1840,refute_0_1878]) ).
cnf(refute_0_1880,plain,
join(join(X_82,one),join(one,one)) = join(one,join(one,join(X_82,one))),
inference(subst,[],[refute_0_1879:[bind(X_82,$fot(join(X_82,one)))]]) ).
cnf(refute_0_1881,plain,
( join(join(X_82,one),join(one,one)) != join(one,join(one,join(X_82,one)))
| join(one,join(X_82,one)) != join(X_82,join(one,one))
| join(join(X_82,one),join(one,one)) = join(one,join(X_82,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_82,one),join(one,one)),join(one,join(one,join(X_82,one)))) ),[1,1],$fot(join(X_82,join(one,one)))]]) ).
cnf(refute_0_1882,plain,
( join(join(X_82,one),join(one,one)) != join(one,join(one,join(X_82,one)))
| join(join(X_82,one),join(one,one)) = join(one,join(X_82,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(one,join(X_82,one)),join(X_82,join(one,one))) )],[refute_0_842,refute_0_1881]) ).
cnf(refute_0_1883,plain,
join(join(X_82,one),join(one,one)) = join(one,join(X_82,join(one,one))),
inference(resolve,[$cnf( $equal(join(join(X_82,one),join(one,one)),join(one,join(one,join(X_82,one)))) )],[refute_0_1880,refute_0_1882]) ).
cnf(refute_0_1884,plain,
( join(join(X_82,one),join(one,one)) != join(one,join(X_82,join(one,one)))
| join(join(X_82,one),join(one,one)) != join(one,join(one,join(X_82,one)))
| join(one,join(one,join(X_82,one))) = join(one,join(X_82,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_82,one),join(one,one)),join(one,join(X_82,join(one,one)))) ),[0],$fot(join(one,join(one,join(X_82,one))))]]) ).
cnf(refute_0_1885,plain,
( join(join(X_82,one),join(one,one)) != join(one,join(X_82,join(one,one)))
| join(one,join(one,join(X_82,one))) = join(one,join(X_82,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(join(X_82,one),join(one,one)),join(one,join(one,join(X_82,one)))) )],[refute_0_1880,refute_0_1884]) ).
cnf(refute_0_1886,plain,
join(one,join(one,join(X_82,one))) = join(one,join(X_82,join(one,one))),
inference(resolve,[$cnf( $equal(join(join(X_82,one),join(one,one)),join(one,join(X_82,join(one,one)))) )],[refute_0_1883,refute_0_1885]) ).
cnf(refute_0_1887,plain,
( join(one,join(one,join(X_82,one))) != join(one,join(X_82,join(one,one)))
| join(one,join(X_82,join(one,one))) = join(one,join(one,join(X_82,one))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(one,join(X_82,one))))),bind(Y,$fot(join(one,join(X_82,join(one,one)))))]]) ).
cnf(refute_0_1888,plain,
join(one,join(X_82,join(one,one))) = join(one,join(one,join(X_82,one))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(X_82,one))),join(one,join(X_82,join(one,one)))) )],[refute_0_1886,refute_0_1887]) ).
cnf(refute_0_1889,plain,
join(one,join(join(A,one),join(one,one))) = join(one,join(one,join(join(A,one),one))),
inference(subst,[],[refute_0_1888:[bind(X_82,$fot(join(A,one)))]]) ).
cnf(refute_0_1890,plain,
( join(one,join(join(A,one),join(one,one))) != join(one,join(one,join(join(A,one),one)))
| join(one,join(one,join(join(A,one),one))) != join(one,join(one,join(one,join(A,one))))
| join(one,join(join(A,one),join(one,one))) = join(one,join(one,join(one,join(A,one)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(join(A,one),join(one,one))))),bind(Y,$fot(join(one,join(one,join(join(A,one),one))))),bind(Z,$fot(join(one,join(one,join(one,join(A,one))))))]]) ).
cnf(refute_0_1891,plain,
( join(one,join(one,join(join(A,one),one))) != join(one,join(one,join(one,join(A,one))))
| join(one,join(join(A,one),join(one,one))) = join(one,join(one,join(one,join(A,one)))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),join(one,one))),join(one,join(one,join(join(A,one),one)))) )],[refute_0_1889,refute_0_1890]) ).
cnf(refute_0_1892,plain,
join(one,join(join(A,one),join(one,one))) = join(one,join(one,join(one,join(A,one)))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(A,one),one))),join(one,join(one,join(one,join(A,one))))) )],[refute_0_1836,refute_0_1891]) ).
cnf(refute_0_1893,plain,
join(A,join(one,join(one,X_86))) = join(join(A,one),join(one,X_86)),
inference(subst,[],[maddux2_join_associativity_2:[bind(B,$fot(one)),bind(C,$fot(join(one,X_86)))]]) ).
cnf(refute_0_1894,plain,
join(X_86,join(one,one)) = join(one,join(one,X_86)),
inference(subst,[],[refute_0_1879:[bind(X_82,$fot(X_86))]]) ).
cnf(refute_0_1895,plain,
( join(X_86,join(one,one)) != join(one,join(one,X_86))
| join(one,join(one,X_86)) = join(X_86,join(one,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_86,join(one,one)))),bind(Y,$fot(join(one,join(one,X_86))))]]) ).
cnf(refute_0_1896,plain,
join(one,join(one,X_86)) = join(X_86,join(one,one)),
inference(resolve,[$cnf( $equal(join(X_86,join(one,one)),join(one,join(one,X_86))) )],[refute_0_1894,refute_0_1895]) ).
cnf(refute_0_1897,plain,
( join(A,join(one,join(one,X_86))) != join(join(A,one),join(one,X_86))
| join(one,join(one,X_86)) != join(X_86,join(one,one))
| join(A,join(X_86,join(one,one))) = join(join(A,one),join(one,X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(one,join(one,X_86))),join(join(A,one),join(one,X_86))) ),[0,1],$fot(join(X_86,join(one,one)))]]) ).
cnf(refute_0_1898,plain,
( join(A,join(one,join(one,X_86))) != join(join(A,one),join(one,X_86))
| join(A,join(X_86,join(one,one))) = join(join(A,one),join(one,X_86)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,X_86)),join(X_86,join(one,one))) )],[refute_0_1896,refute_0_1897]) ).
cnf(refute_0_1899,plain,
join(A,join(X_86,join(one,one))) = join(join(A,one),join(one,X_86)),
inference(resolve,[$cnf( $equal(join(A,join(one,join(one,X_86))),join(join(A,one),join(one,X_86))) )],[refute_0_1893,refute_0_1898]) ).
cnf(refute_0_1900,plain,
join(join(A,one),X_86) = join(A,join(one,X_86)),
inference(subst,[],[refute_0_86:[bind(B,$fot(one)),bind(C,$fot(X_86))]]) ).
cnf(refute_0_1901,plain,
join(one,join(join(A,one),X_86)) = join(one,join(join(A,one),X_86)),
introduced(tautology,[refl,[$fot(join(one,join(join(A,one),X_86)))]]) ).
cnf(refute_0_1902,plain,
( join(join(A,one),X_86) != join(A,join(one,X_86))
| join(one,join(join(A,one),X_86)) != join(one,join(join(A,one),X_86))
| join(one,join(join(A,one),X_86)) = join(one,join(A,join(one,X_86))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(A,one),X_86)),join(one,join(join(A,one),X_86))) ),[1,1],$fot(join(A,join(one,X_86)))]]) ).
cnf(refute_0_1903,plain,
( join(join(A,one),X_86) != join(A,join(one,X_86))
| join(one,join(join(A,one),X_86)) = join(one,join(A,join(one,X_86))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),X_86)),join(one,join(join(A,one),X_86))) )],[refute_0_1901,refute_0_1902]) ).
cnf(refute_0_1904,plain,
join(one,join(join(A,one),X_86)) = join(one,join(A,join(one,X_86))),
inference(resolve,[$cnf( $equal(join(join(A,one),X_86),join(A,join(one,X_86))) )],[refute_0_1900,refute_0_1903]) ).
cnf(refute_0_1905,plain,
join(join(A,one),join(one,X_86)) = join(one,join(join(A,one),X_86)),
inference(subst,[],[refute_0_815:[bind(X_14,$fot(one)),bind(X_15,$fot(join(A,one))),bind(X_16,$fot(X_86))]]) ).
cnf(refute_0_1906,plain,
( join(join(A,one),join(one,X_86)) != join(one,join(join(A,one),X_86))
| join(one,join(join(A,one),X_86)) != join(one,join(A,join(one,X_86)))
| join(join(A,one),join(one,X_86)) = join(one,join(A,join(one,X_86))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(A,one),join(one,X_86)))),bind(Y,$fot(join(one,join(join(A,one),X_86)))),bind(Z,$fot(join(one,join(A,join(one,X_86)))))]]) ).
cnf(refute_0_1907,plain,
( join(one,join(join(A,one),X_86)) != join(one,join(A,join(one,X_86)))
| join(join(A,one),join(one,X_86)) = join(one,join(A,join(one,X_86))) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,X_86)),join(one,join(join(A,one),X_86))) )],[refute_0_1905,refute_0_1906]) ).
cnf(refute_0_1908,plain,
join(join(A,one),join(one,X_86)) = join(one,join(A,join(one,X_86))),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),X_86)),join(one,join(A,join(one,X_86)))) )],[refute_0_1904,refute_0_1907]) ).
cnf(refute_0_1909,plain,
( join(A,join(X_86,join(one,one))) != join(join(A,one),join(one,X_86))
| join(join(A,one),join(one,X_86)) != join(one,join(A,join(one,X_86)))
| join(A,join(X_86,join(one,one))) = join(one,join(A,join(one,X_86))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_86,join(one,one))),join(one,join(A,join(one,X_86)))) ),[0],$fot(join(join(A,one),join(one,X_86)))]]) ).
cnf(refute_0_1910,plain,
( join(A,join(X_86,join(one,one))) != join(join(A,one),join(one,X_86))
| join(A,join(X_86,join(one,one))) = join(one,join(A,join(one,X_86))) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,X_86)),join(one,join(A,join(one,X_86)))) )],[refute_0_1908,refute_0_1909]) ).
cnf(refute_0_1911,plain,
join(A,join(X_86,join(one,one))) = join(one,join(A,join(one,X_86))),
inference(resolve,[$cnf( $equal(join(A,join(X_86,join(one,one))),join(join(A,one),join(one,X_86))) )],[refute_0_1899,refute_0_1910]) ).
cnf(refute_0_1912,plain,
join(join(A,one),join(one,join(one,one))) = join(one,join(join(A,one),join(one,one))),
inference(subst,[],[refute_0_1911:[bind(A,$fot(join(A,one))),bind(X_86,$fot(one))]]) ).
cnf(refute_0_1913,plain,
( join(join(A,one),join(one,join(one,one))) != join(one,join(join(A,one),join(one,one)))
| join(one,join(join(A,one),join(one,one))) != join(one,join(one,join(one,join(A,one))))
| join(join(A,one),join(one,join(one,one))) = join(one,join(one,join(one,join(A,one)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(A,one),join(one,join(one,one))))),bind(Y,$fot(join(one,join(join(A,one),join(one,one))))),bind(Z,$fot(join(one,join(one,join(one,join(A,one))))))]]) ).
cnf(refute_0_1914,plain,
( join(one,join(join(A,one),join(one,one))) != join(one,join(one,join(one,join(A,one))))
| join(join(A,one),join(one,join(one,one))) = join(one,join(one,join(one,join(A,one)))) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,join(one,one))),join(one,join(join(A,one),join(one,one)))) )],[refute_0_1912,refute_0_1913]) ).
cnf(refute_0_1915,plain,
join(join(A,one),join(one,join(one,one))) = join(one,join(one,join(one,join(A,one)))),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),join(one,one))),join(one,join(one,join(one,join(A,one))))) )],[refute_0_1892,refute_0_1914]) ).
cnf(refute_0_1916,plain,
( join(A,one) != join(join(A,one),join(one,join(one,one)))
| join(join(A,one),join(one,join(one,one))) != join(one,join(one,join(one,join(A,one))))
| join(A,one) = join(one,join(one,join(one,join(A,one)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,one),join(one,join(one,join(one,join(A,one))))) ),[0],$fot(join(join(A,one),join(one,join(one,one))))]]) ).
cnf(refute_0_1917,plain,
( join(A,one) != join(join(A,one),join(one,join(one,one)))
| join(A,one) = join(one,join(one,join(one,join(A,one)))) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,join(one,one))),join(one,join(one,join(one,join(A,one))))) )],[refute_0_1915,refute_0_1916]) ).
cnf(refute_0_1918,plain,
join(A,one) = join(one,join(one,join(one,join(A,one)))),
inference(resolve,[$cnf( $equal(join(A,one),join(join(A,one),join(one,join(one,one)))) )],[refute_0_1808,refute_0_1917]) ).
cnf(refute_0_1919,plain,
join(X_114,one) = join(one,join(one,join(one,join(X_114,one)))),
inference(subst,[],[refute_0_1918:[bind(A,$fot(X_114))]]) ).
cnf(refute_0_1920,plain,
( join(X_114,one) != join(one,join(one,join(one,join(X_114,one))))
| join(one,join(one,join(one,join(X_114,one)))) = join(X_114,one) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_114,one))),bind(Y,$fot(join(one,join(one,join(one,join(X_114,one))))))]]) ).
cnf(refute_0_1921,plain,
join(one,join(one,join(one,join(X_114,one)))) = join(X_114,one),
inference(resolve,[$cnf( $equal(join(X_114,one),join(one,join(one,join(one,join(X_114,one))))) )],[refute_0_1919,refute_0_1920]) ).
cnf(refute_0_1922,plain,
( join(one,join(join(one,join(one,join(X_114,one))),C)) != join(join(one,join(one,join(one,join(X_114,one)))),C)
| join(one,join(one,join(one,join(X_114,one)))) != join(X_114,one)
| join(one,join(join(one,join(one,join(X_114,one))),C)) = join(join(X_114,one),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,join(one,join(X_114,one))),C)),join(join(one,join(one,join(one,join(X_114,one)))),C)) ),[1,0],$fot(join(X_114,one))]]) ).
cnf(refute_0_1923,plain,
( join(one,join(join(one,join(one,join(X_114,one))),C)) != join(join(one,join(one,join(one,join(X_114,one)))),C)
| join(one,join(join(one,join(one,join(X_114,one))),C)) = join(join(X_114,one),C) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(X_114,one)))),join(X_114,one)) )],[refute_0_1921,refute_0_1922]) ).
cnf(refute_0_1924,plain,
join(one,join(join(one,join(one,join(X_114,one))),C)) = join(join(X_114,one),C),
inference(resolve,[$cnf( $equal(join(one,join(join(one,join(one,join(X_114,one))),C)),join(join(one,join(one,join(one,join(X_114,one)))),C)) )],[refute_0_1804,refute_0_1923]) ).
cnf(refute_0_1925,plain,
join(join(X_114,one),C) = join(X_114,join(one,C)),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_114)),bind(B,$fot(one))]]) ).
cnf(refute_0_1926,plain,
join(one,join(join(X_114,one),C)) = join(one,join(join(X_114,one),C)),
introduced(tautology,[refl,[$fot(join(one,join(join(X_114,one),C)))]]) ).
cnf(refute_0_1927,plain,
( join(join(X_114,one),C) != join(X_114,join(one,C))
| join(one,join(join(X_114,one),C)) != join(one,join(join(X_114,one),C))
| join(one,join(join(X_114,one),C)) = join(one,join(X_114,join(one,C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(X_114,one),C)),join(one,join(join(X_114,one),C))) ),[1,1],$fot(join(X_114,join(one,C)))]]) ).
cnf(refute_0_1928,plain,
( join(join(X_114,one),C) != join(X_114,join(one,C))
| join(one,join(join(X_114,one),C)) = join(one,join(X_114,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(X_114,one),C)),join(one,join(join(X_114,one),C))) )],[refute_0_1926,refute_0_1927]) ).
cnf(refute_0_1929,plain,
join(one,join(join(X_114,one),C)) = join(one,join(X_114,join(one,C))),
inference(resolve,[$cnf( $equal(join(join(X_114,one),C),join(X_114,join(one,C))) )],[refute_0_1925,refute_0_1928]) ).
cnf(refute_0_1930,plain,
join(join(one,join(X_114,one)),C) = join(one,join(join(X_114,one),C)),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(join(X_114,one)))]]) ).
cnf(refute_0_1931,plain,
( join(join(one,join(X_114,one)),C) != join(one,join(join(X_114,one),C))
| join(one,join(join(X_114,one),C)) != join(one,join(X_114,join(one,C)))
| join(join(one,join(X_114,one)),C) = join(one,join(X_114,join(one,C))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,join(X_114,one)),C))),bind(Y,$fot(join(one,join(join(X_114,one),C)))),bind(Z,$fot(join(one,join(X_114,join(one,C)))))]]) ).
cnf(refute_0_1932,plain,
( join(one,join(join(X_114,one),C)) != join(one,join(X_114,join(one,C)))
| join(join(one,join(X_114,one)),C) = join(one,join(X_114,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(X_114,one)),C),join(one,join(join(X_114,one),C))) )],[refute_0_1930,refute_0_1931]) ).
cnf(refute_0_1933,plain,
join(join(one,join(X_114,one)),C) = join(one,join(X_114,join(one,C))),
inference(resolve,[$cnf( $equal(join(one,join(join(X_114,one),C)),join(one,join(X_114,join(one,C)))) )],[refute_0_1929,refute_0_1932]) ).
cnf(refute_0_1934,plain,
join(one,join(join(one,join(X_114,one)),C)) = join(one,join(join(one,join(X_114,one)),C)),
introduced(tautology,[refl,[$fot(join(one,join(join(one,join(X_114,one)),C)))]]) ).
cnf(refute_0_1935,plain,
( join(join(one,join(X_114,one)),C) != join(one,join(X_114,join(one,C)))
| join(one,join(join(one,join(X_114,one)),C)) != join(one,join(join(one,join(X_114,one)),C))
| join(one,join(join(one,join(X_114,one)),C)) = join(one,join(one,join(X_114,join(one,C)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,join(X_114,one)),C)),join(one,join(join(one,join(X_114,one)),C))) ),[1,1],$fot(join(one,join(X_114,join(one,C))))]]) ).
cnf(refute_0_1936,plain,
( join(join(one,join(X_114,one)),C) != join(one,join(X_114,join(one,C)))
| join(one,join(join(one,join(X_114,one)),C)) = join(one,join(one,join(X_114,join(one,C)))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,join(X_114,one)),C)),join(one,join(join(one,join(X_114,one)),C))) )],[refute_0_1934,refute_0_1935]) ).
cnf(refute_0_1937,plain,
join(one,join(join(one,join(X_114,one)),C)) = join(one,join(one,join(X_114,join(one,C)))),
inference(resolve,[$cnf( $equal(join(join(one,join(X_114,one)),C),join(one,join(X_114,join(one,C)))) )],[refute_0_1933,refute_0_1936]) ).
cnf(refute_0_1938,plain,
join(join(one,join(one,join(X_114,one))),C) = join(one,join(join(one,join(X_114,one)),C)),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(join(one,join(X_114,one))))]]) ).
cnf(refute_0_1939,plain,
( join(join(one,join(one,join(X_114,one))),C) != join(one,join(join(one,join(X_114,one)),C))
| join(one,join(join(one,join(X_114,one)),C)) != join(one,join(one,join(X_114,join(one,C))))
| join(join(one,join(one,join(X_114,one))),C) = join(one,join(one,join(X_114,join(one,C)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,join(one,join(X_114,one))),C))),bind(Y,$fot(join(one,join(join(one,join(X_114,one)),C)))),bind(Z,$fot(join(one,join(one,join(X_114,join(one,C))))))]]) ).
cnf(refute_0_1940,plain,
( join(one,join(join(one,join(X_114,one)),C)) != join(one,join(one,join(X_114,join(one,C))))
| join(join(one,join(one,join(X_114,one))),C) = join(one,join(one,join(X_114,join(one,C)))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,join(X_114,one))),C),join(one,join(join(one,join(X_114,one)),C))) )],[refute_0_1938,refute_0_1939]) ).
cnf(refute_0_1941,plain,
join(join(one,join(one,join(X_114,one))),C) = join(one,join(one,join(X_114,join(one,C)))),
inference(resolve,[$cnf( $equal(join(one,join(join(one,join(X_114,one)),C)),join(one,join(one,join(X_114,join(one,C))))) )],[refute_0_1937,refute_0_1940]) ).
cnf(refute_0_1942,plain,
join(one,join(join(one,join(one,join(X_114,one))),C)) = join(one,join(join(one,join(one,join(X_114,one))),C)),
introduced(tautology,[refl,[$fot(join(one,join(join(one,join(one,join(X_114,one))),C)))]]) ).
cnf(refute_0_1943,plain,
( join(join(one,join(one,join(X_114,one))),C) != join(one,join(one,join(X_114,join(one,C))))
| join(one,join(join(one,join(one,join(X_114,one))),C)) != join(one,join(join(one,join(one,join(X_114,one))),C))
| join(one,join(join(one,join(one,join(X_114,one))),C)) = join(one,join(one,join(one,join(X_114,join(one,C))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,join(one,join(X_114,one))),C)),join(one,join(join(one,join(one,join(X_114,one))),C))) ),[1,1],$fot(join(one,join(one,join(X_114,join(one,C)))))]]) ).
cnf(refute_0_1944,plain,
( join(join(one,join(one,join(X_114,one))),C) != join(one,join(one,join(X_114,join(one,C))))
| join(one,join(join(one,join(one,join(X_114,one))),C)) = join(one,join(one,join(one,join(X_114,join(one,C))))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,join(one,join(X_114,one))),C)),join(one,join(join(one,join(one,join(X_114,one))),C))) )],[refute_0_1942,refute_0_1943]) ).
cnf(refute_0_1945,plain,
join(one,join(join(one,join(one,join(X_114,one))),C)) = join(one,join(one,join(one,join(X_114,join(one,C))))),
inference(resolve,[$cnf( $equal(join(join(one,join(one,join(X_114,one))),C),join(one,join(one,join(X_114,join(one,C))))) )],[refute_0_1941,refute_0_1944]) ).
cnf(refute_0_1946,plain,
( join(one,join(join(one,join(one,join(X_114,one))),C)) != join(join(X_114,one),C)
| join(one,join(join(one,join(one,join(X_114,one))),C)) != join(one,join(one,join(one,join(X_114,join(one,C)))))
| join(one,join(one,join(one,join(X_114,join(one,C))))) = join(join(X_114,one),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,join(one,join(X_114,one))),C)),join(join(X_114,one),C)) ),[0],$fot(join(one,join(one,join(one,join(X_114,join(one,C))))))]]) ).
cnf(refute_0_1947,plain,
( join(one,join(join(one,join(one,join(X_114,one))),C)) != join(join(X_114,one),C)
| join(one,join(one,join(one,join(X_114,join(one,C))))) = join(join(X_114,one),C) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,join(one,join(X_114,one))),C)),join(one,join(one,join(one,join(X_114,join(one,C)))))) )],[refute_0_1945,refute_0_1946]) ).
cnf(refute_0_1948,plain,
( join(join(X_114,one),C) != join(X_114,join(one,C))
| join(one,join(one,join(one,join(X_114,join(one,C))))) != join(join(X_114,one),C)
| join(one,join(one,join(one,join(X_114,join(one,C))))) = join(X_114,join(one,C)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(one,join(X_114,join(one,C))))),join(join(X_114,one),C)) ),[1],$fot(join(X_114,join(one,C)))]]) ).
cnf(refute_0_1949,plain,
( join(one,join(one,join(one,join(X_114,join(one,C))))) != join(join(X_114,one),C)
| join(one,join(one,join(one,join(X_114,join(one,C))))) = join(X_114,join(one,C)) ),
inference(resolve,[$cnf( $equal(join(join(X_114,one),C),join(X_114,join(one,C))) )],[refute_0_1925,refute_0_1948]) ).
cnf(refute_0_1950,plain,
( join(one,join(join(one,join(one,join(X_114,one))),C)) != join(join(X_114,one),C)
| join(one,join(one,join(one,join(X_114,join(one,C))))) = join(X_114,join(one,C)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(X_114,join(one,C))))),join(join(X_114,one),C)) )],[refute_0_1947,refute_0_1949]) ).
cnf(refute_0_1951,plain,
join(one,join(one,join(one,join(X_114,join(one,C))))) = join(X_114,join(one,C)),
inference(resolve,[$cnf( $equal(join(one,join(join(one,join(one,join(X_114,one))),C)),join(join(X_114,one),C)) )],[refute_0_1924,refute_0_1950]) ).
cnf(refute_0_1952,plain,
join(A,join(one,join(one,join(one,join(X_114,one))))) = join(join(A,one),join(one,join(one,join(X_114,one)))),
inference(subst,[],[maddux2_join_associativity_2:[bind(B,$fot(one)),bind(C,$fot(join(one,join(one,join(X_114,one)))))]]) ).
cnf(refute_0_1953,plain,
( join(A,join(one,join(one,join(one,join(X_114,one))))) != join(join(A,one),join(one,join(one,join(X_114,one))))
| join(one,join(one,join(one,join(X_114,one)))) != join(X_114,one)
| join(A,join(X_114,one)) = join(join(A,one),join(one,join(one,join(X_114,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(one,join(one,join(one,join(X_114,one))))),join(join(A,one),join(one,join(one,join(X_114,one))))) ),[0,1],$fot(join(X_114,one))]]) ).
cnf(refute_0_1954,plain,
( join(A,join(one,join(one,join(one,join(X_114,one))))) != join(join(A,one),join(one,join(one,join(X_114,one))))
| join(A,join(X_114,one)) = join(join(A,one),join(one,join(one,join(X_114,one)))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(X_114,one)))),join(X_114,one)) )],[refute_0_1921,refute_0_1953]) ).
cnf(refute_0_1955,plain,
join(A,join(X_114,one)) = join(join(A,one),join(one,join(one,join(X_114,one)))),
inference(resolve,[$cnf( $equal(join(A,join(one,join(one,join(one,join(X_114,one))))),join(join(A,one),join(one,join(one,join(X_114,one))))) )],[refute_0_1952,refute_0_1954]) ).
cnf(refute_0_1956,plain,
join(one,join(one,join(one,join(A,join(one,X_114))))) = join(A,join(one,X_114)),
inference(subst,[],[refute_0_1951:[bind(C,$fot(X_114)),bind(X_114,$fot(A))]]) ).
cnf(refute_0_1957,plain,
join(join(A,one),X_114) = join(A,join(one,X_114)),
inference(subst,[],[refute_0_86:[bind(B,$fot(one)),bind(C,$fot(X_114))]]) ).
cnf(refute_0_1958,plain,
join(one,join(join(A,one),X_114)) = join(one,join(join(A,one),X_114)),
introduced(tautology,[refl,[$fot(join(one,join(join(A,one),X_114)))]]) ).
cnf(refute_0_1959,plain,
( join(join(A,one),X_114) != join(A,join(one,X_114))
| join(one,join(join(A,one),X_114)) != join(one,join(join(A,one),X_114))
| join(one,join(join(A,one),X_114)) = join(one,join(A,join(one,X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(A,one),X_114)),join(one,join(join(A,one),X_114))) ),[1,1],$fot(join(A,join(one,X_114)))]]) ).
cnf(refute_0_1960,plain,
( join(join(A,one),X_114) != join(A,join(one,X_114))
| join(one,join(join(A,one),X_114)) = join(one,join(A,join(one,X_114))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),X_114)),join(one,join(join(A,one),X_114))) )],[refute_0_1958,refute_0_1959]) ).
cnf(refute_0_1961,plain,
join(one,join(join(A,one),X_114)) = join(one,join(A,join(one,X_114))),
inference(resolve,[$cnf( $equal(join(join(A,one),X_114),join(A,join(one,X_114))) )],[refute_0_1957,refute_0_1960]) ).
cnf(refute_0_1962,plain,
join(one,join(one,join(join(A,one),X_114))) = join(one,join(one,join(join(A,one),X_114))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(join(A,one),X_114))))]]) ).
cnf(refute_0_1963,plain,
( join(one,join(join(A,one),X_114)) != join(one,join(A,join(one,X_114)))
| join(one,join(one,join(join(A,one),X_114))) != join(one,join(one,join(join(A,one),X_114)))
| join(one,join(one,join(join(A,one),X_114))) = join(one,join(one,join(A,join(one,X_114)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(join(A,one),X_114))),join(one,join(one,join(join(A,one),X_114)))) ),[1,1],$fot(join(one,join(A,join(one,X_114))))]]) ).
cnf(refute_0_1964,plain,
( join(one,join(join(A,one),X_114)) != join(one,join(A,join(one,X_114)))
| join(one,join(one,join(join(A,one),X_114))) = join(one,join(one,join(A,join(one,X_114)))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(A,one),X_114))),join(one,join(one,join(join(A,one),X_114)))) )],[refute_0_1962,refute_0_1963]) ).
cnf(refute_0_1965,plain,
join(one,join(one,join(join(A,one),X_114))) = join(one,join(one,join(A,join(one,X_114)))),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),X_114)),join(one,join(A,join(one,X_114)))) )],[refute_0_1961,refute_0_1964]) ).
cnf(refute_0_1966,plain,
join(one,join(join(A,one),join(X_114,one))) = join(one,join(one,join(join(A,one),X_114))),
inference(subst,[],[refute_0_1835:[bind(A,$fot(join(A,one))),bind(B,$fot(X_114))]]) ).
cnf(refute_0_1967,plain,
( join(one,join(join(A,one),join(X_114,one))) != join(one,join(one,join(join(A,one),X_114)))
| join(one,join(one,join(join(A,one),X_114))) != join(one,join(one,join(A,join(one,X_114))))
| join(one,join(join(A,one),join(X_114,one))) = join(one,join(one,join(A,join(one,X_114)))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(join(A,one),join(X_114,one))))),bind(Y,$fot(join(one,join(one,join(join(A,one),X_114))))),bind(Z,$fot(join(one,join(one,join(A,join(one,X_114))))))]]) ).
cnf(refute_0_1968,plain,
( join(one,join(one,join(join(A,one),X_114))) != join(one,join(one,join(A,join(one,X_114))))
| join(one,join(join(A,one),join(X_114,one))) = join(one,join(one,join(A,join(one,X_114)))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),join(X_114,one))),join(one,join(one,join(join(A,one),X_114)))) )],[refute_0_1966,refute_0_1967]) ).
cnf(refute_0_1969,plain,
join(one,join(join(A,one),join(X_114,one))) = join(one,join(one,join(A,join(one,X_114)))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(A,one),X_114))),join(one,join(one,join(A,join(one,X_114))))) )],[refute_0_1965,refute_0_1968]) ).
cnf(refute_0_1970,plain,
join(one,join(one,join(join(A,one),join(X_114,one)))) = join(one,join(one,join(join(A,one),join(X_114,one)))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(join(A,one),join(X_114,one)))))]]) ).
cnf(refute_0_1971,plain,
( join(one,join(join(A,one),join(X_114,one))) != join(one,join(one,join(A,join(one,X_114))))
| join(one,join(one,join(join(A,one),join(X_114,one)))) != join(one,join(one,join(join(A,one),join(X_114,one))))
| join(one,join(one,join(join(A,one),join(X_114,one)))) = join(one,join(one,join(one,join(A,join(one,X_114))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(join(A,one),join(X_114,one)))),join(one,join(one,join(join(A,one),join(X_114,one))))) ),[1,1],$fot(join(one,join(one,join(A,join(one,X_114)))))]]) ).
cnf(refute_0_1972,plain,
( join(one,join(join(A,one),join(X_114,one))) != join(one,join(one,join(A,join(one,X_114))))
| join(one,join(one,join(join(A,one),join(X_114,one)))) = join(one,join(one,join(one,join(A,join(one,X_114))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(A,one),join(X_114,one)))),join(one,join(one,join(join(A,one),join(X_114,one))))) )],[refute_0_1970,refute_0_1971]) ).
cnf(refute_0_1973,plain,
join(one,join(one,join(join(A,one),join(X_114,one)))) = join(one,join(one,join(one,join(A,join(one,X_114))))),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),join(X_114,one))),join(one,join(one,join(A,join(one,X_114))))) )],[refute_0_1969,refute_0_1972]) ).
cnf(refute_0_1974,plain,
( join(one,join(one,join(join(A,one),join(X_114,one)))) != join(one,join(one,join(one,join(A,join(one,X_114)))))
| join(one,join(one,join(one,join(A,join(one,X_114))))) != join(A,join(one,X_114))
| join(one,join(one,join(join(A,one),join(X_114,one)))) = join(A,join(one,X_114)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,join(join(A,one),join(X_114,one)))))),bind(Y,$fot(join(one,join(one,join(one,join(A,join(one,X_114))))))),bind(Z,$fot(join(A,join(one,X_114))))]]) ).
cnf(refute_0_1975,plain,
( join(one,join(one,join(one,join(A,join(one,X_114))))) != join(A,join(one,X_114))
| join(one,join(one,join(join(A,one),join(X_114,one)))) = join(A,join(one,X_114)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(A,one),join(X_114,one)))),join(one,join(one,join(one,join(A,join(one,X_114)))))) )],[refute_0_1973,refute_0_1974]) ).
cnf(refute_0_1976,plain,
join(one,join(one,join(join(A,one),join(X_114,one)))) = join(A,join(one,X_114)),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(A,join(one,X_114))))),join(A,join(one,X_114))) )],[refute_0_1956,refute_0_1975]) ).
cnf(refute_0_1977,plain,
join(A,join(join(one,one),C)) = join(join(A,join(one,one)),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(B,$fot(join(one,one)))]]) ).
cnf(refute_0_1978,plain,
join(A,join(one,one)) = join(one,join(one,A)),
inference(subst,[],[refute_0_1879:[bind(X_82,$fot(A))]]) ).
cnf(refute_0_1979,plain,
( join(A,join(join(one,one),C)) != join(join(A,join(one,one)),C)
| join(A,join(one,one)) != join(one,join(one,A))
| join(A,join(join(one,one),C)) = join(join(one,join(one,A)),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(one,one),C)),join(join(A,join(one,one)),C)) ),[1,0],$fot(join(one,join(one,A)))]]) ).
cnf(refute_0_1980,plain,
( join(A,join(join(one,one),C)) != join(join(A,join(one,one)),C)
| join(A,join(join(one,one),C)) = join(join(one,join(one,A)),C) ),
inference(resolve,[$cnf( $equal(join(A,join(one,one)),join(one,join(one,A))) )],[refute_0_1978,refute_0_1979]) ).
cnf(refute_0_1981,plain,
join(A,join(join(one,one),C)) = join(join(one,join(one,A)),C),
inference(resolve,[$cnf( $equal(join(A,join(join(one,one),C)),join(join(A,join(one,one)),C)) )],[refute_0_1977,refute_0_1980]) ).
cnf(refute_0_1982,plain,
join(join(one,one),C) = join(one,join(one,C)),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(one))]]) ).
cnf(refute_0_1983,plain,
join(A,join(join(one,one),C)) = join(A,join(join(one,one),C)),
introduced(tautology,[refl,[$fot(join(A,join(join(one,one),C)))]]) ).
cnf(refute_0_1984,plain,
( join(A,join(join(one,one),C)) != join(A,join(join(one,one),C))
| join(join(one,one),C) != join(one,join(one,C))
| join(A,join(join(one,one),C)) = join(A,join(one,join(one,C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(one,one),C)),join(A,join(join(one,one),C))) ),[1,1],$fot(join(one,join(one,C)))]]) ).
cnf(refute_0_1985,plain,
( join(join(one,one),C) != join(one,join(one,C))
| join(A,join(join(one,one),C)) = join(A,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(A,join(join(one,one),C)),join(A,join(join(one,one),C))) )],[refute_0_1983,refute_0_1984]) ).
cnf(refute_0_1986,plain,
join(A,join(join(one,one),C)) = join(A,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(join(one,one),C),join(one,join(one,C))) )],[refute_0_1982,refute_0_1985]) ).
cnf(refute_0_1987,plain,
( join(A,join(join(one,one),C)) != join(A,join(one,join(one,C)))
| join(A,join(join(one,one),C)) != join(join(one,join(one,A)),C)
| join(A,join(one,join(one,C))) = join(join(one,join(one,A)),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(one,one),C)),join(join(one,join(one,A)),C)) ),[0],$fot(join(A,join(one,join(one,C))))]]) ).
cnf(refute_0_1988,plain,
( join(A,join(join(one,one),C)) != join(join(one,join(one,A)),C)
| join(A,join(one,join(one,C))) = join(join(one,join(one,A)),C) ),
inference(resolve,[$cnf( $equal(join(A,join(join(one,one),C)),join(A,join(one,join(one,C)))) )],[refute_0_1986,refute_0_1987]) ).
cnf(refute_0_1989,plain,
join(join(one,A),C) = join(one,join(A,C)),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(A))]]) ).
cnf(refute_0_1990,plain,
join(one,join(join(one,A),C)) = join(one,join(join(one,A),C)),
introduced(tautology,[refl,[$fot(join(one,join(join(one,A),C)))]]) ).
cnf(refute_0_1991,plain,
( join(join(one,A),C) != join(one,join(A,C))
| join(one,join(join(one,A),C)) != join(one,join(join(one,A),C))
| join(one,join(join(one,A),C)) = join(one,join(one,join(A,C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,A),C)),join(one,join(join(one,A),C))) ),[1,1],$fot(join(one,join(A,C)))]]) ).
cnf(refute_0_1992,plain,
( join(join(one,A),C) != join(one,join(A,C))
| join(one,join(join(one,A),C)) = join(one,join(one,join(A,C))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,A),C)),join(one,join(join(one,A),C))) )],[refute_0_1990,refute_0_1991]) ).
cnf(refute_0_1993,plain,
join(one,join(join(one,A),C)) = join(one,join(one,join(A,C))),
inference(resolve,[$cnf( $equal(join(join(one,A),C),join(one,join(A,C))) )],[refute_0_1989,refute_0_1992]) ).
cnf(refute_0_1994,plain,
join(join(one,join(one,A)),C) = join(one,join(join(one,A),C)),
inference(subst,[],[refute_0_86:[bind(A,$fot(one)),bind(B,$fot(join(one,A)))]]) ).
cnf(refute_0_1995,plain,
( join(join(one,join(one,A)),C) != join(one,join(join(one,A),C))
| join(one,join(join(one,A),C)) != join(one,join(one,join(A,C)))
| join(join(one,join(one,A)),C) = join(one,join(one,join(A,C))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(one,join(one,A)),C))),bind(Y,$fot(join(one,join(join(one,A),C)))),bind(Z,$fot(join(one,join(one,join(A,C)))))]]) ).
cnf(refute_0_1996,plain,
( join(one,join(join(one,A),C)) != join(one,join(one,join(A,C)))
| join(join(one,join(one,A)),C) = join(one,join(one,join(A,C))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,A)),C),join(one,join(join(one,A),C))) )],[refute_0_1994,refute_0_1995]) ).
cnf(refute_0_1997,plain,
join(join(one,join(one,A)),C) = join(one,join(one,join(A,C))),
inference(resolve,[$cnf( $equal(join(one,join(join(one,A),C)),join(one,join(one,join(A,C)))) )],[refute_0_1993,refute_0_1996]) ).
cnf(refute_0_1998,plain,
( join(A,join(one,join(one,C))) != join(join(one,join(one,A)),C)
| join(join(one,join(one,A)),C) != join(one,join(one,join(A,C)))
| join(A,join(one,join(one,C))) = join(one,join(one,join(A,C))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(one,join(one,C))),join(one,join(one,join(A,C)))) ),[0],$fot(join(join(one,join(one,A)),C))]]) ).
cnf(refute_0_1999,plain,
( join(A,join(one,join(one,C))) != join(join(one,join(one,A)),C)
| join(A,join(one,join(one,C))) = join(one,join(one,join(A,C))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,A)),C),join(one,join(one,join(A,C)))) )],[refute_0_1997,refute_0_1998]) ).
cnf(refute_0_2000,plain,
( join(A,join(join(one,one),C)) != join(join(one,join(one,A)),C)
| join(A,join(one,join(one,C))) = join(one,join(one,join(A,C))) ),
inference(resolve,[$cnf( $equal(join(A,join(one,join(one,C))),join(join(one,join(one,A)),C)) )],[refute_0_1988,refute_0_1999]) ).
cnf(refute_0_2001,plain,
join(A,join(one,join(one,C))) = join(one,join(one,join(A,C))),
inference(resolve,[$cnf( $equal(join(A,join(join(one,one),C)),join(join(one,join(one,A)),C)) )],[refute_0_1981,refute_0_2000]) ).
cnf(refute_0_2002,plain,
join(join(A,one),join(one,join(one,join(X_114,one)))) = join(one,join(one,join(join(A,one),join(X_114,one)))),
inference(subst,[],[refute_0_2001:[bind(A,$fot(join(A,one))),bind(C,$fot(join(X_114,one)))]]) ).
cnf(refute_0_2003,plain,
( join(join(A,one),join(one,join(one,join(X_114,one)))) != join(one,join(one,join(join(A,one),join(X_114,one))))
| join(one,join(one,join(join(A,one),join(X_114,one)))) != join(A,join(one,X_114))
| join(join(A,one),join(one,join(one,join(X_114,one)))) = join(A,join(one,X_114)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(A,one),join(one,join(one,join(X_114,one)))))),bind(Y,$fot(join(one,join(one,join(join(A,one),join(X_114,one)))))),bind(Z,$fot(join(A,join(one,X_114))))]]) ).
cnf(refute_0_2004,plain,
( join(one,join(one,join(join(A,one),join(X_114,one)))) != join(A,join(one,X_114))
| join(join(A,one),join(one,join(one,join(X_114,one)))) = join(A,join(one,X_114)) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,join(one,join(X_114,one)))),join(one,join(one,join(join(A,one),join(X_114,one))))) )],[refute_0_2002,refute_0_2003]) ).
cnf(refute_0_2005,plain,
join(join(A,one),join(one,join(one,join(X_114,one)))) = join(A,join(one,X_114)),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(A,one),join(X_114,one)))),join(A,join(one,X_114))) )],[refute_0_1976,refute_0_2004]) ).
cnf(refute_0_2006,plain,
( join(A,join(X_114,one)) != join(join(A,one),join(one,join(one,join(X_114,one))))
| join(join(A,one),join(one,join(one,join(X_114,one)))) != join(A,join(one,X_114))
| join(A,join(X_114,one)) = join(A,join(one,X_114)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_114,one)),join(A,join(one,X_114))) ),[0],$fot(join(join(A,one),join(one,join(one,join(X_114,one)))))]]) ).
cnf(refute_0_2007,plain,
( join(A,join(X_114,one)) != join(join(A,one),join(one,join(one,join(X_114,one))))
| join(A,join(X_114,one)) = join(A,join(one,X_114)) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,join(one,join(X_114,one)))),join(A,join(one,X_114))) )],[refute_0_2005,refute_0_2006]) ).
cnf(refute_0_2008,plain,
join(A,join(X_114,one)) = join(A,join(one,X_114)),
inference(resolve,[$cnf( $equal(join(A,join(X_114,one)),join(join(A,one),join(one,join(one,join(X_114,one))))) )],[refute_0_1955,refute_0_2007]) ).
cnf(refute_0_2009,plain,
join(X_114,join(join(one,C),one)) = join(X_114,join(one,join(one,C))),
inference(subst,[],[refute_0_2008:[bind(A,$fot(X_114)),bind(X_114,$fot(join(one,C)))]]) ).
cnf(refute_0_2010,plain,
join(join(X_114,join(one,C)),one) = join(X_114,join(join(one,C),one)),
inference(subst,[],[refute_0_86:[bind(A,$fot(X_114)),bind(B,$fot(join(one,C))),bind(C,$fot(one))]]) ).
cnf(refute_0_2011,plain,
( join(X_114,join(join(one,C),one)) != join(X_114,join(one,join(one,C)))
| join(join(X_114,join(one,C)),one) != join(X_114,join(join(one,C),one))
| join(join(X_114,join(one,C)),one) = join(X_114,join(one,join(one,C))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(join(X_114,join(one,C)),one))),bind(Y,$fot(join(X_114,join(join(one,C),one)))),bind(Z,$fot(join(X_114,join(one,join(one,C)))))]]) ).
cnf(refute_0_2012,plain,
( join(X_114,join(join(one,C),one)) != join(X_114,join(one,join(one,C)))
| join(join(X_114,join(one,C)),one) = join(X_114,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(join(X_114,join(one,C)),one),join(X_114,join(join(one,C),one))) )],[refute_0_2010,refute_0_2011]) ).
cnf(refute_0_2013,plain,
join(join(X_114,join(one,C)),one) = join(X_114,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(X_114,join(join(one,C),one)),join(X_114,join(one,join(one,C)))) )],[refute_0_2009,refute_0_2012]) ).
cnf(refute_0_2014,plain,
join(one,join(one,join(one,join(X_114,join(one,C))))) = join(join(X_114,join(one,C)),one),
inference(subst,[],[refute_0_1803:[bind(X_82,$fot(join(X_114,join(one,C))))]]) ).
cnf(refute_0_2015,plain,
( join(join(X_114,join(one,C)),one) != join(X_114,join(one,join(one,C)))
| join(one,join(one,join(one,join(X_114,join(one,C))))) != join(join(X_114,join(one,C)),one)
| join(one,join(one,join(one,join(X_114,join(one,C))))) = join(X_114,join(one,join(one,C))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,join(one,join(X_114,join(one,C))))))),bind(Y,$fot(join(join(X_114,join(one,C)),one))),bind(Z,$fot(join(X_114,join(one,join(one,C)))))]]) ).
cnf(refute_0_2016,plain,
( join(join(X_114,join(one,C)),one) != join(X_114,join(one,join(one,C)))
| join(one,join(one,join(one,join(X_114,join(one,C))))) = join(X_114,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(X_114,join(one,C))))),join(join(X_114,join(one,C)),one)) )],[refute_0_2014,refute_0_2015]) ).
cnf(refute_0_2017,plain,
join(one,join(one,join(one,join(X_114,join(one,C))))) = join(X_114,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(join(X_114,join(one,C)),one),join(X_114,join(one,join(one,C)))) )],[refute_0_2013,refute_0_2016]) ).
cnf(refute_0_2018,plain,
( join(one,join(one,join(one,join(X_114,join(one,C))))) != join(X_114,join(one,C))
| join(one,join(one,join(one,join(X_114,join(one,C))))) != join(X_114,join(one,join(one,C)))
| join(X_114,join(one,join(one,C))) = join(X_114,join(one,C)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(one,join(X_114,join(one,C))))),join(X_114,join(one,C))) ),[0],$fot(join(X_114,join(one,join(one,C))))]]) ).
cnf(refute_0_2019,plain,
( join(one,join(one,join(one,join(X_114,join(one,C))))) != join(X_114,join(one,C))
| join(X_114,join(one,join(one,C))) = join(X_114,join(one,C)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(X_114,join(one,C))))),join(X_114,join(one,join(one,C)))) )],[refute_0_2017,refute_0_2018]) ).
cnf(refute_0_2020,plain,
join(X_114,join(one,join(one,C))) = join(X_114,join(one,C)),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(X_114,join(one,C))))),join(X_114,join(one,C))) )],[refute_0_1951,refute_0_2019]) ).
cnf(refute_0_2021,plain,
join(one,join(one,join(one,X_82))) = join(one,join(one,X_82)),
inference(subst,[],[refute_0_2020:[bind(C,$fot(X_82)),bind(X_114,$fot(one))]]) ).
cnf(refute_0_2022,plain,
( join(one,join(one,join(one,X_82))) != join(X_82,one)
| join(one,join(one,join(one,X_82))) != join(one,join(one,X_82))
| join(one,join(one,X_82)) = join(X_82,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(one,X_82))),join(X_82,one)) ),[0],$fot(join(one,join(one,X_82)))]]) ).
cnf(refute_0_2023,plain,
( join(one,join(one,join(one,X_82))) != join(X_82,one)
| join(one,join(one,X_82)) = join(X_82,one) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,X_82))),join(one,join(one,X_82))) )],[refute_0_2021,refute_0_2022]) ).
cnf(refute_0_2024,plain,
join(one,join(one,X_82)) = join(X_82,one),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,X_82))),join(X_82,one)) )],[refute_0_1803,refute_0_2023]) ).
cnf(refute_0_2025,plain,
join(one,join(one,join(top,A))) = join(join(top,A),one),
inference(subst,[],[refute_0_2024:[bind(X_82,$fot(join(top,A)))]]) ).
cnf(refute_0_2026,plain,
( join(join(top,A),one) != join(one,join(top,A))
| join(one,join(one,join(top,A))) != join(join(top,A),one)
| join(one,join(one,join(top,A))) = join(one,join(top,A)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(one,join(one,join(top,A))))),bind(Y,$fot(join(join(top,A),one))),bind(Z,$fot(join(one,join(top,A))))]]) ).
cnf(refute_0_2027,plain,
( join(join(top,A),one) != join(one,join(top,A))
| join(one,join(one,join(top,A))) = join(one,join(top,A)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(top,A))),join(join(top,A),one)) )],[refute_0_2025,refute_0_2026]) ).
cnf(refute_0_2028,plain,
join(one,join(one,join(top,A))) = join(one,join(top,A)),
inference(resolve,[$cnf( $equal(join(join(top,A),one),join(one,join(top,A))) )],[refute_0_1749,refute_0_2027]) ).
cnf(refute_0_2029,plain,
( join(one,join(one,join(top,A))) != join(one,join(top,A))
| join(one,join(one,join(top,A))) != join(top,A)
| join(one,join(top,A)) = join(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(top,A))),join(top,A)) ),[0],$fot(join(one,join(top,A)))]]) ).
cnf(refute_0_2030,plain,
( join(one,join(one,join(top,A))) != join(top,A)
| join(one,join(top,A)) = join(top,A) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(top,A))),join(one,join(top,A))) )],[refute_0_2028,refute_0_2029]) ).
cnf(refute_0_2031,plain,
join(one,join(top,A)) = join(top,A),
inference(resolve,[$cnf( $equal(join(one,join(one,join(top,A))),join(top,A)) )],[refute_0_1735,refute_0_2030]) ).
cnf(refute_0_2032,plain,
join(one,join(top,X_123)) = join(top,X_123),
inference(subst,[],[refute_0_2031:[bind(A,$fot(X_123))]]) ).
cnf(refute_0_2033,plain,
composition(join(one,join(top,X_123)),complement(composition(top,top))) = composition(join(one,join(top,X_123)),complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(join(one,join(top,X_123)),complement(composition(top,top))))]]) ).
cnf(refute_0_2034,plain,
( composition(join(one,join(top,X_123)),complement(composition(top,top))) != composition(join(one,join(top,X_123)),complement(composition(top,top)))
| join(one,join(top,X_123)) != join(top,X_123)
| composition(join(one,join(top,X_123)),complement(composition(top,top))) = composition(join(top,X_123),complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(top,X_123)),complement(composition(top,top))),composition(join(one,join(top,X_123)),complement(composition(top,top)))) ),[1,0],$fot(join(top,X_123))]]) ).
cnf(refute_0_2035,plain,
( join(one,join(top,X_123)) != join(top,X_123)
| composition(join(one,join(top,X_123)),complement(composition(top,top))) = composition(join(top,X_123),complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(top,X_123)),complement(composition(top,top))),composition(join(one,join(top,X_123)),complement(composition(top,top)))) )],[refute_0_2033,refute_0_2034]) ).
cnf(refute_0_2036,plain,
composition(join(one,join(top,X_123)),complement(composition(top,top))) = composition(join(top,X_123),complement(composition(top,top))),
inference(resolve,[$cnf( $equal(join(one,join(top,X_123)),join(top,X_123)) )],[refute_0_2032,refute_0_2035]) ).
cnf(refute_0_2037,plain,
( composition(join(one,join(top,X_123)),complement(composition(top,top))) != composition(join(top,X_123),complement(composition(top,top)))
| composition(join(top,X_123),complement(composition(top,top))) != composition(X_123,complement(composition(top,top)))
| composition(join(one,join(top,X_123)),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(one,join(top,X_123)),complement(composition(top,top))))),bind(Y,$fot(composition(join(top,X_123),complement(composition(top,top))))),bind(Z,$fot(composition(X_123,complement(composition(top,top)))))]]) ).
cnf(refute_0_2038,plain,
( composition(join(top,X_123),complement(composition(top,top))) != composition(X_123,complement(composition(top,top)))
| composition(join(one,join(top,X_123)),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(top,X_123)),complement(composition(top,top))),composition(join(top,X_123),complement(composition(top,top)))) )],[refute_0_2036,refute_0_2037]) ).
cnf(refute_0_2039,plain,
composition(join(one,join(top,X_123)),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(join(top,X_123),complement(composition(top,top))),composition(X_123,complement(composition(top,top)))) )],[refute_0_1371,refute_0_2038]) ).
cnf(refute_0_2040,plain,
composition(join(join(top,X_123),one),complement(composition(top,top))) = composition(join(one,join(top,X_123)),complement(composition(top,top))),
inference(subst,[],[refute_0_874:[bind(X_110,$fot(join(top,X_123))),bind(X_111,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_2041,plain,
( composition(join(join(top,X_123),one),complement(composition(top,top))) != composition(join(one,join(top,X_123)),complement(composition(top,top)))
| composition(join(one,join(top,X_123)),complement(composition(top,top))) != composition(X_123,complement(composition(top,top)))
| composition(join(join(top,X_123),one),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(join(top,X_123),one),complement(composition(top,top))))),bind(Y,$fot(composition(join(one,join(top,X_123)),complement(composition(top,top))))),bind(Z,$fot(composition(X_123,complement(composition(top,top)))))]]) ).
cnf(refute_0_2042,plain,
( composition(join(one,join(top,X_123)),complement(composition(top,top))) != composition(X_123,complement(composition(top,top)))
| composition(join(join(top,X_123),one),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(join(top,X_123),one),complement(composition(top,top))),composition(join(one,join(top,X_123)),complement(composition(top,top)))) )],[refute_0_2040,refute_0_2041]) ).
cnf(refute_0_2043,plain,
composition(join(join(top,X_123),one),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(join(one,join(top,X_123)),complement(composition(top,top))),composition(X_123,complement(composition(top,top)))) )],[refute_0_2039,refute_0_2042]) ).
cnf(refute_0_2044,plain,
( composition(join(join(top,X_123),one),complement(composition(top,top))) != composition(X_123,complement(composition(top,top)))
| composition(join(join(top,X_123),one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))
| composition(X_123,complement(composition(top,top))) = join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(top,X_123),one),complement(composition(top,top))),join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))) ),[0],$fot(composition(X_123,complement(composition(top,top))))]]) ).
cnf(refute_0_2045,plain,
( composition(join(join(top,X_123),one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))
| composition(X_123,complement(composition(top,top))) = join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(join(join(top,X_123),one),complement(composition(top,top))),composition(X_123,complement(composition(top,top)))) )],[refute_0_2043,refute_0_2044]) ).
cnf(refute_0_2046,plain,
join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))) = composition(join(X_123,one),complement(composition(top,top))),
inference(subst,[],[refute_0_868:[bind(X_104,$fot(X_123)),bind(X_106,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_2047,plain,
( composition(X_123,complement(composition(top,top))) != join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))
| join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))) != composition(join(X_123,one),complement(composition(top,top)))
| composition(X_123,complement(composition(top,top))) = composition(join(X_123,one),complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(X_123,complement(composition(top,top))),composition(join(X_123,one),complement(composition(top,top)))) ),[0],$fot(join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))))]]) ).
cnf(refute_0_2048,plain,
( composition(X_123,complement(composition(top,top))) != join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))
| composition(X_123,complement(composition(top,top))) = composition(join(X_123,one),complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),composition(X_123,complement(composition(top,top)))),composition(join(X_123,one),complement(composition(top,top)))) )],[refute_0_2046,refute_0_2047]) ).
cnf(refute_0_2049,plain,
( composition(join(join(top,X_123),one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))
| composition(X_123,complement(composition(top,top))) = composition(join(X_123,one),complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(X_123,complement(composition(top,top))),join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))) )],[refute_0_2045,refute_0_2048]) ).
cnf(refute_0_2050,plain,
composition(X_123,complement(composition(top,top))) = composition(join(X_123,one),complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(join(join(top,X_123),one),complement(composition(top,top))),join(complement(composition(top,top)),composition(X_123,complement(composition(top,top))))) )],[refute_0_1374,refute_0_2049]) ).
cnf(refute_0_2051,plain,
( composition(X_123,complement(composition(top,top))) != composition(join(X_123,one),complement(composition(top,top)))
| composition(join(X_123,one),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(X_123,complement(composition(top,top))))),bind(Y,$fot(composition(join(X_123,one),complement(composition(top,top)))))]]) ).
cnf(refute_0_2052,plain,
composition(join(X_123,one),complement(composition(top,top))) = composition(X_123,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(X_123,complement(composition(top,top))),composition(join(X_123,one),complement(composition(top,top)))) )],[refute_0_2050,refute_0_2051]) ).
cnf(refute_0_2053,plain,
composition(join(top,one),complement(composition(top,top))) = composition(top,complement(composition(top,top))),
inference(subst,[],[refute_0_2052:[bind(X_123,$fot(top))]]) ).
cnf(refute_0_2054,plain,
( composition(join(top,one),complement(composition(top,top))) != composition(top,complement(composition(top,top)))
| composition(top,complement(composition(top,top))) != zero
| composition(join(top,one),complement(composition(top,top))) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(top,one),complement(composition(top,top))))),bind(Y,$fot(composition(top,complement(composition(top,top))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_2055,plain,
( composition(top,complement(composition(top,top))) != zero
| composition(join(top,one),complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_0_2053,refute_0_2054]) ).
cnf(refute_0_2056,plain,
composition(join(top,one),complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1353,refute_0_2055]) ).
cnf(refute_0_2057,plain,
join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) = composition(join(top,one),complement(composition(top,top))),
inference(subst,[],[refute_0_868:[bind(X_104,$fot(top)),bind(X_106,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_2058,plain,
( composition(join(top,one),complement(composition(top,top))) != zero
| join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) != composition(join(top,one),complement(composition(top,top)))
| join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(composition(top,top)),composition(top,complement(composition(top,top)))))),bind(Y,$fot(composition(join(top,one),complement(composition(top,top))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_2059,plain,
( composition(join(top,one),complement(composition(top,top))) != zero
| join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),composition(top,complement(composition(top,top)))),composition(join(top,one),complement(composition(top,top)))) )],[refute_0_2057,refute_0_2058]) ).
cnf(refute_0_2060,plain,
join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) = zero,
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),zero) )],[refute_0_2056,refute_0_2059]) ).
cnf(refute_0_2061,plain,
( complement(composition(top,top)) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| join(complement(composition(top,top)),composition(top,complement(composition(top,top)))) != zero
| complement(composition(top,top)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(top,top)),zero) ),[0],$fot(join(complement(composition(top,top)),composition(top,complement(composition(top,top)))))]]) ).
cnf(refute_0_2062,plain,
( complement(composition(top,top)) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| complement(composition(top,top)) = zero ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),composition(top,complement(composition(top,top)))),zero) )],[refute_0_2060,refute_0_2061]) ).
cnf(refute_0_2063,plain,
( composition(one,complement(composition(top,top))) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| complement(composition(top,top)) = zero ),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),join(complement(composition(top,top)),composition(top,complement(composition(top,top))))) )],[refute_0_1369,refute_0_2062]) ).
cnf(refute_0_2064,plain,
complement(composition(top,top)) = zero,
inference(resolve,[$cnf( $equal(composition(one,complement(composition(top,top))),join(complement(composition(top,top)),composition(top,complement(composition(top,top))))) )],[refute_0_1366,refute_0_2063]) ).
cnf(refute_0_2065,plain,
composition(top,complement(composition(top,top))) = composition(top,complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(top,complement(composition(top,top))))]]) ).
cnf(refute_0_2066,plain,
( complement(composition(top,top)) != zero
| composition(top,complement(composition(top,top))) != composition(top,complement(composition(top,top)))
| composition(top,complement(composition(top,top))) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(top,complement(composition(top,top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2067,plain,
( complement(composition(top,top)) != zero
| composition(top,complement(composition(top,top))) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_0_2065,refute_0_2066]) ).
cnf(refute_0_2068,plain,
composition(top,complement(composition(top,top))) = composition(top,zero),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_2064,refute_0_2067]) ).
cnf(refute_0_2069,plain,
( composition(top,complement(composition(top,top))) != composition(top,zero)
| composition(top,complement(composition(top,top))) != zero
| composition(top,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) ),[0],$fot(composition(top,zero))]]) ).
cnf(refute_0_2070,plain,
( composition(top,complement(composition(top,top))) != zero
| composition(top,zero) = zero ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(top,zero)) )],[refute_0_2068,refute_0_2069]) ).
cnf(refute_0_2071,plain,
composition(top,zero) = zero,
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1353,refute_0_2070]) ).
cnf(refute_0_2072,plain,
composition(zero,composition(top,zero)) = composition(zero,composition(top,zero)),
introduced(tautology,[refl,[$fot(composition(zero,composition(top,zero)))]]) ).
cnf(refute_0_2073,plain,
( composition(top,zero) != zero
| composition(zero,composition(top,zero)) != composition(zero,composition(top,zero))
| composition(zero,composition(top,zero)) = composition(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,composition(top,zero)),composition(zero,composition(top,zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2074,plain,
( composition(top,zero) != zero
| composition(zero,composition(top,zero)) = composition(zero,zero) ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,zero)),composition(zero,composition(top,zero))) )],[refute_0_2072,refute_0_2073]) ).
cnf(refute_0_2075,plain,
composition(zero,composition(top,zero)) = composition(zero,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_0_2071,refute_0_2074]) ).
cnf(refute_0_2076,plain,
( composition(zero,composition(top,zero)) != composition(zero,zero)
| composition(zero,zero) != zero
| composition(zero,composition(top,zero)) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(zero,composition(top,zero)))),bind(Y,$fot(composition(zero,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_2077,plain,
( composition(zero,zero) != zero
| composition(zero,composition(top,zero)) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,zero)),composition(zero,zero)) )],[refute_0_2075,refute_0_2076]) ).
cnf(refute_0_2078,plain,
composition(zero,composition(top,zero)) = zero,
inference(resolve,[$cnf( $equal(composition(zero,zero),zero) )],[refute_0_1341,refute_0_2077]) ).
cnf(refute_0_2079,plain,
complement(composition(zero,composition(top,zero))) = complement(composition(zero,composition(top,zero))),
introduced(tautology,[refl,[$fot(complement(composition(zero,composition(top,zero))))]]) ).
cnf(refute_0_2080,plain,
( complement(composition(zero,composition(top,zero))) != complement(composition(zero,composition(top,zero)))
| composition(zero,composition(top,zero)) != zero
| complement(composition(zero,composition(top,zero))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(zero,composition(top,zero))),complement(composition(zero,composition(top,zero)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_2081,plain,
( composition(zero,composition(top,zero)) != zero
| complement(composition(zero,composition(top,zero))) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(composition(zero,composition(top,zero))),complement(composition(zero,composition(top,zero)))) )],[refute_0_2079,refute_0_2080]) ).
cnf(refute_0_2082,plain,
complement(composition(zero,composition(top,zero))) = complement(zero),
inference(resolve,[$cnf( $equal(composition(zero,composition(top,zero)),zero) )],[refute_0_2078,refute_0_2081]) ).
cnf(refute_0_2083,plain,
( complement(composition(zero,composition(top,zero))) != complement(zero)
| complement(zero) != top
| complement(composition(zero,composition(top,zero))) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(complement(composition(zero,composition(top,zero))))),bind(Y,$fot(complement(zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_2084,plain,
( complement(zero) != top
| complement(composition(zero,composition(top,zero))) = top ),
inference(resolve,[$cnf( $equal(complement(composition(zero,composition(top,zero))),complement(zero)) )],[refute_0_2082,refute_0_2083]) ).
cnf(refute_0_2085,plain,
complement(composition(zero,composition(top,zero))) = top,
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_2084]) ).
cnf(refute_0_2086,plain,
composition(zero,complement(composition(zero,composition(top,zero)))) = composition(zero,complement(composition(zero,composition(top,zero)))),
introduced(tautology,[refl,[$fot(composition(zero,complement(composition(zero,composition(top,zero)))))]]) ).
cnf(refute_0_2087,plain,
( complement(composition(zero,composition(top,zero))) != top
| composition(zero,complement(composition(zero,composition(top,zero)))) != composition(zero,complement(composition(zero,composition(top,zero))))
| composition(zero,complement(composition(zero,composition(top,zero)))) = composition(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(zero,complement(composition(zero,composition(top,zero)))),composition(zero,complement(composition(zero,composition(top,zero))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_2088,plain,
( complement(composition(zero,composition(top,zero))) != top
| composition(zero,complement(composition(zero,composition(top,zero)))) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(zero,composition(top,zero)))),composition(zero,complement(composition(zero,composition(top,zero))))) )],[refute_0_2086,refute_0_2087]) ).
cnf(refute_0_2089,plain,
composition(zero,complement(composition(zero,composition(top,zero)))) = composition(zero,top),
inference(resolve,[$cnf( $equal(complement(composition(zero,composition(top,zero))),top) )],[refute_0_2085,refute_0_2088]) ).
cnf(refute_0_2090,plain,
composition(top,composition(complement(composition(top,top)),C)) = composition(composition(top,complement(composition(top,top))),C),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(top)),bind(B,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_2091,plain,
( composition(top,complement(composition(top,top))) != zero
| composition(top,composition(complement(composition(top,top)),C)) != composition(composition(top,complement(composition(top,top))),C)
| composition(top,composition(complement(composition(top,top)),C)) = composition(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(complement(composition(top,top)),C)),composition(composition(top,complement(composition(top,top))),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_2092,plain,
( composition(top,composition(complement(composition(top,top)),C)) != composition(composition(top,complement(composition(top,top))),C)
| composition(top,composition(complement(composition(top,top)),C)) = composition(zero,C) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1353,refute_0_2091]) ).
cnf(refute_0_2093,plain,
composition(top,composition(complement(composition(top,top)),C)) = composition(zero,C),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(composition(top,top)),C)),composition(composition(top,complement(composition(top,top))),C)) )],[refute_0_2090,refute_0_2092]) ).
cnf(refute_0_2094,plain,
composition(complement(composition(top,top)),C) = composition(complement(composition(top,top)),C),
introduced(tautology,[refl,[$fot(composition(complement(composition(top,top)),C))]]) ).
cnf(refute_0_2095,plain,
( complement(composition(top,top)) != zero
| composition(complement(composition(top,top)),C) != composition(complement(composition(top,top)),C)
| composition(complement(composition(top,top)),C) = composition(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(top,top)),C),composition(complement(composition(top,top)),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_2096,plain,
( complement(composition(top,top)) != zero
| composition(complement(composition(top,top)),C) = composition(zero,C) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,top)),C),composition(complement(composition(top,top)),C)) )],[refute_0_2094,refute_0_2095]) ).
cnf(refute_0_2097,plain,
composition(complement(composition(top,top)),C) = composition(zero,C),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_2064,refute_0_2096]) ).
cnf(refute_0_2098,plain,
composition(top,composition(complement(composition(top,top)),C)) = composition(top,composition(complement(composition(top,top)),C)),
introduced(tautology,[refl,[$fot(composition(top,composition(complement(composition(top,top)),C)))]]) ).
cnf(refute_0_2099,plain,
( composition(complement(composition(top,top)),C) != composition(zero,C)
| composition(top,composition(complement(composition(top,top)),C)) != composition(top,composition(complement(composition(top,top)),C))
| composition(top,composition(complement(composition(top,top)),C)) = composition(top,composition(zero,C)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(complement(composition(top,top)),C)),composition(top,composition(complement(composition(top,top)),C))) ),[1,1],$fot(composition(zero,C))]]) ).
cnf(refute_0_2100,plain,
( composition(complement(composition(top,top)),C) != composition(zero,C)
| composition(top,composition(complement(composition(top,top)),C)) = composition(top,composition(zero,C)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(composition(top,top)),C)),composition(top,composition(complement(composition(top,top)),C))) )],[refute_0_2098,refute_0_2099]) ).
cnf(refute_0_2101,plain,
composition(top,composition(complement(composition(top,top)),C)) = composition(top,composition(zero,C)),
inference(resolve,[$cnf( $equal(composition(complement(composition(top,top)),C),composition(zero,C)) )],[refute_0_2097,refute_0_2100]) ).
cnf(refute_0_2102,plain,
( composition(top,composition(complement(composition(top,top)),C)) != composition(top,composition(zero,C))
| composition(top,composition(complement(composition(top,top)),C)) != composition(zero,C)
| composition(top,composition(zero,C)) = composition(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(complement(composition(top,top)),C)),composition(zero,C)) ),[0],$fot(composition(top,composition(zero,C)))]]) ).
cnf(refute_0_2103,plain,
( composition(top,composition(complement(composition(top,top)),C)) != composition(zero,C)
| composition(top,composition(zero,C)) = composition(zero,C) ),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(composition(top,top)),C)),composition(top,composition(zero,C))) )],[refute_0_2101,refute_0_2102]) ).
cnf(refute_0_2104,plain,
composition(top,composition(zero,C)) = composition(zero,C),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(composition(top,top)),C)),composition(zero,C)) )],[refute_0_2093,refute_0_2103]) ).
cnf(refute_0_2105,plain,
composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) = composition(zero,complement(composition(zero,composition(top,zero)))),
inference(subst,[],[refute_0_2104:[bind(C,$fot(complement(composition(zero,composition(top,zero)))))]]) ).
cnf(refute_0_2106,plain,
( composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) != composition(zero,complement(composition(zero,composition(top,zero))))
| composition(zero,complement(composition(zero,composition(top,zero)))) != composition(zero,top)
| composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) = composition(zero,top) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),bind(Y,$fot(composition(zero,complement(composition(zero,composition(top,zero)))))),bind(Z,$fot(composition(zero,top)))]]) ).
cnf(refute_0_2107,plain,
( composition(zero,complement(composition(zero,composition(top,zero)))) != composition(zero,top)
| composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) = composition(zero,top) ),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(zero,composition(top,zero))))),composition(zero,complement(composition(zero,composition(top,zero))))) )],[refute_0_2105,refute_0_2106]) ).
cnf(refute_0_2108,plain,
composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) = composition(zero,top),
inference(resolve,[$cnf( $equal(composition(zero,complement(composition(zero,composition(top,zero)))),composition(zero,top)) )],[refute_0_2089,refute_0_2107]) ).
cnf(refute_0_2109,plain,
join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) = join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))),
introduced(tautology,[refl,[$fot(join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))]]) ).
cnf(refute_0_2110,plain,
( composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) != composition(zero,top)
| join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) != join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))
| join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) = join(X_118,composition(zero,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))),join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) ),[1,1],$fot(composition(zero,top))]]) ).
cnf(refute_0_2111,plain,
( composition(top,composition(zero,complement(composition(zero,composition(top,zero))))) != composition(zero,top)
| join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) = join(X_118,composition(zero,top)) ),
inference(resolve,[$cnf( $equal(join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))),join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) )],[refute_0_2109,refute_0_2110]) ).
cnf(refute_0_2112,plain,
join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) = join(X_118,composition(zero,top)),
inference(resolve,[$cnf( $equal(composition(top,composition(zero,complement(composition(zero,composition(top,zero))))),composition(zero,top)) )],[refute_0_2108,refute_0_2111]) ).
cnf(refute_0_2113,plain,
join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) = join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),
introduced(tautology,[refl,[$fot(join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))))]]) ).
cnf(refute_0_2114,plain,
( join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) != join(X_118,composition(zero,top))
| join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) != join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))
| join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) = join(top,join(X_118,composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))) ),[1,1],$fot(join(X_118,composition(zero,top)))]]) ).
cnf(refute_0_2115,plain,
( join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))) != join(X_118,composition(zero,top))
| join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) = join(top,join(X_118,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))) )],[refute_0_2113,refute_0_2114]) ).
cnf(refute_0_2116,plain,
join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) = join(top,join(X_118,composition(zero,top))),
inference(resolve,[$cnf( $equal(join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))),join(X_118,composition(zero,top))) )],[refute_0_2112,refute_0_2115]) ).
cnf(refute_0_2117,plain,
( join(X_118,top) != join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))
| join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))) != join(top,join(X_118,composition(zero,top)))
| join(X_118,top) = join(top,join(X_118,composition(zero,top))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_118,top),join(top,join(X_118,composition(zero,top)))) ),[0],$fot(join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))))]]) ).
cnf(refute_0_2118,plain,
( join(X_118,top) != join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))
| join(X_118,top) = join(top,join(X_118,composition(zero,top))) ),
inference(resolve,[$cnf( $equal(join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero))))))),join(top,join(X_118,composition(zero,top)))) )],[refute_0_2116,refute_0_2117]) ).
cnf(refute_0_2119,plain,
join(X_118,top) = join(top,join(X_118,composition(zero,top))),
inference(resolve,[$cnf( $equal(join(X_118,top),join(top,join(X_118,composition(top,composition(zero,complement(composition(zero,composition(top,zero)))))))) )],[refute_0_1329,refute_0_2118]) ).
cnf(refute_0_2120,plain,
converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))) = composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(X_124))),bind(B,$fot(composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2121,plain,
composition(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),complement(composition(top,top))) = composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))),
inference(subst,[],[refute_0_1362:[bind(X_105,$fot(composition(converse(X_45),complement(composition(X_45,zero)))))]]) ).
cnf(refute_0_2122,plain,
( composition(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),complement(composition(top,top))) != composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))
| join(top,composition(converse(X_45),complement(composition(X_45,zero)))) != top
| composition(top,complement(composition(top,top))) = composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),complement(composition(top,top))),composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_2123,plain,
( composition(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),complement(composition(top,top))) != composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))
| composition(top,complement(composition(top,top))) = composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),top) )],[refute_0_664,refute_0_2122]) ).
cnf(refute_0_2124,plain,
composition(top,complement(composition(top,top))) = composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))),
inference(resolve,[$cnf( $equal(composition(join(top,composition(converse(X_45),complement(composition(X_45,zero)))),complement(composition(top,top))),composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))) )],[refute_0_2121,refute_0_2123]) ).
cnf(refute_0_2125,plain,
( composition(top,complement(composition(top,top))) != composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))
| composition(top,complement(composition(top,top))) != zero
| zero = composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_2126,plain,
( composition(top,complement(composition(top,top))) != composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))
| zero = composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1353,refute_0_2125]) ).
cnf(refute_0_2127,plain,
composition(complement(composition(X_45,zero)),complement(composition(top,top))) = composition(complement(composition(X_45,zero)),complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(complement(composition(X_45,zero)),complement(composition(top,top))))]]) ).
cnf(refute_0_2128,plain,
( complement(composition(top,top)) != zero
| composition(complement(composition(X_45,zero)),complement(composition(top,top))) != composition(complement(composition(X_45,zero)),complement(composition(top,top)))
| composition(complement(composition(X_45,zero)),complement(composition(top,top))) = composition(complement(composition(X_45,zero)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(X_45,zero)),complement(composition(top,top))),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2129,plain,
( complement(composition(top,top)) != zero
| composition(complement(composition(X_45,zero)),complement(composition(top,top))) = composition(complement(composition(X_45,zero)),zero) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(X_45,zero)),complement(composition(top,top))),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) )],[refute_0_2127,refute_0_2128]) ).
cnf(refute_0_2130,plain,
composition(complement(composition(X_45,zero)),complement(composition(top,top))) = composition(complement(composition(X_45,zero)),zero),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_2064,refute_0_2129]) ).
cnf(refute_0_2131,plain,
composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))),
introduced(tautology,[refl,[$fot(composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))))]]) ).
cnf(refute_0_2132,plain,
( composition(complement(composition(X_45,zero)),complement(composition(top,top))) != composition(complement(composition(X_45,zero)),zero)
| composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) != composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top))))
| composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))),composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top))))) ),[1,1],$fot(composition(complement(composition(X_45,zero)),zero))]]) ).
cnf(refute_0_2133,plain,
( composition(complement(composition(X_45,zero)),complement(composition(top,top))) != composition(complement(composition(X_45,zero)),zero)
| composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))),composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top))))) )],[refute_0_2131,refute_0_2132]) ).
cnf(refute_0_2134,plain,
composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)),
inference(resolve,[$cnf( $equal(composition(complement(composition(X_45,zero)),complement(composition(top,top))),composition(complement(composition(X_45,zero)),zero)) )],[refute_0_2130,refute_0_2133]) ).
cnf(refute_0_2135,plain,
composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))),
inference(subst,[],[refute_0_1299:[bind(A,$fot(converse(X_45))),bind(B,$fot(complement(composition(X_45,zero)))),bind(C,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_2136,plain,
( composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) != composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top))))
| composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) != composition(converse(X_45),composition(complement(composition(X_45,zero)),zero))
| composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))))),bind(Y,$fot(composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))))),bind(Z,$fot(composition(converse(X_45),composition(complement(composition(X_45,zero)),zero))))]]) ).
cnf(refute_0_2137,plain,
( composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))) != composition(converse(X_45),composition(complement(composition(X_45,zero)),zero))
| composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)) ),
inference(resolve,[$cnf( $equal(composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))),composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top))))) )],[refute_0_2135,refute_0_2136]) ).
cnf(refute_0_2138,plain,
composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)),
inference(resolve,[$cnf( $equal(composition(converse(X_45),composition(complement(composition(X_45,zero)),complement(composition(top,top)))),composition(converse(X_45),composition(complement(composition(X_45,zero)),zero))) )],[refute_0_2134,refute_0_2137]) ).
cnf(refute_0_2139,plain,
( composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))) != composition(converse(X_45),composition(complement(composition(X_45,zero)),zero))
| zero != composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))
| zero = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))) ),[1],$fot(composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)))]]) ).
cnf(refute_0_2140,plain,
( zero != composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))
| zero = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)) ),
inference(resolve,[$cnf( $equal(composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top))),composition(converse(X_45),composition(complement(composition(X_45,zero)),zero))) )],[refute_0_2138,refute_0_2139]) ).
cnf(refute_0_2141,plain,
( composition(top,complement(composition(top,top))) != composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))
| zero = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)) ),
inference(resolve,[$cnf( $equal(zero,composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))) )],[refute_0_2126,refute_0_2140]) ).
cnf(refute_0_2142,plain,
zero = composition(converse(X_45),composition(complement(composition(X_45,zero)),zero)),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(composition(converse(X_45),complement(composition(X_45,zero))),complement(composition(top,top)))) )],[refute_0_2124,refute_0_2141]) ).
cnf(refute_0_2143,plain,
zero = composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)),
inference(subst,[],[refute_0_2142:[bind(X_45,$fot(X_124))]]) ).
cnf(refute_0_2144,plain,
( zero != composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))
| composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))))]]) ).
cnf(refute_0_2145,plain,
composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)) = zero,
inference(resolve,[$cnf( $equal(zero,composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))) )],[refute_0_2143,refute_0_2144]) ).
cnf(refute_0_2146,plain,
( composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)) != zero
| converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))) != composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))
| converse(zero) = composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))),composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_2147,plain,
( converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))) != composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))
| converse(zero) = composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) ),
inference(resolve,[$cnf( $equal(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)),zero) )],[refute_0_2145,refute_0_2146]) ).
cnf(refute_0_2148,plain,
converse(zero) = composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))),composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))) )],[refute_0_2120,refute_0_2147]) ).
cnf(refute_0_2149,plain,
( converse(zero) != composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))
| converse(zero) != zero
| zero = composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_2150,plain,
( converse(zero) != composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))
| zero = composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_1267,refute_0_2149]) ).
cnf(refute_0_2151,plain,
converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))) = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_124)),bind(X_23,$fot(composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2152,plain,
( converse(composition(A,B)) != composition(converse(B),converse(A))
| composition(converse(B),converse(A)) = converse(composition(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(A,B)))),bind(Y,$fot(composition(converse(B),converse(A))))]]) ).
cnf(refute_0_2153,plain,
composition(converse(B),converse(A)) = converse(composition(A,B)),
inference(resolve,[$cnf( $equal(converse(composition(A,B)),composition(converse(B),converse(A))) )],[converse_multiplicativity_10,refute_0_2152]) ).
cnf(refute_0_2154,plain,
composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) = converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))),
inference(subst,[],[refute_0_2153:[bind(A,$fot(converse(X_124))),bind(B,$fot(composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2155,plain,
( composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) != converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)))
| converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))) != composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)
| composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))))),bind(Y,$fot(converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))))),bind(Z,$fot(composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)))]]) ).
cnf(refute_0_2156,plain,
( converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))) != composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)
| composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) ),
inference(resolve,[$cnf( $equal(composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))),converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)))) )],[refute_0_2154,refute_0_2155]) ).
cnf(refute_0_2157,plain,
composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))),composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)) )],[refute_0_2151,refute_0_2156]) ).
cnf(refute_0_2158,plain,
( composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))) != composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)
| zero != composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))
| zero = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))) ),[1],$fot(composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124))]]) ).
cnf(refute_0_2159,plain,
( zero != composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))
| zero = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) ),
inference(resolve,[$cnf( $equal(composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124))),composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)) )],[refute_0_2157,refute_0_2158]) ).
cnf(refute_0_2160,plain,
( converse(zero) != composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))
| zero = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) ),
inference(resolve,[$cnf( $equal(zero,composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))) )],[refute_0_2150,refute_0_2159]) ).
cnf(refute_0_2161,plain,
zero = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(composition(complement(composition(X_124,zero)),zero)),converse(converse(X_124)))) )],[refute_0_2148,refute_0_2160]) ).
cnf(refute_0_2162,plain,
zero = composition(converse(composition(X_22,converse(A))),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)),
inference(subst,[],[refute_0_2142:[bind(X_45,$fot(composition(X_22,converse(A))))]]) ).
cnf(refute_0_2163,plain,
converse(composition(X_22,converse(A))) = composition(converse(converse(A)),converse(X_22)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_22)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_2164,plain,
( converse(composition(X_22,converse(A))) != composition(converse(converse(A)),converse(X_22))
| converse(converse(A)) != A
| converse(composition(X_22,converse(A))) = composition(A,converse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_22,converse(A))),composition(converse(converse(A)),converse(X_22))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_2165,plain,
( converse(composition(X_22,converse(A))) != composition(converse(converse(A)),converse(X_22))
| converse(composition(X_22,converse(A))) = composition(A,converse(X_22)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_2164]) ).
cnf(refute_0_2166,plain,
converse(composition(X_22,converse(A))) = composition(A,converse(X_22)),
inference(resolve,[$cnf( $equal(converse(composition(X_22,converse(A))),composition(converse(converse(A)),converse(X_22))) )],[refute_0_2163,refute_0_2165]) ).
cnf(refute_0_2167,plain,
( converse(composition(X_22,converse(A))) != composition(A,converse(X_22))
| zero != composition(converse(composition(X_22,converse(A))),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))
| zero = composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(composition(X_22,converse(A))),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) ),[1,0],$fot(composition(A,converse(X_22)))]]) ).
cnf(refute_0_2168,plain,
( zero != composition(converse(composition(X_22,converse(A))),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))
| zero = composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) ),
inference(resolve,[$cnf( $equal(converse(composition(X_22,converse(A))),composition(A,converse(X_22))) )],[refute_0_2166,refute_0_2167]) ).
cnf(refute_0_2169,plain,
zero = composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)),
inference(resolve,[$cnf( $equal(zero,composition(converse(composition(X_22,converse(A))),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) )],[refute_0_2162,refute_0_2168]) ).
cnf(refute_0_2170,plain,
zero = composition(converse(composition(converse(A),X_23)),composition(complement(composition(composition(converse(A),X_23),zero)),zero)),
inference(subst,[],[refute_0_2142:[bind(X_45,$fot(composition(converse(A),X_23)))]]) ).
cnf(refute_0_2171,plain,
( converse(composition(converse(A),X_23)) != composition(converse(X_23),A)
| zero != composition(converse(composition(converse(A),X_23)),composition(complement(composition(composition(converse(A),X_23),zero)),zero))
| zero = composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(composition(converse(A),X_23)),composition(complement(composition(composition(converse(A),X_23),zero)),zero))) ),[1,0],$fot(composition(converse(X_23),A))]]) ).
cnf(refute_0_2172,plain,
( zero != composition(converse(composition(converse(A),X_23)),composition(complement(composition(composition(converse(A),X_23),zero)),zero))
| zero = composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_23)),composition(converse(X_23),A)) )],[refute_0_165,refute_0_2171]) ).
cnf(refute_0_2173,plain,
zero = composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)),
inference(resolve,[$cnf( $equal(zero,composition(converse(composition(converse(A),X_23)),composition(complement(composition(composition(converse(A),X_23),zero)),zero))) )],[refute_0_2170,refute_0_2172]) ).
cnf(refute_0_2174,plain,
zero = composition(converse(join(one,X_107)),composition(complement(composition(join(one,X_107),zero)),zero)),
inference(subst,[],[refute_0_2142:[bind(X_45,$fot(join(one,X_107)))]]) ).
cnf(refute_0_2175,plain,
( composition(join(one,X_107),zero) != composition(X_107,zero)
| zero != composition(converse(join(one,X_107)),composition(complement(composition(join(one,X_107),zero)),zero))
| zero = composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(join(one,X_107)),composition(complement(composition(join(one,X_107),zero)),zero))) ),[1,1,0,0],$fot(composition(X_107,zero))]]) ).
cnf(refute_0_2176,plain,
( zero != composition(converse(join(one,X_107)),composition(complement(composition(join(one,X_107),zero)),zero))
| zero = composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero)) ),
inference(resolve,[$cnf( $equal(composition(join(one,X_107),zero),composition(X_107,zero)) )],[refute_0_1085,refute_0_2175]) ).
cnf(refute_0_2177,plain,
zero = composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero)),
inference(resolve,[$cnf( $equal(zero,composition(converse(join(one,X_107)),composition(complement(composition(join(one,X_107),zero)),zero))) )],[refute_0_2174,refute_0_2176]) ).
cnf(refute_0_2178,plain,
composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = join(composition(complement(composition(X_124,zero)),zero),composition(converse(X_124),composition(complement(composition(X_124,zero)),zero))),
inference(subst,[],[refute_0_676:[bind(X_104,$fot(converse(X_124))),bind(X_106,$fot(composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2179,plain,
( composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)) != zero
| composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) != join(composition(complement(composition(X_124,zero)),zero),composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)))
| composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = join(composition(complement(composition(X_124,zero)),zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)),join(composition(complement(composition(X_124,zero)),zero),composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2180,plain,
( composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) != join(composition(complement(composition(X_124,zero)),zero),composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)))
| composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = join(composition(complement(composition(X_124,zero)),zero),zero) ),
inference(resolve,[$cnf( $equal(composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)),zero) )],[refute_0_2145,refute_0_2179]) ).
cnf(refute_0_2181,plain,
composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = join(composition(complement(composition(X_124,zero)),zero),zero),
inference(resolve,[$cnf( $equal(composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)),join(composition(complement(composition(X_124,zero)),zero),composition(converse(X_124),composition(complement(composition(X_124,zero)),zero)))) )],[refute_0_2178,refute_0_2180]) ).
cnf(refute_0_2182,plain,
join(one,converse(X_124)) = converse(join(one,X_124)),
inference(subst,[],[refute_0_803:[bind(B,$fot(X_124))]]) ).
cnf(refute_0_2183,plain,
composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)),
introduced(tautology,[refl,[$fot(composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2184,plain,
( composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)) != composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero))
| join(one,converse(X_124)) != converse(join(one,X_124))
| composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)),composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero))) ),[1,0],$fot(converse(join(one,X_124)))]]) ).
cnf(refute_0_2185,plain,
( join(one,converse(X_124)) != converse(join(one,X_124))
| composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)),composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero))) )],[refute_0_2183,refute_0_2184]) ).
cnf(refute_0_2186,plain,
composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)),
inference(resolve,[$cnf( $equal(join(one,converse(X_124)),converse(join(one,X_124))) )],[refute_0_2182,refute_0_2185]) ).
cnf(refute_0_2187,plain,
composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)),
inference(subst,[],[refute_0_874:[bind(X_110,$fot(converse(X_124))),bind(X_111,$fot(composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2188,plain,
( composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) != composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero))
| composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)) != composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero))
| composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)))),bind(Y,$fot(composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)))),bind(Z,$fot(composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero))))]]) ).
cnf(refute_0_2189,plain,
( composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)) != composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero))
| composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) ),
inference(resolve,[$cnf( $equal(composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)),composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero))) )],[refute_0_2187,refute_0_2188]) ).
cnf(refute_0_2190,plain,
composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) = composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_124)),composition(complement(composition(X_124,zero)),zero)),composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero))) )],[refute_0_2186,refute_0_2189]) ).
cnf(refute_0_2191,plain,
( composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) != composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero))
| composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) != join(composition(complement(composition(X_124,zero)),zero),zero)
| composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) = join(composition(complement(composition(X_124,zero)),zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)),join(composition(complement(composition(X_124,zero)),zero),zero)) ),[0],$fot(composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2192,plain,
( composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) != join(composition(complement(composition(X_124,zero)),zero),zero)
| composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) = join(composition(complement(composition(X_124,zero)),zero),zero) ),
inference(resolve,[$cnf( $equal(composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)),composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero))) )],[refute_0_2190,refute_0_2191]) ).
cnf(refute_0_2193,plain,
join(composition(complement(composition(X_124,zero)),zero),zero) = composition(complement(composition(X_124,zero)),zero),
inference(subst,[],[refute_0_464:[bind(X_10,$fot(composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2194,plain,
( composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) != join(composition(complement(composition(X_124,zero)),zero),zero)
| join(composition(complement(composition(X_124,zero)),zero),zero) != composition(complement(composition(X_124,zero)),zero)
| composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(complement(composition(X_124,zero)),zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)),composition(complement(composition(X_124,zero)),zero)) ),[0],$fot(join(composition(complement(composition(X_124,zero)),zero),zero))]]) ).
cnf(refute_0_2195,plain,
( composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) != join(composition(complement(composition(X_124,zero)),zero),zero)
| composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(complement(composition(X_124,zero)),zero) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(X_124,zero)),zero),zero),composition(complement(composition(X_124,zero)),zero)) )],[refute_0_2193,refute_0_2194]) ).
cnf(refute_0_2196,plain,
( composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)) != join(composition(complement(composition(X_124,zero)),zero),zero)
| composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(complement(composition(X_124,zero)),zero) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)),join(composition(complement(composition(X_124,zero)),zero),zero)) )],[refute_0_2192,refute_0_2195]) ).
cnf(refute_0_2197,plain,
composition(converse(join(one,X_124)),composition(complement(composition(X_124,zero)),zero)) = composition(complement(composition(X_124,zero)),zero),
inference(resolve,[$cnf( $equal(composition(join(converse(X_124),one),composition(complement(composition(X_124,zero)),zero)),join(composition(complement(composition(X_124,zero)),zero),zero)) )],[refute_0_2181,refute_0_2196]) ).
cnf(refute_0_2198,plain,
composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero)) = composition(complement(composition(X_107,zero)),zero),
inference(subst,[],[refute_0_2197:[bind(X_124,$fot(X_107))]]) ).
cnf(refute_0_2199,plain,
( composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero)) != composition(complement(composition(X_107,zero)),zero)
| zero != composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero))
| zero = composition(complement(composition(X_107,zero)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero))) ),[1],$fot(composition(complement(composition(X_107,zero)),zero))]]) ).
cnf(refute_0_2200,plain,
( zero != composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero))
| zero = composition(complement(composition(X_107,zero)),zero) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero)),composition(complement(composition(X_107,zero)),zero)) )],[refute_0_2198,refute_0_2199]) ).
cnf(refute_0_2201,plain,
zero = composition(complement(composition(X_107,zero)),zero),
inference(resolve,[$cnf( $equal(zero,composition(converse(join(one,X_107)),composition(complement(composition(X_107,zero)),zero))) )],[refute_0_2177,refute_0_2200]) ).
cnf(refute_0_2202,plain,
( zero != composition(complement(composition(X_107,zero)),zero)
| composition(complement(composition(X_107,zero)),zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(complement(composition(X_107,zero)),zero)))]]) ).
cnf(refute_0_2203,plain,
composition(complement(composition(X_107,zero)),zero) = zero,
inference(resolve,[$cnf( $equal(zero,composition(complement(composition(X_107,zero)),zero)) )],[refute_0_2201,refute_0_2202]) ).
cnf(refute_0_2204,plain,
composition(complement(composition(composition(converse(A),X_23),zero)),zero) = zero,
inference(subst,[],[refute_0_2203:[bind(X_107,$fot(composition(converse(A),X_23)))]]) ).
cnf(refute_0_2205,plain,
composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)),
introduced(tautology,[refl,[$fot(composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)))]]) ).
cnf(refute_0_2206,plain,
( composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)) != composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))
| composition(complement(composition(composition(converse(A),X_23),zero)),zero) != zero
| composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(A,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2207,plain,
( composition(complement(composition(composition(converse(A),X_23),zero)),zero) != zero
| composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(A,zero) ),
inference(resolve,[$cnf( $equal(composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) )],[refute_0_2205,refute_0_2206]) ).
cnf(refute_0_2208,plain,
composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(A,zero),
inference(resolve,[$cnf( $equal(composition(complement(composition(composition(converse(A),X_23),zero)),zero),zero) )],[refute_0_2204,refute_0_2207]) ).
cnf(refute_0_2209,plain,
composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) = composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))),
introduced(tautology,[refl,[$fot(composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))))]]) ).
cnf(refute_0_2210,plain,
( composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)) != composition(A,zero)
| composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) != composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)))
| composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) = composition(converse(X_23),composition(A,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))),composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)))) ),[1,1],$fot(composition(A,zero))]]) ).
cnf(refute_0_2211,plain,
( composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)) != composition(A,zero)
| composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) = composition(converse(X_23),composition(A,zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))),composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)))) )],[refute_0_2209,refute_0_2210]) ).
cnf(refute_0_2212,plain,
composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) = composition(converse(X_23),composition(A,zero)),
inference(resolve,[$cnf( $equal(composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)),composition(A,zero)) )],[refute_0_2208,refute_0_2211]) ).
cnf(refute_0_2213,plain,
composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))),
inference(subst,[],[refute_0_1299:[bind(A,$fot(converse(X_23))),bind(B,$fot(A)),bind(C,$fot(composition(complement(composition(composition(converse(A),X_23),zero)),zero)))]]) ).
cnf(refute_0_2214,plain,
( composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) != composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)))
| composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) != composition(converse(X_23),composition(A,zero))
| composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(converse(X_23),composition(A,zero)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)))),bind(Y,$fot(composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))))),bind(Z,$fot(composition(converse(X_23),composition(A,zero))))]]) ).
cnf(refute_0_2215,plain,
( composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))) != composition(converse(X_23),composition(A,zero))
| composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(converse(X_23),composition(A,zero)) ),
inference(resolve,[$cnf( $equal(composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)),composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero)))) )],[refute_0_2213,refute_0_2214]) ).
cnf(refute_0_2216,plain,
composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) = composition(converse(X_23),composition(A,zero)),
inference(resolve,[$cnf( $equal(composition(converse(X_23),composition(A,composition(complement(composition(composition(converse(A),X_23),zero)),zero))),composition(converse(X_23),composition(A,zero))) )],[refute_0_2212,refute_0_2215]) ).
cnf(refute_0_2217,plain,
( composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)) != composition(converse(X_23),composition(A,zero))
| zero != composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero))
| zero = composition(converse(X_23),composition(A,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero))) ),[1],$fot(composition(converse(X_23),composition(A,zero)))]]) ).
cnf(refute_0_2218,plain,
( zero != composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero))
| zero = composition(converse(X_23),composition(A,zero)) ),
inference(resolve,[$cnf( $equal(composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero)),composition(converse(X_23),composition(A,zero))) )],[refute_0_2216,refute_0_2217]) ).
cnf(refute_0_2219,plain,
zero = composition(converse(X_23),composition(A,zero)),
inference(resolve,[$cnf( $equal(zero,composition(composition(converse(X_23),A),composition(complement(composition(composition(converse(A),X_23),zero)),zero))) )],[refute_0_2173,refute_0_2218]) ).
cnf(refute_0_2220,plain,
( zero != composition(converse(X_23),composition(A,zero))
| composition(converse(X_23),composition(A,zero)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(converse(X_23),composition(A,zero))))]]) ).
cnf(refute_0_2221,plain,
composition(converse(X_23),composition(A,zero)) = zero,
inference(resolve,[$cnf( $equal(zero,composition(converse(X_23),composition(A,zero))) )],[refute_0_2219,refute_0_2220]) ).
cnf(refute_0_2222,plain,
composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) = zero,
inference(subst,[],[refute_0_2221:[bind(A,$fot(complement(composition(composition(X_22,converse(A)),zero)))),bind(X_23,$fot(X_22))]]) ).
cnf(refute_0_2223,plain,
composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) = composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))),
introduced(tautology,[refl,[$fot(composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))))]]) ).
cnf(refute_0_2224,plain,
( composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) != composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)))
| composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) != zero
| composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) = composition(A,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))),composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2225,plain,
( composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) != zero
| composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) = composition(A,zero) ),
inference(resolve,[$cnf( $equal(composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))),composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)))) )],[refute_0_2223,refute_0_2224]) ).
cnf(refute_0_2226,plain,
composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) = composition(A,zero),
inference(resolve,[$cnf( $equal(composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)),zero) )],[refute_0_2222,refute_0_2225]) ).
cnf(refute_0_2227,plain,
composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) = composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))),
inference(subst,[],[refute_0_1299:[bind(B,$fot(converse(X_22))),bind(C,$fot(composition(complement(composition(composition(X_22,converse(A)),zero)),zero)))]]) ).
cnf(refute_0_2228,plain,
( composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) != composition(A,zero)
| composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) != composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)))
| composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) = composition(A,zero) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)))),bind(Y,$fot(composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))))),bind(Z,$fot(composition(A,zero)))]]) ).
cnf(refute_0_2229,plain,
( composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) != composition(A,zero)
| composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) = composition(A,zero) ),
inference(resolve,[$cnf( $equal(composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)),composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)))) )],[refute_0_2227,refute_0_2228]) ).
cnf(refute_0_2230,plain,
composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) = composition(A,zero),
inference(resolve,[$cnf( $equal(composition(A,composition(converse(X_22),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))),composition(A,zero)) )],[refute_0_2226,refute_0_2229]) ).
cnf(refute_0_2231,plain,
( composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)) != composition(A,zero)
| zero != composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))
| zero = composition(A,zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) ),[1],$fot(composition(A,zero))]]) ).
cnf(refute_0_2232,plain,
( zero != composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))
| zero = composition(A,zero) ),
inference(resolve,[$cnf( $equal(composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero)),composition(A,zero)) )],[refute_0_2230,refute_0_2231]) ).
cnf(refute_0_2233,plain,
zero = composition(A,zero),
inference(resolve,[$cnf( $equal(zero,composition(composition(A,converse(X_22)),composition(complement(composition(composition(X_22,converse(A)),zero)),zero))) )],[refute_0_2169,refute_0_2232]) ).
cnf(refute_0_2234,plain,
( zero != composition(A,zero)
| composition(A,zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(A,zero)))]]) ).
cnf(refute_0_2235,plain,
composition(A,zero) = zero,
inference(resolve,[$cnf( $equal(zero,composition(A,zero)) )],[refute_0_2233,refute_0_2234]) ).
cnf(refute_0_2236,plain,
composition(complement(composition(X_124,zero)),zero) = zero,
inference(subst,[],[refute_0_2235:[bind(A,$fot(complement(composition(X_124,zero))))]]) ).
cnf(refute_0_2237,plain,
converse(composition(complement(composition(X_124,zero)),zero)) = converse(composition(complement(composition(X_124,zero)),zero)),
introduced(tautology,[refl,[$fot(converse(composition(complement(composition(X_124,zero)),zero)))]]) ).
cnf(refute_0_2238,plain,
( composition(complement(composition(X_124,zero)),zero) != zero
| converse(composition(complement(composition(X_124,zero)),zero)) != converse(composition(complement(composition(X_124,zero)),zero))
| converse(composition(complement(composition(X_124,zero)),zero)) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(complement(composition(X_124,zero)),zero)),converse(composition(complement(composition(X_124,zero)),zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_2239,plain,
( composition(complement(composition(X_124,zero)),zero) != zero
| converse(composition(complement(composition(X_124,zero)),zero)) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(composition(complement(composition(X_124,zero)),zero)),converse(composition(complement(composition(X_124,zero)),zero))) )],[refute_0_2237,refute_0_2238]) ).
cnf(refute_0_2240,plain,
converse(composition(complement(composition(X_124,zero)),zero)) = converse(zero),
inference(resolve,[$cnf( $equal(composition(complement(composition(X_124,zero)),zero),zero) )],[refute_0_2236,refute_0_2239]) ).
cnf(refute_0_2241,plain,
( converse(composition(complement(composition(X_124,zero)),zero)) != converse(zero)
| converse(zero) != zero
| converse(composition(complement(composition(X_124,zero)),zero)) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(converse(composition(complement(composition(X_124,zero)),zero)))),bind(Y,$fot(converse(zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_2242,plain,
( converse(zero) != zero
| converse(composition(complement(composition(X_124,zero)),zero)) = zero ),
inference(resolve,[$cnf( $equal(converse(composition(complement(composition(X_124,zero)),zero)),converse(zero)) )],[refute_0_2240,refute_0_2241]) ).
cnf(refute_0_2243,plain,
converse(composition(complement(composition(X_124,zero)),zero)) = zero,
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_1267,refute_0_2242]) ).
cnf(refute_0_2244,plain,
composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) = composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124),
introduced(tautology,[refl,[$fot(composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124))]]) ).
cnf(refute_0_2245,plain,
( composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) != composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)
| converse(composition(complement(composition(X_124,zero)),zero)) != zero
| composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) = composition(zero,X_124) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124),composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_2246,plain,
( converse(composition(complement(composition(X_124,zero)),zero)) != zero
| composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) = composition(zero,X_124) ),
inference(resolve,[$cnf( $equal(composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124),composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)) )],[refute_0_2244,refute_0_2245]) ).
cnf(refute_0_2247,plain,
composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) = composition(zero,X_124),
inference(resolve,[$cnf( $equal(converse(composition(complement(composition(X_124,zero)),zero)),zero) )],[refute_0_2243,refute_0_2246]) ).
cnf(refute_0_2248,plain,
( composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124) != composition(zero,X_124)
| zero != composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)
| zero = composition(zero,X_124) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)) ),[1],$fot(composition(zero,X_124))]]) ).
cnf(refute_0_2249,plain,
( zero != composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)
| zero = composition(zero,X_124) ),
inference(resolve,[$cnf( $equal(composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124),composition(zero,X_124)) )],[refute_0_2247,refute_0_2248]) ).
cnf(refute_0_2250,plain,
zero = composition(zero,X_124),
inference(resolve,[$cnf( $equal(zero,composition(converse(composition(complement(composition(X_124,zero)),zero)),X_124)) )],[refute_0_2161,refute_0_2249]) ).
cnf(refute_0_2251,plain,
( zero != composition(zero,X_124)
| composition(zero,X_124) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(zero,X_124)))]]) ).
cnf(refute_0_2252,plain,
composition(zero,X_124) = zero,
inference(resolve,[$cnf( $equal(zero,composition(zero,X_124)) )],[refute_0_2250,refute_0_2251]) ).
cnf(refute_0_2253,plain,
composition(zero,top) = zero,
inference(subst,[],[refute_0_2252:[bind(X_124,$fot(top))]]) ).
cnf(refute_0_2254,plain,
join(X_118,composition(zero,top)) = join(X_118,composition(zero,top)),
introduced(tautology,[refl,[$fot(join(X_118,composition(zero,top)))]]) ).
cnf(refute_0_2255,plain,
( composition(zero,top) != zero
| join(X_118,composition(zero,top)) != join(X_118,composition(zero,top))
| join(X_118,composition(zero,top)) = join(X_118,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_118,composition(zero,top)),join(X_118,composition(zero,top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2256,plain,
( composition(zero,top) != zero
| join(X_118,composition(zero,top)) = join(X_118,zero) ),
inference(resolve,[$cnf( $equal(join(X_118,composition(zero,top)),join(X_118,composition(zero,top))) )],[refute_0_2254,refute_0_2255]) ).
cnf(refute_0_2257,plain,
join(X_118,composition(zero,top)) = join(X_118,zero),
inference(resolve,[$cnf( $equal(composition(zero,top),zero) )],[refute_0_2253,refute_0_2256]) ).
cnf(refute_0_2258,plain,
( join(X_118,composition(zero,top)) != join(X_118,zero)
| join(X_118,zero) != X_118
| join(X_118,composition(zero,top)) = X_118 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(X_118,composition(zero,top)))),bind(Y,$fot(join(X_118,zero))),bind(Z,$fot(X_118))]]) ).
cnf(refute_0_2259,plain,
( join(X_118,zero) != X_118
| join(X_118,composition(zero,top)) = X_118 ),
inference(resolve,[$cnf( $equal(join(X_118,composition(zero,top)),join(X_118,zero)) )],[refute_0_2257,refute_0_2258]) ).
cnf(refute_0_2260,plain,
join(X_118,composition(zero,top)) = X_118,
inference(resolve,[$cnf( $equal(join(X_118,zero),X_118) )],[refute_0_465,refute_0_2259]) ).
cnf(refute_0_2261,plain,
join(top,join(X_118,composition(zero,top))) = join(top,join(X_118,composition(zero,top))),
introduced(tautology,[refl,[$fot(join(top,join(X_118,composition(zero,top))))]]) ).
cnf(refute_0_2262,plain,
( join(X_118,composition(zero,top)) != X_118
| join(top,join(X_118,composition(zero,top))) != join(top,join(X_118,composition(zero,top)))
| join(top,join(X_118,composition(zero,top))) = join(top,X_118) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(X_118,composition(zero,top))),join(top,join(X_118,composition(zero,top)))) ),[1,1],$fot(X_118)]]) ).
cnf(refute_0_2263,plain,
( join(X_118,composition(zero,top)) != X_118
| join(top,join(X_118,composition(zero,top))) = join(top,X_118) ),
inference(resolve,[$cnf( $equal(join(top,join(X_118,composition(zero,top))),join(top,join(X_118,composition(zero,top)))) )],[refute_0_2261,refute_0_2262]) ).
cnf(refute_0_2264,plain,
join(top,join(X_118,composition(zero,top))) = join(top,X_118),
inference(resolve,[$cnf( $equal(join(X_118,composition(zero,top)),X_118) )],[refute_0_2260,refute_0_2263]) ).
cnf(refute_0_2265,plain,
( join(X_118,top) != join(top,join(X_118,composition(zero,top)))
| join(top,join(X_118,composition(zero,top))) != join(top,X_118)
| join(X_118,top) = join(top,X_118) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_118,top),join(top,X_118)) ),[0],$fot(join(top,join(X_118,composition(zero,top))))]]) ).
cnf(refute_0_2266,plain,
( join(X_118,top) != join(top,join(X_118,composition(zero,top)))
| join(X_118,top) = join(top,X_118) ),
inference(resolve,[$cnf( $equal(join(top,join(X_118,composition(zero,top))),join(top,X_118)) )],[refute_0_2264,refute_0_2265]) ).
cnf(refute_0_2267,plain,
join(X_118,top) = join(top,X_118),
inference(resolve,[$cnf( $equal(join(X_118,top),join(top,join(X_118,composition(zero,top)))) )],[refute_0_2119,refute_0_2266]) ).
cnf(refute_0_2268,plain,
join(complement(X_128),top) = join(top,complement(X_128)),
inference(subst,[],[refute_0_2267:[bind(X_118,$fot(complement(X_128)))]]) ).
cnf(refute_0_2269,plain,
( join(complement(X_128),top) != join(top,complement(X_128))
| join(top,complement(X_128)) != complement(meet(zero,X_128))
| join(complement(X_128),top) = complement(meet(zero,X_128)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(X_128),top))),bind(Y,$fot(join(top,complement(X_128)))),bind(Z,$fot(complement(meet(zero,X_128))))]]) ).
cnf(refute_0_2270,plain,
( join(top,complement(X_128)) != complement(meet(zero,X_128))
| join(complement(X_128),top) = complement(meet(zero,X_128)) ),
inference(resolve,[$cnf( $equal(join(complement(X_128),top),join(top,complement(X_128))) )],[refute_0_2268,refute_0_2269]) ).
cnf(refute_0_2271,plain,
join(complement(X_128),top) = complement(meet(zero,X_128)),
inference(resolve,[$cnf( $equal(join(top,complement(X_128)),complement(meet(zero,X_128))) )],[refute_0_656,refute_0_2270]) ).
cnf(refute_0_2272,plain,
join(X_118,join(X_119,complement(X_119))) = join(X_119,join(X_118,complement(X_119))),
inference(subst,[],[refute_0_90:[bind(X_14,$fot(X_118)),bind(X_15,$fot(X_119)),bind(X_16,$fot(complement(X_119)))]]) ).
cnf(refute_0_2273,plain,
top = join(X_119,complement(X_119)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_119))]]) ).
cnf(refute_0_2274,plain,
( top != join(X_119,complement(X_119))
| join(X_119,complement(X_119)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_119,complement(X_119))))]]) ).
cnf(refute_0_2275,plain,
join(X_119,complement(X_119)) = top,
inference(resolve,[$cnf( $equal(top,join(X_119,complement(X_119))) )],[refute_0_2273,refute_0_2274]) ).
cnf(refute_0_2276,plain,
( join(X_118,join(X_119,complement(X_119))) != join(X_119,join(X_118,complement(X_119)))
| join(X_119,complement(X_119)) != top
| join(X_118,top) = join(X_119,join(X_118,complement(X_119))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_118,join(X_119,complement(X_119))),join(X_119,join(X_118,complement(X_119)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_2277,plain,
( join(X_118,join(X_119,complement(X_119))) != join(X_119,join(X_118,complement(X_119)))
| join(X_118,top) = join(X_119,join(X_118,complement(X_119))) ),
inference(resolve,[$cnf( $equal(join(X_119,complement(X_119)),top) )],[refute_0_2275,refute_0_2276]) ).
cnf(refute_0_2278,plain,
join(X_118,top) = join(X_119,join(X_118,complement(X_119))),
inference(resolve,[$cnf( $equal(join(X_118,join(X_119,complement(X_119))),join(X_119,join(X_118,complement(X_119)))) )],[refute_0_2272,refute_0_2277]) ).
cnf(refute_0_2279,plain,
( join(X_118,top) != join(X_119,join(X_118,complement(X_119)))
| join(X_119,join(X_118,complement(X_119))) = join(X_118,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_118,top))),bind(Y,$fot(join(X_119,join(X_118,complement(X_119)))))]]) ).
cnf(refute_0_2280,plain,
join(X_119,join(X_118,complement(X_119))) = join(X_118,top),
inference(resolve,[$cnf( $equal(join(X_118,top),join(X_119,join(X_118,complement(X_119)))) )],[refute_0_2278,refute_0_2279]) ).
cnf(refute_0_2281,plain,
join(X_128,join(complement(X_128),complement(X_128))) = join(complement(X_128),top),
inference(subst,[],[refute_0_2280:[bind(X_118,$fot(complement(X_128))),bind(X_119,$fot(X_128))]]) ).
cnf(refute_0_2282,plain,
( join(X_128,join(complement(X_128),complement(X_128))) != join(complement(X_128),top)
| join(complement(X_128),top) != complement(meet(zero,X_128))
| join(X_128,join(complement(X_128),complement(X_128))) = complement(meet(zero,X_128)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(X_128,join(complement(X_128),complement(X_128))))),bind(Y,$fot(join(complement(X_128),top))),bind(Z,$fot(complement(meet(zero,X_128))))]]) ).
cnf(refute_0_2283,plain,
( join(complement(X_128),top) != complement(meet(zero,X_128))
| join(X_128,join(complement(X_128),complement(X_128))) = complement(meet(zero,X_128)) ),
inference(resolve,[$cnf( $equal(join(X_128,join(complement(X_128),complement(X_128))),join(complement(X_128),top)) )],[refute_0_2281,refute_0_2282]) ).
cnf(refute_0_2284,plain,
join(X_128,join(complement(X_128),complement(X_128))) = complement(meet(zero,X_128)),
inference(resolve,[$cnf( $equal(join(complement(X_128),top),complement(meet(zero,X_128))) )],[refute_0_2271,refute_0_2283]) ).
cnf(refute_0_2285,plain,
join(X_118,join(X_119,X_120)) = join(X_119,join(X_118,X_120)),
inference(subst,[],[refute_0_90:[bind(X_14,$fot(X_118)),bind(X_15,$fot(X_119)),bind(X_16,$fot(X_120))]]) ).
cnf(refute_0_2286,plain,
join(X_120,X_119) = join(X_119,X_120),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_120)),bind(B,$fot(X_119))]]) ).
cnf(refute_0_2287,plain,
( join(X_120,X_119) != join(X_119,X_120)
| join(X_119,X_120) = join(X_120,X_119) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_120,X_119))),bind(Y,$fot(join(X_119,X_120)))]]) ).
cnf(refute_0_2288,plain,
join(X_119,X_120) = join(X_120,X_119),
inference(resolve,[$cnf( $equal(join(X_120,X_119),join(X_119,X_120)) )],[refute_0_2286,refute_0_2287]) ).
cnf(refute_0_2289,plain,
( join(X_118,join(X_119,X_120)) != join(X_119,join(X_118,X_120))
| join(X_119,X_120) != join(X_120,X_119)
| join(X_118,join(X_120,X_119)) = join(X_119,join(X_118,X_120)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_118,join(X_119,X_120)),join(X_119,join(X_118,X_120))) ),[0,1],$fot(join(X_120,X_119))]]) ).
cnf(refute_0_2290,plain,
( join(X_118,join(X_119,X_120)) != join(X_119,join(X_118,X_120))
| join(X_118,join(X_120,X_119)) = join(X_119,join(X_118,X_120)) ),
inference(resolve,[$cnf( $equal(join(X_119,X_120),join(X_120,X_119)) )],[refute_0_2288,refute_0_2289]) ).
cnf(refute_0_2291,plain,
join(X_118,join(X_120,X_119)) = join(X_119,join(X_118,X_120)),
inference(resolve,[$cnf( $equal(join(X_118,join(X_119,X_120)),join(X_119,join(X_118,X_120))) )],[refute_0_2285,refute_0_2290]) ).
cnf(refute_0_2292,plain,
( join(X_118,join(X_120,X_119)) != join(X_119,join(X_118,X_120))
| join(X_119,join(X_118,X_120)) = join(X_118,join(X_120,X_119)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_118,join(X_120,X_119)))),bind(Y,$fot(join(X_119,join(X_118,X_120))))]]) ).
cnf(refute_0_2293,plain,
join(X_119,join(X_118,X_120)) = join(X_118,join(X_120,X_119)),
inference(resolve,[$cnf( $equal(join(X_118,join(X_120,X_119)),join(X_119,join(X_118,X_120))) )],[refute_0_2291,refute_0_2292]) ).
cnf(refute_0_2294,plain,
join(complement(X_128),join(X_128,complement(X_128))) = join(X_128,join(complement(X_128),complement(X_128))),
inference(subst,[],[refute_0_2293:[bind(X_118,$fot(X_128)),bind(X_119,$fot(complement(X_128))),bind(X_120,$fot(complement(X_128)))]]) ).
cnf(refute_0_2295,plain,
( join(X_128,join(complement(X_128),complement(X_128))) != complement(meet(zero,X_128))
| join(complement(X_128),join(X_128,complement(X_128))) != join(X_128,join(complement(X_128),complement(X_128)))
| join(complement(X_128),join(X_128,complement(X_128))) = complement(meet(zero,X_128)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(X_128),join(X_128,complement(X_128))))),bind(Y,$fot(join(X_128,join(complement(X_128),complement(X_128))))),bind(Z,$fot(complement(meet(zero,X_128))))]]) ).
cnf(refute_0_2296,plain,
( join(X_128,join(complement(X_128),complement(X_128))) != complement(meet(zero,X_128))
| join(complement(X_128),join(X_128,complement(X_128))) = complement(meet(zero,X_128)) ),
inference(resolve,[$cnf( $equal(join(complement(X_128),join(X_128,complement(X_128))),join(X_128,join(complement(X_128),complement(X_128)))) )],[refute_0_2294,refute_0_2295]) ).
cnf(refute_0_2297,plain,
join(complement(X_128),join(X_128,complement(X_128))) = complement(meet(zero,X_128)),
inference(resolve,[$cnf( $equal(join(X_128,join(complement(X_128),complement(X_128))),complement(meet(zero,X_128))) )],[refute_0_2284,refute_0_2296]) ).
cnf(refute_0_2298,plain,
join(complement(X_128),join(complement(X_128),X_128)) = join(complement(X_128),join(X_128,complement(X_128))),
inference(subst,[],[refute_0_2293:[bind(X_118,$fot(complement(X_128))),bind(X_119,$fot(complement(X_128))),bind(X_120,$fot(X_128))]]) ).
cnf(refute_0_2299,plain,
( join(complement(X_128),join(X_128,complement(X_128))) != complement(meet(zero,X_128))
| join(complement(X_128),join(complement(X_128),X_128)) != join(complement(X_128),join(X_128,complement(X_128)))
| join(complement(X_128),join(complement(X_128),X_128)) = complement(meet(zero,X_128)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(X_128),join(complement(X_128),X_128)))),bind(Y,$fot(join(complement(X_128),join(X_128,complement(X_128))))),bind(Z,$fot(complement(meet(zero,X_128))))]]) ).
cnf(refute_0_2300,plain,
( join(complement(X_128),join(X_128,complement(X_128))) != complement(meet(zero,X_128))
| join(complement(X_128),join(complement(X_128),X_128)) = complement(meet(zero,X_128)) ),
inference(resolve,[$cnf( $equal(join(complement(X_128),join(complement(X_128),X_128)),join(complement(X_128),join(X_128,complement(X_128)))) )],[refute_0_2298,refute_0_2299]) ).
cnf(refute_0_2301,plain,
join(complement(X_128),join(complement(X_128),X_128)) = complement(meet(zero,X_128)),
inference(resolve,[$cnf( $equal(join(complement(X_128),join(X_128,complement(X_128))),complement(meet(zero,X_128))) )],[refute_0_2297,refute_0_2300]) ).
cnf(refute_0_2302,plain,
( join(complement(X_128),join(complement(X_128),X_128)) != complement(meet(zero,X_128))
| join(complement(X_128),join(complement(X_128),X_128)) != top
| complement(meet(zero,X_128)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_128),join(complement(X_128),X_128)),top) ),[0],$fot(complement(meet(zero,X_128)))]]) ).
cnf(refute_0_2303,plain,
( join(complement(X_128),join(complement(X_128),X_128)) != top
| complement(meet(zero,X_128)) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_128),join(complement(X_128),X_128)),complement(meet(zero,X_128))) )],[refute_0_2301,refute_0_2302]) ).
cnf(refute_0_2304,plain,
complement(meet(zero,X_128)) = top,
inference(resolve,[$cnf( $equal(join(complement(X_128),join(complement(X_128),X_128)),top) )],[refute_0_513,refute_0_2303]) ).
cnf(refute_0_2305,plain,
complement(meet(zero,X_129)) = top,
inference(subst,[],[refute_0_2304:[bind(X_128,$fot(X_129))]]) ).
cnf(refute_0_2306,plain,
( complement(meet(zero,X_129)) != top
| meet(zero,X_129) != join(meet(B,meet(zero,X_129)),complement(join(complement(meet(zero,X_129)),B)))
| meet(zero,X_129) = join(meet(B,meet(zero,X_129)),complement(join(top,B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,X_129),join(meet(B,meet(zero,X_129)),complement(join(complement(meet(zero,X_129)),B)))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_2307,plain,
( meet(zero,X_129) != join(meet(B,meet(zero,X_129)),complement(join(complement(meet(zero,X_129)),B)))
| meet(zero,X_129) = join(meet(B,meet(zero,X_129)),complement(join(top,B))) ),
inference(resolve,[$cnf( $equal(complement(meet(zero,X_129)),top) )],[refute_0_2305,refute_0_2306]) ).
cnf(refute_0_2308,plain,
meet(zero,X_129) = join(meet(B,meet(zero,X_129)),complement(join(top,B))),
inference(resolve,[$cnf( $equal(meet(zero,X_129),join(meet(B,meet(zero,X_129)),complement(join(complement(meet(zero,X_129)),B)))) )],[refute_0_470,refute_0_2307]) ).
cnf(refute_0_2309,plain,
join(meet(B,meet(zero,X_129)),complement(join(top,B))) = join(complement(join(top,B)),meet(B,meet(zero,X_129))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(top,B)))),bind(B,$fot(meet(B,meet(zero,X_129))))]]) ).
cnf(refute_0_2310,plain,
( join(meet(B,meet(zero,X_129)),complement(join(top,B))) != join(complement(join(top,B)),meet(B,meet(zero,X_129)))
| meet(zero,X_129) != join(meet(B,meet(zero,X_129)),complement(join(top,B)))
| meet(zero,X_129) = join(complement(join(top,B)),meet(B,meet(zero,X_129))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,X_129),join(meet(B,meet(zero,X_129)),complement(join(top,B)))) ),[1],$fot(join(complement(join(top,B)),meet(B,meet(zero,X_129))))]]) ).
cnf(refute_0_2311,plain,
( meet(zero,X_129) != join(meet(B,meet(zero,X_129)),complement(join(top,B)))
| meet(zero,X_129) = join(complement(join(top,B)),meet(B,meet(zero,X_129))) ),
inference(resolve,[$cnf( $equal(join(meet(B,meet(zero,X_129)),complement(join(top,B))),join(complement(join(top,B)),meet(B,meet(zero,X_129)))) )],[refute_0_2309,refute_0_2310]) ).
cnf(refute_0_2312,plain,
meet(zero,X_129) = join(complement(join(top,B)),meet(B,meet(zero,X_129))),
inference(resolve,[$cnf( $equal(meet(zero,X_129),join(meet(B,meet(zero,X_129)),complement(join(top,B)))) )],[refute_0_2308,refute_0_2311]) ).
cnf(refute_0_2313,plain,
meet(zero,X_129) = complement(complement(meet(zero,X_129))),
inference(subst,[],[refute_0_395:[bind(X_10,$fot(meet(zero,X_129)))]]) ).
cnf(refute_0_2314,plain,
( complement(meet(zero,X_129)) != top
| meet(zero,X_129) != complement(complement(meet(zero,X_129)))
| meet(zero,X_129) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,X_129),complement(complement(meet(zero,X_129)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_2315,plain,
( meet(zero,X_129) != complement(complement(meet(zero,X_129)))
| meet(zero,X_129) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(meet(zero,X_129)),top) )],[refute_0_2305,refute_0_2314]) ).
cnf(refute_0_2316,plain,
meet(zero,X_129) = complement(top),
inference(resolve,[$cnf( $equal(meet(zero,X_129),complement(complement(meet(zero,X_129)))) )],[refute_0_2313,refute_0_2315]) ).
cnf(refute_0_2317,plain,
( complement(top) != zero
| meet(zero,X_129) != complement(top)
| meet(zero,X_129) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,X_129),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_2318,plain,
( meet(zero,X_129) != complement(top)
| meet(zero,X_129) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_118,refute_0_2317]) ).
cnf(refute_0_2319,plain,
meet(zero,X_129) = zero,
inference(resolve,[$cnf( $equal(meet(zero,X_129),complement(top)) )],[refute_0_2316,refute_0_2318]) ).
cnf(refute_0_2320,plain,
( meet(zero,X_129) != join(complement(join(top,B)),meet(B,meet(zero,X_129)))
| meet(zero,X_129) != zero
| zero = join(complement(join(top,B)),meet(B,meet(zero,X_129))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,X_129),join(complement(join(top,B)),meet(B,meet(zero,X_129)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_2321,plain,
( meet(zero,X_129) != join(complement(join(top,B)),meet(B,meet(zero,X_129)))
| zero = join(complement(join(top,B)),meet(B,meet(zero,X_129))) ),
inference(resolve,[$cnf( $equal(meet(zero,X_129),zero) )],[refute_0_2319,refute_0_2320]) ).
cnf(refute_0_2322,plain,
join(zero,meet(B,zero)) = meet(B,zero),
inference(subst,[],[refute_0_418:[bind(X_10,$fot(meet(B,zero)))]]) ).
cnf(refute_0_2323,plain,
meet(B,meet(zero,X_129)) = meet(B,meet(zero,X_129)),
introduced(tautology,[refl,[$fot(meet(B,meet(zero,X_129)))]]) ).
cnf(refute_0_2324,plain,
( meet(B,meet(zero,X_129)) != meet(B,meet(zero,X_129))
| meet(zero,X_129) != zero
| meet(B,meet(zero,X_129)) = meet(B,zero) ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,meet(zero,X_129)),meet(B,meet(zero,X_129))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2325,plain,
( meet(zero,X_129) != zero
| meet(B,meet(zero,X_129)) = meet(B,zero) ),
inference(resolve,[$cnf( $equal(meet(B,meet(zero,X_129)),meet(B,meet(zero,X_129))) )],[refute_0_2323,refute_0_2324]) ).
cnf(refute_0_2326,plain,
meet(B,meet(zero,X_129)) = meet(B,zero),
inference(resolve,[$cnf( $equal(meet(zero,X_129),zero) )],[refute_0_2319,refute_0_2325]) ).
cnf(refute_0_2327,plain,
join(zero,meet(B,meet(zero,X_129))) = join(zero,meet(B,meet(zero,X_129))),
introduced(tautology,[refl,[$fot(join(zero,meet(B,meet(zero,X_129))))]]) ).
cnf(refute_0_2328,plain,
( join(zero,meet(B,meet(zero,X_129))) != join(zero,meet(B,meet(zero,X_129)))
| meet(B,meet(zero,X_129)) != meet(B,zero)
| join(zero,meet(B,meet(zero,X_129))) = join(zero,meet(B,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(B,meet(zero,X_129))),join(zero,meet(B,meet(zero,X_129)))) ),[1,1],$fot(meet(B,zero))]]) ).
cnf(refute_0_2329,plain,
( meet(B,meet(zero,X_129)) != meet(B,zero)
| join(zero,meet(B,meet(zero,X_129))) = join(zero,meet(B,zero)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(B,meet(zero,X_129))),join(zero,meet(B,meet(zero,X_129)))) )],[refute_0_2327,refute_0_2328]) ).
cnf(refute_0_2330,plain,
join(zero,meet(B,meet(zero,X_129))) = join(zero,meet(B,zero)),
inference(resolve,[$cnf( $equal(meet(B,meet(zero,X_129)),meet(B,zero)) )],[refute_0_2326,refute_0_2329]) ).
cnf(refute_0_2331,plain,
meet(zero,X_129) = join(meet(meet(zero,X_129),B),complement(join(complement(meet(zero,X_129)),B))),
inference(subst,[],[refute_0_38:[bind(A,$fot(meet(zero,X_129)))]]) ).
cnf(refute_0_2332,plain,
( complement(meet(zero,X_129)) != top
| meet(zero,X_129) != join(meet(meet(zero,X_129),B),complement(join(complement(meet(zero,X_129)),B)))
| meet(zero,X_129) = join(meet(meet(zero,X_129),B),complement(join(top,B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,X_129),join(meet(meet(zero,X_129),B),complement(join(complement(meet(zero,X_129)),B)))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_2333,plain,
( meet(zero,X_129) != join(meet(meet(zero,X_129),B),complement(join(complement(meet(zero,X_129)),B)))
| meet(zero,X_129) = join(meet(meet(zero,X_129),B),complement(join(top,B))) ),
inference(resolve,[$cnf( $equal(complement(meet(zero,X_129)),top) )],[refute_0_2305,refute_0_2332]) ).
cnf(refute_0_2334,plain,
meet(zero,X_129) = join(meet(meet(zero,X_129),B),complement(join(top,B))),
inference(resolve,[$cnf( $equal(meet(zero,X_129),join(meet(meet(zero,X_129),B),complement(join(complement(meet(zero,X_129)),B)))) )],[refute_0_2331,refute_0_2333]) ).
cnf(refute_0_2335,plain,
( meet(zero,X_129) != join(meet(meet(zero,X_129),B),complement(join(top,B)))
| meet(zero,X_129) != zero
| zero = join(meet(meet(zero,X_129),B),complement(join(top,B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,X_129),join(meet(meet(zero,X_129),B),complement(join(top,B)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_2336,plain,
( meet(zero,X_129) != join(meet(meet(zero,X_129),B),complement(join(top,B)))
| zero = join(meet(meet(zero,X_129),B),complement(join(top,B))) ),
inference(resolve,[$cnf( $equal(meet(zero,X_129),zero) )],[refute_0_2319,refute_0_2335]) ).
cnf(refute_0_2337,plain,
join(complement(join(top,B)),zero) = complement(join(top,B)),
inference(subst,[],[refute_0_464:[bind(X_10,$fot(complement(join(top,B))))]]) ).
cnf(refute_0_2338,plain,
meet(zero,B) = zero,
inference(subst,[],[refute_0_2319:[bind(X_129,$fot(B))]]) ).
cnf(refute_0_2339,plain,
meet(meet(zero,X_129),B) = meet(meet(zero,X_129),B),
introduced(tautology,[refl,[$fot(meet(meet(zero,X_129),B))]]) ).
cnf(refute_0_2340,plain,
( meet(meet(zero,X_129),B) != meet(meet(zero,X_129),B)
| meet(zero,X_129) != zero
| meet(meet(zero,X_129),B) = meet(zero,B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(zero,X_129),B),meet(meet(zero,X_129),B)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_2341,plain,
( meet(zero,X_129) != zero
| meet(meet(zero,X_129),B) = meet(zero,B) ),
inference(resolve,[$cnf( $equal(meet(meet(zero,X_129),B),meet(meet(zero,X_129),B)) )],[refute_0_2339,refute_0_2340]) ).
cnf(refute_0_2342,plain,
meet(meet(zero,X_129),B) = meet(zero,B),
inference(resolve,[$cnf( $equal(meet(zero,X_129),zero) )],[refute_0_2319,refute_0_2341]) ).
cnf(refute_0_2343,plain,
( meet(meet(zero,X_129),B) != meet(zero,B)
| meet(zero,B) != zero
| meet(meet(zero,X_129),B) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(meet(zero,X_129),B))),bind(Y,$fot(meet(zero,B))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_2344,plain,
( meet(zero,B) != zero
| meet(meet(zero,X_129),B) = zero ),
inference(resolve,[$cnf( $equal(meet(meet(zero,X_129),B),meet(zero,B)) )],[refute_0_2342,refute_0_2343]) ).
cnf(refute_0_2345,plain,
meet(meet(zero,X_129),B) = zero,
inference(resolve,[$cnf( $equal(meet(zero,B),zero) )],[refute_0_2338,refute_0_2344]) ).
cnf(refute_0_2346,plain,
join(complement(join(top,B)),meet(meet(zero,X_129),B)) = join(complement(join(top,B)),meet(meet(zero,X_129),B)),
introduced(tautology,[refl,[$fot(join(complement(join(top,B)),meet(meet(zero,X_129),B)))]]) ).
cnf(refute_0_2347,plain,
( join(complement(join(top,B)),meet(meet(zero,X_129),B)) != join(complement(join(top,B)),meet(meet(zero,X_129),B))
| meet(meet(zero,X_129),B) != zero
| join(complement(join(top,B)),meet(meet(zero,X_129),B)) = join(complement(join(top,B)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(top,B)),meet(meet(zero,X_129),B)),join(complement(join(top,B)),meet(meet(zero,X_129),B))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2348,plain,
( meet(meet(zero,X_129),B) != zero
| join(complement(join(top,B)),meet(meet(zero,X_129),B)) = join(complement(join(top,B)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(meet(zero,X_129),B)),join(complement(join(top,B)),meet(meet(zero,X_129),B))) )],[refute_0_2346,refute_0_2347]) ).
cnf(refute_0_2349,plain,
join(complement(join(top,B)),meet(meet(zero,X_129),B)) = join(complement(join(top,B)),zero),
inference(resolve,[$cnf( $equal(meet(meet(zero,X_129),B),zero) )],[refute_0_2345,refute_0_2348]) ).
cnf(refute_0_2350,plain,
( join(complement(join(top,B)),meet(meet(zero,X_129),B)) != join(complement(join(top,B)),zero)
| join(complement(join(top,B)),zero) != complement(join(top,B))
| join(complement(join(top,B)),meet(meet(zero,X_129),B)) = complement(join(top,B)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(top,B)),meet(meet(zero,X_129),B)))),bind(Y,$fot(join(complement(join(top,B)),zero))),bind(Z,$fot(complement(join(top,B))))]]) ).
cnf(refute_0_2351,plain,
( join(complement(join(top,B)),zero) != complement(join(top,B))
| join(complement(join(top,B)),meet(meet(zero,X_129),B)) = complement(join(top,B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(meet(zero,X_129),B)),join(complement(join(top,B)),zero)) )],[refute_0_2349,refute_0_2350]) ).
cnf(refute_0_2352,plain,
join(complement(join(top,B)),meet(meet(zero,X_129),B)) = complement(join(top,B)),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),zero),complement(join(top,B))) )],[refute_0_2337,refute_0_2351]) ).
cnf(refute_0_2353,plain,
join(meet(meet(zero,X_129),B),complement(join(top,B))) = join(complement(join(top,B)),meet(meet(zero,X_129),B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(top,B)))),bind(B,$fot(meet(meet(zero,X_129),B)))]]) ).
cnf(refute_0_2354,plain,
( join(complement(join(top,B)),meet(meet(zero,X_129),B)) != complement(join(top,B))
| join(meet(meet(zero,X_129),B),complement(join(top,B))) != join(complement(join(top,B)),meet(meet(zero,X_129),B))
| join(meet(meet(zero,X_129),B),complement(join(top,B))) = complement(join(top,B)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(meet(zero,X_129),B),complement(join(top,B))))),bind(Y,$fot(join(complement(join(top,B)),meet(meet(zero,X_129),B)))),bind(Z,$fot(complement(join(top,B))))]]) ).
cnf(refute_0_2355,plain,
( join(complement(join(top,B)),meet(meet(zero,X_129),B)) != complement(join(top,B))
| join(meet(meet(zero,X_129),B),complement(join(top,B))) = complement(join(top,B)) ),
inference(resolve,[$cnf( $equal(join(meet(meet(zero,X_129),B),complement(join(top,B))),join(complement(join(top,B)),meet(meet(zero,X_129),B))) )],[refute_0_2353,refute_0_2354]) ).
cnf(refute_0_2356,plain,
join(meet(meet(zero,X_129),B),complement(join(top,B))) = complement(join(top,B)),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(meet(zero,X_129),B)),complement(join(top,B))) )],[refute_0_2352,refute_0_2355]) ).
cnf(refute_0_2357,plain,
( join(meet(meet(zero,X_129),B),complement(join(top,B))) != complement(join(top,B))
| zero != join(meet(meet(zero,X_129),B),complement(join(top,B)))
| zero = complement(join(top,B)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(meet(zero,X_129),B),complement(join(top,B)))) ),[1],$fot(complement(join(top,B)))]]) ).
cnf(refute_0_2358,plain,
( zero != join(meet(meet(zero,X_129),B),complement(join(top,B)))
| zero = complement(join(top,B)) ),
inference(resolve,[$cnf( $equal(join(meet(meet(zero,X_129),B),complement(join(top,B))),complement(join(top,B))) )],[refute_0_2356,refute_0_2357]) ).
cnf(refute_0_2359,plain,
( meet(zero,X_129) != join(meet(meet(zero,X_129),B),complement(join(top,B)))
| zero = complement(join(top,B)) ),
inference(resolve,[$cnf( $equal(zero,join(meet(meet(zero,X_129),B),complement(join(top,B)))) )],[refute_0_2336,refute_0_2358]) ).
cnf(refute_0_2360,plain,
zero = complement(join(top,B)),
inference(resolve,[$cnf( $equal(meet(zero,X_129),join(meet(meet(zero,X_129),B),complement(join(top,B)))) )],[refute_0_2334,refute_0_2359]) ).
cnf(refute_0_2361,plain,
( zero != complement(join(top,B))
| complement(join(top,B)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(join(top,B))))]]) ).
cnf(refute_0_2362,plain,
complement(join(top,B)) = zero,
inference(resolve,[$cnf( $equal(zero,complement(join(top,B))) )],[refute_0_2360,refute_0_2361]) ).
cnf(refute_0_2363,plain,
join(complement(join(top,B)),meet(B,meet(zero,X_129))) = join(complement(join(top,B)),meet(B,meet(zero,X_129))),
introduced(tautology,[refl,[$fot(join(complement(join(top,B)),meet(B,meet(zero,X_129))))]]) ).
cnf(refute_0_2364,plain,
( complement(join(top,B)) != zero
| join(complement(join(top,B)),meet(B,meet(zero,X_129))) != join(complement(join(top,B)),meet(B,meet(zero,X_129)))
| join(complement(join(top,B)),meet(B,meet(zero,X_129))) = join(zero,meet(B,meet(zero,X_129))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(top,B)),meet(B,meet(zero,X_129))),join(complement(join(top,B)),meet(B,meet(zero,X_129)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_2365,plain,
( complement(join(top,B)) != zero
| join(complement(join(top,B)),meet(B,meet(zero,X_129))) = join(zero,meet(B,meet(zero,X_129))) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(B,meet(zero,X_129))),join(complement(join(top,B)),meet(B,meet(zero,X_129)))) )],[refute_0_2363,refute_0_2364]) ).
cnf(refute_0_2366,plain,
join(complement(join(top,B)),meet(B,meet(zero,X_129))) = join(zero,meet(B,meet(zero,X_129))),
inference(resolve,[$cnf( $equal(complement(join(top,B)),zero) )],[refute_0_2362,refute_0_2365]) ).
cnf(refute_0_2367,plain,
( join(complement(join(top,B)),meet(B,meet(zero,X_129))) != join(zero,meet(B,meet(zero,X_129)))
| join(zero,meet(B,meet(zero,X_129))) != join(zero,meet(B,zero))
| join(complement(join(top,B)),meet(B,meet(zero,X_129))) = join(zero,meet(B,zero)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(top,B)),meet(B,meet(zero,X_129))))),bind(Y,$fot(join(zero,meet(B,meet(zero,X_129))))),bind(Z,$fot(join(zero,meet(B,zero))))]]) ).
cnf(refute_0_2368,plain,
( join(zero,meet(B,meet(zero,X_129))) != join(zero,meet(B,zero))
| join(complement(join(top,B)),meet(B,meet(zero,X_129))) = join(zero,meet(B,zero)) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(B,meet(zero,X_129))),join(zero,meet(B,meet(zero,X_129)))) )],[refute_0_2366,refute_0_2367]) ).
cnf(refute_0_2369,plain,
join(complement(join(top,B)),meet(B,meet(zero,X_129))) = join(zero,meet(B,zero)),
inference(resolve,[$cnf( $equal(join(zero,meet(B,meet(zero,X_129))),join(zero,meet(B,zero))) )],[refute_0_2330,refute_0_2368]) ).
cnf(refute_0_2370,plain,
( join(complement(join(top,B)),meet(B,meet(zero,X_129))) != join(zero,meet(B,zero))
| join(zero,meet(B,zero)) != meet(B,zero)
| join(complement(join(top,B)),meet(B,meet(zero,X_129))) = meet(B,zero) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(complement(join(top,B)),meet(B,meet(zero,X_129))))),bind(Y,$fot(join(zero,meet(B,zero)))),bind(Z,$fot(meet(B,zero)))]]) ).
cnf(refute_0_2371,plain,
( join(zero,meet(B,zero)) != meet(B,zero)
| join(complement(join(top,B)),meet(B,meet(zero,X_129))) = meet(B,zero) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(B,meet(zero,X_129))),join(zero,meet(B,zero))) )],[refute_0_2369,refute_0_2370]) ).
cnf(refute_0_2372,plain,
join(complement(join(top,B)),meet(B,meet(zero,X_129))) = meet(B,zero),
inference(resolve,[$cnf( $equal(join(zero,meet(B,zero)),meet(B,zero)) )],[refute_0_2322,refute_0_2371]) ).
cnf(refute_0_2373,plain,
( join(complement(join(top,B)),meet(B,meet(zero,X_129))) != meet(B,zero)
| zero != join(complement(join(top,B)),meet(B,meet(zero,X_129)))
| zero = meet(B,zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(complement(join(top,B)),meet(B,meet(zero,X_129)))) ),[1],$fot(meet(B,zero))]]) ).
cnf(refute_0_2374,plain,
( zero != join(complement(join(top,B)),meet(B,meet(zero,X_129)))
| zero = meet(B,zero) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(B,meet(zero,X_129))),meet(B,zero)) )],[refute_0_2372,refute_0_2373]) ).
cnf(refute_0_2375,plain,
( meet(zero,X_129) != join(complement(join(top,B)),meet(B,meet(zero,X_129)))
| zero = meet(B,zero) ),
inference(resolve,[$cnf( $equal(zero,join(complement(join(top,B)),meet(B,meet(zero,X_129)))) )],[refute_0_2321,refute_0_2374]) ).
cnf(refute_0_2376,plain,
zero = meet(B,zero),
inference(resolve,[$cnf( $equal(meet(zero,X_129),join(complement(join(top,B)),meet(B,meet(zero,X_129)))) )],[refute_0_2312,refute_0_2375]) ).
cnf(refute_0_2377,plain,
( zero != meet(B,zero)
| meet(B,zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(B,zero)))]]) ).
cnf(refute_0_2378,plain,
meet(B,zero) = zero,
inference(resolve,[$cnf( $equal(zero,meet(B,zero)) )],[refute_0_2376,refute_0_2377]) ).
cnf(refute_0_2379,plain,
meet(X_119,zero) = zero,
inference(subst,[],[refute_0_2378:[bind(B,$fot(X_119))]]) ).
cnf(refute_0_2380,plain,
join(X_118,meet(X_119,zero)) = join(X_118,meet(X_119,zero)),
introduced(tautology,[refl,[$fot(join(X_118,meet(X_119,zero)))]]) ).
cnf(refute_0_2381,plain,
( join(X_118,meet(X_119,zero)) != join(X_118,meet(X_119,zero))
| meet(X_119,zero) != zero
| join(X_118,meet(X_119,zero)) = join(X_118,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_118,meet(X_119,zero)),join(X_118,meet(X_119,zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2382,plain,
( meet(X_119,zero) != zero
| join(X_118,meet(X_119,zero)) = join(X_118,zero) ),
inference(resolve,[$cnf( $equal(join(X_118,meet(X_119,zero)),join(X_118,meet(X_119,zero))) )],[refute_0_2380,refute_0_2381]) ).
cnf(refute_0_2383,plain,
join(X_118,meet(X_119,zero)) = join(X_118,zero),
inference(resolve,[$cnf( $equal(meet(X_119,zero),zero) )],[refute_0_2379,refute_0_2382]) ).
cnf(refute_0_2384,plain,
( join(X_118,meet(X_119,zero)) != join(X_118,zero)
| join(X_118,zero) != X_118
| join(X_118,meet(X_119,zero)) = X_118 ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(X_118,meet(X_119,zero)))),bind(Y,$fot(join(X_118,zero))),bind(Z,$fot(X_118))]]) ).
cnf(refute_0_2385,plain,
( join(X_118,zero) != X_118
| join(X_118,meet(X_119,zero)) = X_118 ),
inference(resolve,[$cnf( $equal(join(X_118,meet(X_119,zero)),join(X_118,zero)) )],[refute_0_2383,refute_0_2384]) ).
cnf(refute_0_2386,plain,
join(X_118,meet(X_119,zero)) = X_118,
inference(resolve,[$cnf( $equal(join(X_118,zero),X_118) )],[refute_0_465,refute_0_2385]) ).
cnf(refute_0_2387,plain,
join(X_119,join(X_118,meet(X_119,zero))) = join(X_119,join(X_118,meet(X_119,zero))),
introduced(tautology,[refl,[$fot(join(X_119,join(X_118,meet(X_119,zero))))]]) ).
cnf(refute_0_2388,plain,
( join(X_118,meet(X_119,zero)) != X_118
| join(X_119,join(X_118,meet(X_119,zero))) != join(X_119,join(X_118,meet(X_119,zero)))
| join(X_119,join(X_118,meet(X_119,zero))) = join(X_119,X_118) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_119,join(X_118,meet(X_119,zero))),join(X_119,join(X_118,meet(X_119,zero)))) ),[1,1],$fot(X_118)]]) ).
cnf(refute_0_2389,plain,
( join(X_118,meet(X_119,zero)) != X_118
| join(X_119,join(X_118,meet(X_119,zero))) = join(X_119,X_118) ),
inference(resolve,[$cnf( $equal(join(X_119,join(X_118,meet(X_119,zero))),join(X_119,join(X_118,meet(X_119,zero)))) )],[refute_0_2387,refute_0_2388]) ).
cnf(refute_0_2390,plain,
join(X_119,join(X_118,meet(X_119,zero))) = join(X_119,X_118),
inference(resolve,[$cnf( $equal(join(X_118,meet(X_119,zero)),X_118) )],[refute_0_2386,refute_0_2389]) ).
cnf(refute_0_2391,plain,
( join(X_118,X_119) != join(X_119,join(X_118,meet(X_119,zero)))
| join(X_119,join(X_118,meet(X_119,zero))) != join(X_119,X_118)
| join(X_118,X_119) = join(X_119,X_118) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_118,X_119),join(X_119,X_118)) ),[0],$fot(join(X_119,join(X_118,meet(X_119,zero))))]]) ).
cnf(refute_0_2392,plain,
( join(X_118,X_119) != join(X_119,join(X_118,meet(X_119,zero)))
| join(X_118,X_119) = join(X_119,X_118) ),
inference(resolve,[$cnf( $equal(join(X_119,join(X_118,meet(X_119,zero))),join(X_119,X_118)) )],[refute_0_2390,refute_0_2391]) ).
cnf(refute_0_2393,plain,
join(X_118,X_119) = join(X_119,X_118),
inference(resolve,[$cnf( $equal(join(X_118,X_119),join(X_119,join(X_118,meet(X_119,zero)))) )],[refute_0_443,refute_0_2392]) ).
cnf(refute_0_2394,plain,
( join(X_118,X_119) != join(X_119,X_118)
| join(X_119,X_118) = join(X_118,X_119) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_118,X_119))),bind(Y,$fot(join(X_119,X_118)))]]) ).
cnf(refute_0_2395,plain,
join(X_119,X_118) = join(X_118,X_119),
inference(resolve,[$cnf( $equal(join(X_118,X_119),join(X_119,X_118)) )],[refute_0_2393,refute_0_2394]) ).
cnf(refute_0_2396,plain,
join(meet(X_315,X_316),X_315) = join(X_315,meet(X_315,X_316)),
inference(subst,[],[refute_0_2395:[bind(X_118,$fot(X_315)),bind(X_119,$fot(meet(X_315,X_316)))]]) ).
cnf(refute_0_2397,plain,
( join(meet(X_315,X_316),X_315) != join(X_315,meet(X_315,X_316))
| join(meet(X_315,X_316),X_315) != join(X_315,meet(complement(complement(X_316)),X_315))
| join(X_315,meet(X_315,X_316)) = join(X_315,meet(complement(complement(X_316)),X_315)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_315,X_316),X_315),join(X_315,meet(complement(complement(X_316)),X_315))) ),[0],$fot(join(X_315,meet(X_315,X_316)))]]) ).
cnf(refute_0_2398,plain,
( join(meet(X_315,X_316),X_315) != join(X_315,meet(complement(complement(X_316)),X_315))
| join(X_315,meet(X_315,X_316)) = join(X_315,meet(complement(complement(X_316)),X_315)) ),
inference(resolve,[$cnf( $equal(join(meet(X_315,X_316),X_315),join(X_315,meet(X_315,X_316))) )],[refute_0_2396,refute_0_2397]) ).
cnf(refute_0_2399,plain,
meet(join(complement(X_17),complement(X_18)),B) = meet(join(complement(X_17),complement(X_18)),B),
introduced(tautology,[refl,[$fot(meet(join(complement(X_17),complement(X_18)),B))]]) ).
cnf(refute_0_2400,plain,
( join(complement(X_17),complement(X_18)) != complement(meet(X_17,X_18))
| meet(join(complement(X_17),complement(X_18)),B) != meet(join(complement(X_17),complement(X_18)),B)
| meet(join(complement(X_17),complement(X_18)),B) = meet(complement(meet(X_17,X_18)),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),B),meet(join(complement(X_17),complement(X_18)),B)) ),[1,0],$fot(complement(meet(X_17,X_18)))]]) ).
cnf(refute_0_2401,plain,
( join(complement(X_17),complement(X_18)) != complement(meet(X_17,X_18))
| meet(join(complement(X_17),complement(X_18)),B) = meet(complement(meet(X_17,X_18)),B) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),B),meet(join(complement(X_17),complement(X_18)),B)) )],[refute_0_2399,refute_0_2400]) ).
cnf(refute_0_2402,plain,
meet(join(complement(X_17),complement(X_18)),B) = meet(complement(meet(X_17,X_18)),B),
inference(resolve,[$cnf( $equal(join(complement(X_17),complement(X_18)),complement(meet(X_17,X_18))) )],[refute_0_318,refute_0_2401]) ).
cnf(refute_0_2403,plain,
( meet(join(complement(X_17),complement(X_18)),B) != complement(join(meet(X_17,X_18),complement(B)))
| meet(join(complement(X_17),complement(X_18)),B) != meet(complement(meet(X_17,X_18)),B)
| meet(complement(meet(X_17,X_18)),B) = complement(join(meet(X_17,X_18),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),B),complement(join(meet(X_17,X_18),complement(B)))) ),[0],$fot(meet(complement(meet(X_17,X_18)),B))]]) ).
cnf(refute_0_2404,plain,
( meet(join(complement(X_17),complement(X_18)),B) != complement(join(meet(X_17,X_18),complement(B)))
| meet(complement(meet(X_17,X_18)),B) = complement(join(meet(X_17,X_18),complement(B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),B),meet(complement(meet(X_17,X_18)),B)) )],[refute_0_2402,refute_0_2403]) ).
cnf(refute_0_2405,plain,
meet(complement(meet(X_17,X_18)),B) = complement(join(meet(X_17,X_18),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_17),complement(X_18)),B),complement(join(meet(X_17,X_18),complement(B)))) )],[refute_0_109,refute_0_2404]) ).
cnf(refute_0_2406,plain,
meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)) = complement(join(meet(X_224,X_225),complement(join(complement(X_224),X_225)))),
inference(subst,[],[refute_0_2405:[bind(B,$fot(join(complement(X_224),X_225))),bind(X_17,$fot(X_224)),bind(X_18,$fot(X_225))]]) ).
cnf(refute_0_2407,plain,
X_224 = join(meet(X_224,X_225),complement(join(complement(X_224),X_225))),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_224)),bind(B,$fot(X_225))]]) ).
cnf(refute_0_2408,plain,
( X_224 != join(meet(X_224,X_225),complement(join(complement(X_224),X_225)))
| join(meet(X_224,X_225),complement(join(complement(X_224),X_225))) = X_224 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_224)),bind(Y,$fot(join(meet(X_224,X_225),complement(join(complement(X_224),X_225)))))]]) ).
cnf(refute_0_2409,plain,
join(meet(X_224,X_225),complement(join(complement(X_224),X_225))) = X_224,
inference(resolve,[$cnf( $equal(X_224,join(meet(X_224,X_225),complement(join(complement(X_224),X_225)))) )],[refute_0_2407,refute_0_2408]) ).
cnf(refute_0_2410,plain,
( join(meet(X_224,X_225),complement(join(complement(X_224),X_225))) != X_224
| meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)) != complement(join(meet(X_224,X_225),complement(join(complement(X_224),X_225))))
| meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)) = complement(X_224) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)),complement(join(meet(X_224,X_225),complement(join(complement(X_224),X_225))))) ),[1,0],$fot(X_224)]]) ).
cnf(refute_0_2411,plain,
( meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)) != complement(join(meet(X_224,X_225),complement(join(complement(X_224),X_225))))
| meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)) = complement(X_224) ),
inference(resolve,[$cnf( $equal(join(meet(X_224,X_225),complement(join(complement(X_224),X_225))),X_224) )],[refute_0_2409,refute_0_2410]) ).
cnf(refute_0_2412,plain,
meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)) = complement(X_224),
inference(resolve,[$cnf( $equal(meet(complement(meet(X_224,X_225)),join(complement(X_224),X_225)),complement(join(meet(X_224,X_225),complement(join(complement(X_224),X_225))))) )],[refute_0_2406,refute_0_2411]) ).
cnf(refute_0_2413,plain,
meet(complement(meet(complement(X_10),X_236)),join(complement(complement(X_10)),X_236)) = complement(complement(X_10)),
inference(subst,[],[refute_0_2412:[bind(X_224,$fot(complement(X_10))),bind(X_225,$fot(X_236))]]) ).
cnf(refute_0_2414,plain,
( complement(complement(X_10)) != X_10
| meet(complement(meet(complement(X_10),X_236)),join(complement(complement(X_10)),X_236)) != complement(complement(X_10))
| meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) = complement(complement(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(complement(X_10),X_236)),join(complement(complement(X_10)),X_236)),complement(complement(X_10))) ),[0,1,0],$fot(X_10)]]) ).
cnf(refute_0_2415,plain,
( meet(complement(meet(complement(X_10),X_236)),join(complement(complement(X_10)),X_236)) != complement(complement(X_10))
| meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_10)),X_10) )],[refute_0_397,refute_0_2414]) ).
cnf(refute_0_2416,plain,
meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) = complement(complement(X_10)),
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_10),X_236)),join(complement(complement(X_10)),X_236)),complement(complement(X_10))) )],[refute_0_2413,refute_0_2415]) ).
cnf(refute_0_2417,plain,
join(X_227,complement(X_226)) = complement(complement(join(X_227,complement(X_226)))),
inference(subst,[],[refute_0_395:[bind(X_10,$fot(join(X_227,complement(X_226))))]]) ).
cnf(refute_0_2418,plain,
meet(complement(meet(top,X_225)),X_223) = complement(join(meet(top,X_225),complement(X_223))),
inference(subst,[],[refute_0_2405:[bind(B,$fot(X_223)),bind(X_17,$fot(top)),bind(X_18,$fot(X_225))]]) ).
cnf(refute_0_2419,plain,
meet(top,X_225) = X_225,
inference(subst,[],[refute_0_429:[bind(B,$fot(X_225))]]) ).
cnf(refute_0_2420,plain,
( meet(complement(meet(top,X_225)),X_223) != complement(join(meet(top,X_225),complement(X_223)))
| meet(top,X_225) != X_225
| meet(complement(meet(top,X_225)),X_223) = complement(join(X_225,complement(X_223))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_225)),X_223),complement(join(meet(top,X_225),complement(X_223)))) ),[1,0,0],$fot(X_225)]]) ).
cnf(refute_0_2421,plain,
( meet(complement(meet(top,X_225)),X_223) != complement(join(meet(top,X_225),complement(X_223)))
| meet(complement(meet(top,X_225)),X_223) = complement(join(X_225,complement(X_223))) ),
inference(resolve,[$cnf( $equal(meet(top,X_225),X_225) )],[refute_0_2419,refute_0_2420]) ).
cnf(refute_0_2422,plain,
meet(complement(meet(top,X_225)),X_223) = complement(join(X_225,complement(X_223))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_225)),X_223),complement(join(meet(top,X_225),complement(X_223)))) )],[refute_0_2418,refute_0_2421]) ).
cnf(refute_0_2423,plain,
complement(meet(top,X_225)) = complement(meet(top,X_225)),
introduced(tautology,[refl,[$fot(complement(meet(top,X_225)))]]) ).
cnf(refute_0_2424,plain,
( complement(meet(top,X_225)) != complement(meet(top,X_225))
| meet(top,X_225) != X_225
| complement(meet(top,X_225)) = complement(X_225) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,X_225)),complement(meet(top,X_225))) ),[1,0],$fot(X_225)]]) ).
cnf(refute_0_2425,plain,
( meet(top,X_225) != X_225
| complement(meet(top,X_225)) = complement(X_225) ),
inference(resolve,[$cnf( $equal(complement(meet(top,X_225)),complement(meet(top,X_225))) )],[refute_0_2423,refute_0_2424]) ).
cnf(refute_0_2426,plain,
complement(meet(top,X_225)) = complement(X_225),
inference(resolve,[$cnf( $equal(meet(top,X_225),X_225) )],[refute_0_2419,refute_0_2425]) ).
cnf(refute_0_2427,plain,
meet(complement(meet(top,X_225)),X_223) = meet(complement(meet(top,X_225)),X_223),
introduced(tautology,[refl,[$fot(meet(complement(meet(top,X_225)),X_223))]]) ).
cnf(refute_0_2428,plain,
( complement(meet(top,X_225)) != complement(X_225)
| meet(complement(meet(top,X_225)),X_223) != meet(complement(meet(top,X_225)),X_223)
| meet(complement(meet(top,X_225)),X_223) = meet(complement(X_225),X_223) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_225)),X_223),meet(complement(meet(top,X_225)),X_223)) ),[1,0],$fot(complement(X_225))]]) ).
cnf(refute_0_2429,plain,
( complement(meet(top,X_225)) != complement(X_225)
| meet(complement(meet(top,X_225)),X_223) = meet(complement(X_225),X_223) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_225)),X_223),meet(complement(meet(top,X_225)),X_223)) )],[refute_0_2427,refute_0_2428]) ).
cnf(refute_0_2430,plain,
meet(complement(meet(top,X_225)),X_223) = meet(complement(X_225),X_223),
inference(resolve,[$cnf( $equal(complement(meet(top,X_225)),complement(X_225)) )],[refute_0_2426,refute_0_2429]) ).
cnf(refute_0_2431,plain,
( meet(complement(meet(top,X_225)),X_223) != complement(join(X_225,complement(X_223)))
| meet(complement(meet(top,X_225)),X_223) != meet(complement(X_225),X_223)
| meet(complement(X_225),X_223) = complement(join(X_225,complement(X_223))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_225)),X_223),complement(join(X_225,complement(X_223)))) ),[0],$fot(meet(complement(X_225),X_223))]]) ).
cnf(refute_0_2432,plain,
( meet(complement(meet(top,X_225)),X_223) != complement(join(X_225,complement(X_223)))
| meet(complement(X_225),X_223) = complement(join(X_225,complement(X_223))) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_225)),X_223),meet(complement(X_225),X_223)) )],[refute_0_2430,refute_0_2431]) ).
cnf(refute_0_2433,plain,
meet(complement(X_225),X_223) = complement(join(X_225,complement(X_223))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_225)),X_223),complement(join(X_225,complement(X_223)))) )],[refute_0_2422,refute_0_2432]) ).
cnf(refute_0_2434,plain,
meet(complement(X_227),X_226) = complement(join(X_227,complement(X_226))),
inference(subst,[],[refute_0_2433:[bind(X_223,$fot(X_226)),bind(X_225,$fot(X_227))]]) ).
cnf(refute_0_2435,plain,
( meet(complement(X_227),X_226) != complement(join(X_227,complement(X_226)))
| complement(join(X_227,complement(X_226))) = meet(complement(X_227),X_226) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_227),X_226))),bind(Y,$fot(complement(join(X_227,complement(X_226)))))]]) ).
cnf(refute_0_2436,plain,
complement(join(X_227,complement(X_226))) = meet(complement(X_227),X_226),
inference(resolve,[$cnf( $equal(meet(complement(X_227),X_226),complement(join(X_227,complement(X_226)))) )],[refute_0_2434,refute_0_2435]) ).
cnf(refute_0_2437,plain,
( complement(join(X_227,complement(X_226))) != meet(complement(X_227),X_226)
| join(X_227,complement(X_226)) != complement(complement(join(X_227,complement(X_226))))
| join(X_227,complement(X_226)) = complement(meet(complement(X_227),X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_227,complement(X_226)),complement(complement(join(X_227,complement(X_226))))) ),[1,0],$fot(meet(complement(X_227),X_226))]]) ).
cnf(refute_0_2438,plain,
( join(X_227,complement(X_226)) != complement(complement(join(X_227,complement(X_226))))
| join(X_227,complement(X_226)) = complement(meet(complement(X_227),X_226)) ),
inference(resolve,[$cnf( $equal(complement(join(X_227,complement(X_226))),meet(complement(X_227),X_226)) )],[refute_0_2436,refute_0_2437]) ).
cnf(refute_0_2439,plain,
join(X_227,complement(X_226)) = complement(meet(complement(X_227),X_226)),
inference(resolve,[$cnf( $equal(join(X_227,complement(X_226)),complement(complement(join(X_227,complement(X_226))))) )],[refute_0_2417,refute_0_2438]) ).
cnf(refute_0_2440,plain,
( join(X_227,complement(X_226)) != complement(meet(complement(X_227),X_226))
| complement(meet(complement(X_227),X_226)) = join(X_227,complement(X_226)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_227,complement(X_226)))),bind(Y,$fot(complement(meet(complement(X_227),X_226))))]]) ).
cnf(refute_0_2441,plain,
complement(meet(complement(X_227),X_226)) = join(X_227,complement(X_226)),
inference(resolve,[$cnf( $equal(join(X_227,complement(X_226)),complement(meet(complement(X_227),X_226))) )],[refute_0_2439,refute_0_2440]) ).
cnf(refute_0_2442,plain,
complement(meet(complement(X_10),X_236)) = join(X_10,complement(X_236)),
inference(subst,[],[refute_0_2441:[bind(X_226,$fot(X_236)),bind(X_227,$fot(X_10))]]) ).
cnf(refute_0_2443,plain,
meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))) = meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))),
introduced(tautology,[refl,[$fot(meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))))]]) ).
cnf(refute_0_2444,plain,
( complement(meet(complement(X_10),X_236)) != join(X_10,complement(X_236))
| meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))) != meet(join(X_10,X_236),complement(meet(complement(X_10),X_236)))
| meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))) = meet(join(X_10,X_236),join(X_10,complement(X_236))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))),meet(join(X_10,X_236),complement(meet(complement(X_10),X_236)))) ),[1,1],$fot(join(X_10,complement(X_236)))]]) ).
cnf(refute_0_2445,plain,
( complement(meet(complement(X_10),X_236)) != join(X_10,complement(X_236))
| meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))) = meet(join(X_10,X_236),join(X_10,complement(X_236))) ),
inference(resolve,[$cnf( $equal(meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))),meet(join(X_10,X_236),complement(meet(complement(X_10),X_236)))) )],[refute_0_2443,refute_0_2444]) ).
cnf(refute_0_2446,plain,
meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))) = meet(join(X_10,X_236),join(X_10,complement(X_236))),
inference(resolve,[$cnf( $equal(complement(meet(complement(X_10),X_236)),join(X_10,complement(X_236))) )],[refute_0_2442,refute_0_2445]) ).
cnf(refute_0_2447,plain,
meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) = meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))),
inference(subst,[],[refute_0_274:[bind(X_17,$fot(join(X_10,X_236))),bind(X_18,$fot(complement(meet(complement(X_10),X_236))))]]) ).
cnf(refute_0_2448,plain,
( meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) != meet(join(X_10,X_236),complement(meet(complement(X_10),X_236)))
| meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))) != meet(join(X_10,X_236),join(X_10,complement(X_236)))
| meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) = meet(join(X_10,X_236),join(X_10,complement(X_236))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)))),bind(Y,$fot(meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))))),bind(Z,$fot(meet(join(X_10,X_236),join(X_10,complement(X_236)))))]]) ).
cnf(refute_0_2449,plain,
( meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))) != meet(join(X_10,X_236),join(X_10,complement(X_236)))
| meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) = meet(join(X_10,X_236),join(X_10,complement(X_236))) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)),meet(join(X_10,X_236),complement(meet(complement(X_10),X_236)))) )],[refute_0_2447,refute_0_2448]) ).
cnf(refute_0_2450,plain,
meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) = meet(join(X_10,X_236),join(X_10,complement(X_236))),
inference(resolve,[$cnf( $equal(meet(join(X_10,X_236),complement(meet(complement(X_10),X_236))),meet(join(X_10,X_236),join(X_10,complement(X_236)))) )],[refute_0_2446,refute_0_2449]) ).
cnf(refute_0_2451,plain,
( meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) != complement(complement(X_10))
| meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) != meet(join(X_10,X_236),join(X_10,complement(X_236)))
| meet(join(X_10,X_236),join(X_10,complement(X_236))) = complement(complement(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)),complement(complement(X_10))) ),[0],$fot(meet(join(X_10,X_236),join(X_10,complement(X_236))))]]) ).
cnf(refute_0_2452,plain,
( meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) != complement(complement(X_10))
| meet(join(X_10,X_236),join(X_10,complement(X_236))) = complement(complement(X_10)) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)),meet(join(X_10,X_236),join(X_10,complement(X_236)))) )],[refute_0_2450,refute_0_2451]) ).
cnf(refute_0_2453,plain,
( complement(complement(X_10)) != X_10
| meet(join(X_10,X_236),join(X_10,complement(X_236))) != complement(complement(X_10))
| meet(join(X_10,X_236),join(X_10,complement(X_236))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_10,X_236),join(X_10,complement(X_236))),complement(complement(X_10))) ),[1],$fot(X_10)]]) ).
cnf(refute_0_2454,plain,
( meet(join(X_10,X_236),join(X_10,complement(X_236))) != complement(complement(X_10))
| meet(join(X_10,X_236),join(X_10,complement(X_236))) = X_10 ),
inference(resolve,[$cnf( $equal(complement(complement(X_10)),X_10) )],[refute_0_397,refute_0_2453]) ).
cnf(refute_0_2455,plain,
( meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)) != complement(complement(X_10))
| meet(join(X_10,X_236),join(X_10,complement(X_236))) = X_10 ),
inference(resolve,[$cnf( $equal(meet(join(X_10,X_236),join(X_10,complement(X_236))),complement(complement(X_10))) )],[refute_0_2452,refute_0_2454]) ).
cnf(refute_0_2456,plain,
meet(join(X_10,X_236),join(X_10,complement(X_236))) = X_10,
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_10),X_236)),join(X_10,X_236)),complement(complement(X_10))) )],[refute_0_2416,refute_0_2455]) ).
cnf(refute_0_2457,plain,
meet(join(X_311,join(complement(X_311),X_16)),join(X_311,complement(join(complement(X_311),X_16)))) = X_311,
inference(subst,[],[refute_0_2456:[bind(X_10,$fot(X_311)),bind(X_236,$fot(join(complement(X_311),X_16)))]]) ).
cnf(refute_0_2458,plain,
join(X_14,join(complement(X_14),X_16)) = join(join(X_14,complement(X_14)),X_16),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_14)),bind(B,$fot(complement(X_14))),bind(C,$fot(X_16))]]) ).
cnf(refute_0_2459,plain,
top = join(X_14,complement(X_14)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_2460,plain,
( top != join(X_14,complement(X_14))
| join(X_14,complement(X_14)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_14,complement(X_14))))]]) ).
cnf(refute_0_2461,plain,
join(X_14,complement(X_14)) = top,
inference(resolve,[$cnf( $equal(top,join(X_14,complement(X_14))) )],[refute_0_2459,refute_0_2460]) ).
cnf(refute_0_2462,plain,
( join(X_14,complement(X_14)) != top
| join(X_14,join(complement(X_14),X_16)) != join(join(X_14,complement(X_14)),X_16)
| join(X_14,join(complement(X_14),X_16)) = join(top,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_14,join(complement(X_14),X_16)),join(join(X_14,complement(X_14)),X_16)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_2463,plain,
( join(X_14,join(complement(X_14),X_16)) != join(join(X_14,complement(X_14)),X_16)
| join(X_14,join(complement(X_14),X_16)) = join(top,X_16) ),
inference(resolve,[$cnf( $equal(join(X_14,complement(X_14)),top) )],[refute_0_2461,refute_0_2462]) ).
cnf(refute_0_2464,plain,
join(X_14,join(complement(X_14),X_16)) = join(top,X_16),
inference(resolve,[$cnf( $equal(join(X_14,join(complement(X_14),X_16)),join(join(X_14,complement(X_14)),X_16)) )],[refute_0_2458,refute_0_2463]) ).
cnf(refute_0_2465,plain,
join(top,X_76) = join(meet(join(top,X_76),meet(zero,X_76)),complement(join(meet(zero,X_76),complement(join(top,X_76))))),
inference(subst,[],[refute_0_155:[bind(X_10,$fot(join(top,X_76))),bind(X_11,$fot(meet(zero,X_76)))]]) ).
cnf(refute_0_2466,plain,
zero = join(meet(zero,X_76),complement(join(top,X_76))),
inference(subst,[],[refute_0_1515:[bind(B,$fot(X_76))]]) ).
cnf(refute_0_2467,plain,
( zero != join(meet(zero,X_76),complement(join(top,X_76)))
| join(meet(zero,X_76),complement(join(top,X_76))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(join(meet(zero,X_76),complement(join(top,X_76)))))]]) ).
cnf(refute_0_2468,plain,
join(meet(zero,X_76),complement(join(top,X_76))) = zero,
inference(resolve,[$cnf( $equal(zero,join(meet(zero,X_76),complement(join(top,X_76)))) )],[refute_0_2466,refute_0_2467]) ).
cnf(refute_0_2469,plain,
( join(meet(zero,X_76),complement(join(top,X_76))) != zero
| join(top,X_76) != join(meet(join(top,X_76),meet(zero,X_76)),complement(join(meet(zero,X_76),complement(join(top,X_76)))))
| join(top,X_76) = join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,X_76),join(meet(join(top,X_76),meet(zero,X_76)),complement(join(meet(zero,X_76),complement(join(top,X_76)))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_2470,plain,
( join(top,X_76) != join(meet(join(top,X_76),meet(zero,X_76)),complement(join(meet(zero,X_76),complement(join(top,X_76)))))
| join(top,X_76) = join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) ),
inference(resolve,[$cnf( $equal(join(meet(zero,X_76),complement(join(top,X_76))),zero) )],[refute_0_2468,refute_0_2469]) ).
cnf(refute_0_2471,plain,
join(top,X_76) = join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)),
inference(resolve,[$cnf( $equal(join(top,X_76),join(meet(join(top,X_76),meet(zero,X_76)),complement(join(meet(zero,X_76),complement(join(top,X_76)))))) )],[refute_0_2465,refute_0_2470]) ).
cnf(refute_0_2472,plain,
join(complement(zero),meet(join(top,X_76),meet(zero,X_76))) = join(complement(zero),meet(join(top,X_76),meet(zero,X_76))),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(join(top,X_76),meet(zero,X_76))))]]) ).
cnf(refute_0_2473,plain,
( complement(zero) != top
| join(complement(zero),meet(join(top,X_76),meet(zero,X_76))) != join(complement(zero),meet(join(top,X_76),meet(zero,X_76)))
| join(complement(zero),meet(join(top,X_76),meet(zero,X_76))) = join(top,meet(join(top,X_76),meet(zero,X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(join(top,X_76),meet(zero,X_76))),join(complement(zero),meet(join(top,X_76),meet(zero,X_76)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_2474,plain,
( complement(zero) != top
| join(complement(zero),meet(join(top,X_76),meet(zero,X_76))) = join(top,meet(join(top,X_76),meet(zero,X_76))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(top,X_76),meet(zero,X_76))),join(complement(zero),meet(join(top,X_76),meet(zero,X_76)))) )],[refute_0_2472,refute_0_2473]) ).
cnf(refute_0_2475,plain,
join(complement(zero),meet(join(top,X_76),meet(zero,X_76))) = join(top,meet(join(top,X_76),meet(zero,X_76))),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_618,refute_0_2474]) ).
cnf(refute_0_2476,plain,
join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) = join(complement(zero),meet(join(top,X_76),meet(zero,X_76))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(zero))),bind(B,$fot(meet(join(top,X_76),meet(zero,X_76))))]]) ).
cnf(refute_0_2477,plain,
( join(complement(zero),meet(join(top,X_76),meet(zero,X_76))) != join(top,meet(join(top,X_76),meet(zero,X_76)))
| join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) != join(complement(zero),meet(join(top,X_76),meet(zero,X_76)))
| join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) = join(top,meet(join(top,X_76),meet(zero,X_76))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)))),bind(Y,$fot(join(complement(zero),meet(join(top,X_76),meet(zero,X_76))))),bind(Z,$fot(join(top,meet(join(top,X_76),meet(zero,X_76)))))]]) ).
cnf(refute_0_2478,plain,
( join(complement(zero),meet(join(top,X_76),meet(zero,X_76))) != join(top,meet(join(top,X_76),meet(zero,X_76)))
| join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) = join(top,meet(join(top,X_76),meet(zero,X_76))) ),
inference(resolve,[$cnf( $equal(join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)),join(complement(zero),meet(join(top,X_76),meet(zero,X_76)))) )],[refute_0_2476,refute_0_2477]) ).
cnf(refute_0_2479,plain,
join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) = join(top,meet(join(top,X_76),meet(zero,X_76))),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(top,X_76),meet(zero,X_76))),join(top,meet(join(top,X_76),meet(zero,X_76)))) )],[refute_0_2475,refute_0_2478]) ).
cnf(refute_0_2480,plain,
( join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)) != join(top,meet(join(top,X_76),meet(zero,X_76)))
| join(top,X_76) != join(meet(join(top,X_76),meet(zero,X_76)),complement(zero))
| join(top,X_76) = join(top,meet(join(top,X_76),meet(zero,X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,X_76),join(meet(join(top,X_76),meet(zero,X_76)),complement(zero))) ),[1],$fot(join(top,meet(join(top,X_76),meet(zero,X_76))))]]) ).
cnf(refute_0_2481,plain,
( join(top,X_76) != join(meet(join(top,X_76),meet(zero,X_76)),complement(zero))
| join(top,X_76) = join(top,meet(join(top,X_76),meet(zero,X_76))) ),
inference(resolve,[$cnf( $equal(join(meet(join(top,X_76),meet(zero,X_76)),complement(zero)),join(top,meet(join(top,X_76),meet(zero,X_76)))) )],[refute_0_2479,refute_0_2480]) ).
cnf(refute_0_2482,plain,
join(top,X_76) = join(top,meet(join(top,X_76),meet(zero,X_76))),
inference(resolve,[$cnf( $equal(join(top,X_76),join(meet(join(top,X_76),meet(zero,X_76)),complement(zero))) )],[refute_0_2471,refute_0_2481]) ).
cnf(refute_0_2483,plain,
meet(join(top,X_76),zero) = zero,
inference(subst,[],[refute_0_2378:[bind(B,$fot(join(top,X_76)))]]) ).
cnf(refute_0_2484,plain,
meet(zero,X_76) = zero,
inference(subst,[],[refute_0_2319:[bind(X_129,$fot(X_76))]]) ).
cnf(refute_0_2485,plain,
meet(join(top,X_76),meet(zero,X_76)) = meet(join(top,X_76),meet(zero,X_76)),
introduced(tautology,[refl,[$fot(meet(join(top,X_76),meet(zero,X_76)))]]) ).
cnf(refute_0_2486,plain,
( meet(join(top,X_76),meet(zero,X_76)) != meet(join(top,X_76),meet(zero,X_76))
| meet(zero,X_76) != zero
| meet(join(top,X_76),meet(zero,X_76)) = meet(join(top,X_76),zero) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(top,X_76),meet(zero,X_76)),meet(join(top,X_76),meet(zero,X_76))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2487,plain,
( meet(zero,X_76) != zero
| meet(join(top,X_76),meet(zero,X_76)) = meet(join(top,X_76),zero) ),
inference(resolve,[$cnf( $equal(meet(join(top,X_76),meet(zero,X_76)),meet(join(top,X_76),meet(zero,X_76))) )],[refute_0_2485,refute_0_2486]) ).
cnf(refute_0_2488,plain,
meet(join(top,X_76),meet(zero,X_76)) = meet(join(top,X_76),zero),
inference(resolve,[$cnf( $equal(meet(zero,X_76),zero) )],[refute_0_2484,refute_0_2487]) ).
cnf(refute_0_2489,plain,
( meet(join(top,X_76),meet(zero,X_76)) != meet(join(top,X_76),zero)
| meet(join(top,X_76),zero) != zero
| meet(join(top,X_76),meet(zero,X_76)) = zero ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(join(top,X_76),meet(zero,X_76)))),bind(Y,$fot(meet(join(top,X_76),zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_2490,plain,
( meet(join(top,X_76),zero) != zero
| meet(join(top,X_76),meet(zero,X_76)) = zero ),
inference(resolve,[$cnf( $equal(meet(join(top,X_76),meet(zero,X_76)),meet(join(top,X_76),zero)) )],[refute_0_2488,refute_0_2489]) ).
cnf(refute_0_2491,plain,
meet(join(top,X_76),meet(zero,X_76)) = zero,
inference(resolve,[$cnf( $equal(meet(join(top,X_76),zero),zero) )],[refute_0_2483,refute_0_2490]) ).
cnf(refute_0_2492,plain,
join(top,meet(join(top,X_76),meet(zero,X_76))) = join(top,meet(join(top,X_76),meet(zero,X_76))),
introduced(tautology,[refl,[$fot(join(top,meet(join(top,X_76),meet(zero,X_76))))]]) ).
cnf(refute_0_2493,plain,
( join(top,meet(join(top,X_76),meet(zero,X_76))) != join(top,meet(join(top,X_76),meet(zero,X_76)))
| meet(join(top,X_76),meet(zero,X_76)) != zero
| join(top,meet(join(top,X_76),meet(zero,X_76))) = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,meet(join(top,X_76),meet(zero,X_76))),join(top,meet(join(top,X_76),meet(zero,X_76)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_2494,plain,
( meet(join(top,X_76),meet(zero,X_76)) != zero
| join(top,meet(join(top,X_76),meet(zero,X_76))) = join(top,zero) ),
inference(resolve,[$cnf( $equal(join(top,meet(join(top,X_76),meet(zero,X_76))),join(top,meet(join(top,X_76),meet(zero,X_76)))) )],[refute_0_2492,refute_0_2493]) ).
cnf(refute_0_2495,plain,
join(top,meet(join(top,X_76),meet(zero,X_76))) = join(top,zero),
inference(resolve,[$cnf( $equal(meet(join(top,X_76),meet(zero,X_76)),zero) )],[refute_0_2491,refute_0_2494]) ).
cnf(refute_0_2496,plain,
( join(top,meet(join(top,X_76),meet(zero,X_76))) != join(top,zero)
| join(top,zero) != top
| join(top,meet(join(top,X_76),meet(zero,X_76))) = top ),
inference(subst,[],[refute_0_14:[bind(X,$fot(join(top,meet(join(top,X_76),meet(zero,X_76))))),bind(Y,$fot(join(top,zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_2497,plain,
( join(top,zero) != top
| join(top,meet(join(top,X_76),meet(zero,X_76))) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(join(top,X_76),meet(zero,X_76))),join(top,zero)) )],[refute_0_2495,refute_0_2496]) ).
cnf(refute_0_2498,plain,
join(top,meet(join(top,X_76),meet(zero,X_76))) = top,
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_555,refute_0_2497]) ).
cnf(refute_0_2499,plain,
( join(top,X_76) != join(top,meet(join(top,X_76),meet(zero,X_76)))
| join(top,meet(join(top,X_76),meet(zero,X_76))) != top
| join(top,X_76) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(top,X_76),top) ),[0],$fot(join(top,meet(join(top,X_76),meet(zero,X_76))))]]) ).
cnf(refute_0_2500,plain,
( join(top,X_76) != join(top,meet(join(top,X_76),meet(zero,X_76)))
| join(top,X_76) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(join(top,X_76),meet(zero,X_76))),top) )],[refute_0_2498,refute_0_2499]) ).
cnf(refute_0_2501,plain,
join(top,X_76) = top,
inference(resolve,[$cnf( $equal(join(top,X_76),join(top,meet(join(top,X_76),meet(zero,X_76)))) )],[refute_0_2482,refute_0_2500]) ).
cnf(refute_0_2502,plain,
join(top,X_16) = top,
inference(subst,[],[refute_0_2501:[bind(X_76,$fot(X_16))]]) ).
cnf(refute_0_2503,plain,
( join(X_14,join(complement(X_14),X_16)) != join(top,X_16)
| join(top,X_16) != top
| join(X_14,join(complement(X_14),X_16)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_14,join(complement(X_14),X_16)),top) ),[0],$fot(join(top,X_16))]]) ).
cnf(refute_0_2504,plain,
( join(X_14,join(complement(X_14),X_16)) != join(top,X_16)
| join(X_14,join(complement(X_14),X_16)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_16),top) )],[refute_0_2502,refute_0_2503]) ).
cnf(refute_0_2505,plain,
join(X_14,join(complement(X_14),X_16)) = top,
inference(resolve,[$cnf( $equal(join(X_14,join(complement(X_14),X_16)),join(top,X_16)) )],[refute_0_2464,refute_0_2504]) ).
cnf(refute_0_2506,plain,
join(X_311,join(complement(X_311),X_16)) = top,
inference(subst,[],[refute_0_2505:[bind(X_14,$fot(X_311))]]) ).
cnf(refute_0_2507,plain,
( join(X_311,join(complement(X_311),X_16)) != top
| meet(join(X_311,join(complement(X_311),X_16)),join(X_311,complement(join(complement(X_311),X_16)))) != X_311
| meet(top,join(X_311,complement(join(complement(X_311),X_16)))) = X_311 ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_311,join(complement(X_311),X_16)),join(X_311,complement(join(complement(X_311),X_16)))),X_311) ),[0,0],$fot(top)]]) ).
cnf(refute_0_2508,plain,
( meet(join(X_311,join(complement(X_311),X_16)),join(X_311,complement(join(complement(X_311),X_16)))) != X_311
| meet(top,join(X_311,complement(join(complement(X_311),X_16)))) = X_311 ),
inference(resolve,[$cnf( $equal(join(X_311,join(complement(X_311),X_16)),top) )],[refute_0_2506,refute_0_2507]) ).
cnf(refute_0_2509,plain,
meet(top,join(X_311,complement(join(complement(X_311),X_16)))) = X_311,
inference(resolve,[$cnf( $equal(meet(join(X_311,join(complement(X_311),X_16)),join(X_311,complement(join(complement(X_311),X_16)))),X_311) )],[refute_0_2457,refute_0_2508]) ).
cnf(refute_0_2510,plain,
join(complement(X_226),X_227) = join(X_227,complement(X_226)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_226))),bind(B,$fot(X_227))]]) ).
cnf(refute_0_2511,plain,
( join(complement(X_226),X_227) != join(X_227,complement(X_226))
| join(X_227,complement(X_226)) = join(complement(X_226),X_227) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_226),X_227))),bind(Y,$fot(join(X_227,complement(X_226))))]]) ).
cnf(refute_0_2512,plain,
join(X_227,complement(X_226)) = join(complement(X_226),X_227),
inference(resolve,[$cnf( $equal(join(complement(X_226),X_227),join(X_227,complement(X_226))) )],[refute_0_2510,refute_0_2511]) ).
cnf(refute_0_2513,plain,
( join(X_227,complement(X_226)) != join(complement(X_226),X_227)
| meet(complement(X_227),X_226) != complement(join(X_227,complement(X_226)))
| meet(complement(X_227),X_226) = complement(join(complement(X_226),X_227)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_227),X_226),complement(join(X_227,complement(X_226)))) ),[1,0],$fot(join(complement(X_226),X_227))]]) ).
cnf(refute_0_2514,plain,
( meet(complement(X_227),X_226) != complement(join(X_227,complement(X_226)))
| meet(complement(X_227),X_226) = complement(join(complement(X_226),X_227)) ),
inference(resolve,[$cnf( $equal(join(X_227,complement(X_226)),join(complement(X_226),X_227)) )],[refute_0_2512,refute_0_2513]) ).
cnf(refute_0_2515,plain,
meet(complement(X_227),X_226) = complement(join(complement(X_226),X_227)),
inference(resolve,[$cnf( $equal(meet(complement(X_227),X_226),complement(join(X_227,complement(X_226)))) )],[refute_0_2434,refute_0_2514]) ).
cnf(refute_0_2516,plain,
( meet(complement(X_227),X_226) != complement(join(complement(X_226),X_227))
| complement(join(complement(X_226),X_227)) = meet(complement(X_227),X_226) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_227),X_226))),bind(Y,$fot(complement(join(complement(X_226),X_227))))]]) ).
cnf(refute_0_2517,plain,
complement(join(complement(X_226),X_227)) = meet(complement(X_227),X_226),
inference(resolve,[$cnf( $equal(meet(complement(X_227),X_226),complement(join(complement(X_226),X_227))) )],[refute_0_2515,refute_0_2516]) ).
cnf(refute_0_2518,plain,
complement(join(complement(X_311),X_16)) = meet(complement(X_16),X_311),
inference(subst,[],[refute_0_2517:[bind(X_226,$fot(X_311)),bind(X_227,$fot(X_16))]]) ).
cnf(refute_0_2519,plain,
join(X_311,complement(join(complement(X_311),X_16))) = join(X_311,complement(join(complement(X_311),X_16))),
introduced(tautology,[refl,[$fot(join(X_311,complement(join(complement(X_311),X_16))))]]) ).
cnf(refute_0_2520,plain,
( complement(join(complement(X_311),X_16)) != meet(complement(X_16),X_311)
| join(X_311,complement(join(complement(X_311),X_16))) != join(X_311,complement(join(complement(X_311),X_16)))
| join(X_311,complement(join(complement(X_311),X_16))) = join(X_311,meet(complement(X_16),X_311)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_311,complement(join(complement(X_311),X_16))),join(X_311,complement(join(complement(X_311),X_16)))) ),[1,1],$fot(meet(complement(X_16),X_311))]]) ).
cnf(refute_0_2521,plain,
( complement(join(complement(X_311),X_16)) != meet(complement(X_16),X_311)
| join(X_311,complement(join(complement(X_311),X_16))) = join(X_311,meet(complement(X_16),X_311)) ),
inference(resolve,[$cnf( $equal(join(X_311,complement(join(complement(X_311),X_16))),join(X_311,complement(join(complement(X_311),X_16)))) )],[refute_0_2519,refute_0_2520]) ).
cnf(refute_0_2522,plain,
join(X_311,complement(join(complement(X_311),X_16))) = join(X_311,meet(complement(X_16),X_311)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_311),X_16)),meet(complement(X_16),X_311)) )],[refute_0_2518,refute_0_2521]) ).
cnf(refute_0_2523,plain,
meet(top,join(X_311,complement(join(complement(X_311),X_16)))) = join(X_311,complement(join(complement(X_311),X_16))),
inference(subst,[],[refute_0_429:[bind(B,$fot(join(X_311,complement(join(complement(X_311),X_16)))))]]) ).
cnf(refute_0_2524,plain,
( join(X_311,complement(join(complement(X_311),X_16))) != join(X_311,meet(complement(X_16),X_311))
| meet(top,join(X_311,complement(join(complement(X_311),X_16)))) != join(X_311,complement(join(complement(X_311),X_16)))
| meet(top,join(X_311,complement(join(complement(X_311),X_16)))) = join(X_311,meet(complement(X_16),X_311)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(meet(top,join(X_311,complement(join(complement(X_311),X_16)))))),bind(Y,$fot(join(X_311,complement(join(complement(X_311),X_16))))),bind(Z,$fot(join(X_311,meet(complement(X_16),X_311))))]]) ).
cnf(refute_0_2525,plain,
( join(X_311,complement(join(complement(X_311),X_16))) != join(X_311,meet(complement(X_16),X_311))
| meet(top,join(X_311,complement(join(complement(X_311),X_16)))) = join(X_311,meet(complement(X_16),X_311)) ),
inference(resolve,[$cnf( $equal(meet(top,join(X_311,complement(join(complement(X_311),X_16)))),join(X_311,complement(join(complement(X_311),X_16)))) )],[refute_0_2523,refute_0_2524]) ).
cnf(refute_0_2526,plain,
meet(top,join(X_311,complement(join(complement(X_311),X_16)))) = join(X_311,meet(complement(X_16),X_311)),
inference(resolve,[$cnf( $equal(join(X_311,complement(join(complement(X_311),X_16))),join(X_311,meet(complement(X_16),X_311))) )],[refute_0_2522,refute_0_2525]) ).
cnf(refute_0_2527,plain,
( meet(top,join(X_311,complement(join(complement(X_311),X_16)))) != X_311
| meet(top,join(X_311,complement(join(complement(X_311),X_16)))) != join(X_311,meet(complement(X_16),X_311))
| join(X_311,meet(complement(X_16),X_311)) = X_311 ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(X_311,complement(join(complement(X_311),X_16)))),X_311) ),[0],$fot(join(X_311,meet(complement(X_16),X_311)))]]) ).
cnf(refute_0_2528,plain,
( meet(top,join(X_311,complement(join(complement(X_311),X_16)))) != X_311
| join(X_311,meet(complement(X_16),X_311)) = X_311 ),
inference(resolve,[$cnf( $equal(meet(top,join(X_311,complement(join(complement(X_311),X_16)))),join(X_311,meet(complement(X_16),X_311))) )],[refute_0_2526,refute_0_2527]) ).
cnf(refute_0_2529,plain,
join(X_311,meet(complement(X_16),X_311)) = X_311,
inference(resolve,[$cnf( $equal(meet(top,join(X_311,complement(join(complement(X_311),X_16)))),X_311) )],[refute_0_2509,refute_0_2528]) ).
cnf(refute_0_2530,plain,
join(X_315,meet(complement(complement(X_316)),X_315)) = X_315,
inference(subst,[],[refute_0_2529:[bind(X_16,$fot(complement(X_316))),bind(X_311,$fot(X_315))]]) ).
cnf(refute_0_2531,plain,
( join(X_315,meet(X_315,X_316)) != join(X_315,meet(complement(complement(X_316)),X_315))
| join(X_315,meet(complement(complement(X_316)),X_315)) != X_315
| join(X_315,meet(X_315,X_316)) = X_315 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_315,meet(X_315,X_316)),X_315) ),[0],$fot(join(X_315,meet(complement(complement(X_316)),X_315)))]]) ).
cnf(refute_0_2532,plain,
( join(X_315,meet(X_315,X_316)) != join(X_315,meet(complement(complement(X_316)),X_315))
| join(X_315,meet(X_315,X_316)) = X_315 ),
inference(resolve,[$cnf( $equal(join(X_315,meet(complement(complement(X_316)),X_315)),X_315) )],[refute_0_2530,refute_0_2531]) ).
cnf(refute_0_2533,plain,
( join(meet(X_315,X_316),X_315) != join(X_315,meet(complement(complement(X_316)),X_315))
| join(X_315,meet(X_315,X_316)) = X_315 ),
inference(resolve,[$cnf( $equal(join(X_315,meet(X_315,X_316)),join(X_315,meet(complement(complement(X_316)),X_315))) )],[refute_0_2398,refute_0_2532]) ).
cnf(refute_0_2534,plain,
join(X_315,meet(X_315,X_316)) = X_315,
inference(resolve,[$cnf( $equal(join(meet(X_315,X_316),X_315),join(X_315,meet(complement(complement(X_316)),X_315))) )],[refute_0_77,refute_0_2533]) ).
cnf(refute_0_2535,plain,
join(sk1,meet(sk1,converse(sk2))) = sk1,
inference(subst,[],[refute_0_2534:[bind(X_315,$fot(sk1)),bind(X_316,$fot(converse(sk2)))]]) ).
cnf(refute_0_2536,plain,
composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),
introduced(tautology,[refl,[$fot(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)))]]) ).
cnf(refute_0_2537,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))
| join(sk1,meet(sk1,converse(sk2))) != sk1
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) ),[1,0],$fot(sk1)]]) ).
cnf(refute_0_2538,plain,
( join(sk1,meet(sk1,converse(sk2))) != sk1
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3))) )],[refute_0_2536,refute_0_2537]) ).
cnf(refute_0_2539,plain,
composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(sk1,meet(sk1,converse(sk2))),sk1) )],[refute_0_2535,refute_0_2538]) ).
cnf(refute_0_2540,plain,
( composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| composition(sk1,meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) ),[0],$fot(composition(sk1,meet(sk2,sk3)))]]) ).
cnf(refute_0_2541,plain,
( composition(sk1,meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3))
| composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) )],[refute_0_2539,refute_0_2540]) ).
cnf(refute_0_2542,plain,
composition(sk1,meet(sk2,sk3)) != composition(sk1,meet(sk2,sk3)),
inference(resolve,[$cnf( $equal(composition(join(sk1,meet(sk1,converse(sk2))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) )],[refute_0_2541,refute_0_20]) ).
cnf(refute_0_2543,plain,
composition(sk1,meet(sk2,sk3)) = composition(sk1,meet(sk2,sk3)),
introduced(tautology,[refl,[$fot(composition(sk1,meet(sk2,sk3)))]]) ).
cnf(refute_0_2544,plain,
$false,
inference(resolve,[$cnf( $equal(composition(sk1,meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) )],[refute_0_2543,refute_0_2542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL023-2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 11:47:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.19/4.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.19/4.36
% 4.19/4.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.48/4.68
%------------------------------------------------------------------------------